This trapezoid has been divided into two right triangles and a rectangle. how can the area of the trapezoid be determined using the area of each shape? enter your answers in the boxes. the area of the triangle on left is in², the area of the triangle on the right is in², and the area of the rectangle is in². the area of the trapezoid is the sum of these areas, which is in².
Answers
A trapezoid has been divided into two right triangles and a rectangle, see the above figure. Area of the triangle on left is 9 in². The area of the triangle on the right is 9 in², and the area of the rectangle is 108 in². The area of the trapezoid is the sum of these areas, which is 126 in².
We have a trapezoid, ABCD see in above figure has been divided into two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. We have to determine the area of trapezoid. Now, as we know area of a figure divides into pieces is equals to the sum of areas of each piece of figure. So, the area of trapezoid, ABCD is sum of area of two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. From above figure, In case of right triangles,
The base length of the triangle BEC= 2 in
height of triangle BEC = 9 in
Area of triangle BEC = (1/2)× base× height
=> Area of ∆BEC = (1/2)× 9× 2
= 9 in² Similarly, Area of triangle DAF = 9 in²
Therefore, the required area is 2×( Area of the triangle), A₁ = 2× 9 sq. in
= 18 in²
Now, length of rectangle ABEF, l = 12 in
width of rectangle, w = 9 in
Area of rectangle ABEF, A₂ = l×w
= 12× 9 = 108 in²
Thus, the required area = A₁ + A₂
= 18 in² + 108 in² = 126 in²
Hence required area is 126 in².
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Complete question:
This trapezoid has been divided into two right triangles and a rectangle, see the above figure. how can the area of the trapezoid be determined using the area of each shape? enter your answers in the boxes. the area of the triangle on left is ___ in², the area of the triangle on the right is___ in², and the area of the rectangle is__ in². the area of the trapezoid is the sum of these areas, which is___ in².
Related Questions
Please help me I want to finish this so I can get the full grade
Answers
The population density of the town is 13,000 people per square mile.
How to calculate population density in an area?To calculate the population density in an area, you need two pieces of information: the total population of the area and the total land area of the area. Population density calculation refers to the process of determining the number of individuals living in a particular area, expressed as a ratio or proportion of the size of that area.
[tex]Population Density =\frac{Total Population }{Total Land Area}[/tex]
According to the question the total land area of the town can be calculated as follows:
Total Land Area = 20 blocks x ([tex]\frac{1}{20}[/tex] mile) x ([tex]\frac{1}{2}[/tex] mile) = 0.5 miles²
We are also given that there are 6,500 people in the town. Therefore, the population density can be calculated as follows:
[tex]Population Density =\frac{6,500}{0.5}[/tex] = 13,000 people per square miles.
Therefore, the population density of the town is 13,000 people per square mile.
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1. If we are only interested in one side of the curve, a p = 0.05 has a z-score of ___.
2. The population standard deviation is the square root of the population variance.
True
False
3. If we are interested in both sides of the curve, a p = 0.05 has a z-score of ___.
4. If an IQ score is in the lower 5%, what is the equivalent z-score?
-1.96
-1.64
-2.58
2.58
Answers
According to the given information, a significance level is of 0.05, the population standard deviation is the square root of the population variance is true, the critical z-score is 1.96, z-score is -1.64.
What is the mean and standard deviation?
The mean, also known as the average, is the sum of all the values in the data set divided by the number of values. The standard deviation measures the amount of variability or dispersion in the data set.
1) When we are only interested in one side of the curve, we use a one-tailed test with a significance level of 0.05. For a one-tailed test with a significance level of 0.05, the critical z-score is 1.645 for a right-tailed test and -1.645 for a left-tailed test.
2) The population standard deviation is the square root of the population variance: True. The population standard deviation is the square root of the population variance. The formula for population variance is:
[tex]$\sigma^2 = \frac{\sum_{i=1}^N (x_i - \mu)^2}{N}$[/tex]
where [tex]$\sigma^2$[/tex] is the population variance, [tex]$\mu$[/tex] is the population mean, [tex]$x_i$[/tex] are the individual values in the population, and [tex]$N$[/tex] is the size of the population. The formula for population standard deviation is:
[tex]$\sigma = \sqrt{\sigma^2}$[/tex]
3) When we are interested in both sides of the curve, we use a two-tailed test with a significance level of 0.05. For a two-tailed test with a significance level of 0.05, the critical z-score is 1.96.
4) To find the z-score for an IQ score in the lower 5%, we need to find the z-score that corresponds to a cumulative probability of 0.05. Using a standard normal distribution table, we find that the z-score for a cumulative probability of 0.05 is approximately -1.64. Therefore, an IQ score in the lower 5% corresponds to a z-score of approximately -1.64.
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(5x-2y)(a-b)-(2x-y)(a-b)
Answers
Answer:
First, let's simplify the expression by combining like terms:
(5x-2y)(a-b) - (2x-y)(a-b)
= (5x-2y-2x+y)(a-b) // Distribute the (a-b) to each term
= (3x-y)(a-b)
Therefore, (5x-2y)(a-b) - (2x-y)(a-b) simplifies to (3x-y)(a-b).
The goal of this research is to evaluate the expression (5x-2y)(a-b)-(2x-y)(a-b). First, it is important to review the basic principles of algebra and the technical definitions of expressions and powers. This involves a recap of addition, subtraction, multiplication, and division of algebraic expressions.
Next, the expression under analysis needs to be broken down into the terms and factors. To achieve this, parentheses and binsomials need to be grouped and identified. This is a critical step in the evaluation process of the expression.
After this has been done, the algebraic steps for simplifying the expression need to be taken. This involves applying the commutative, associative, distributive and other relevant laws of algebra to achieve an answer in the simplest way. It is important to remember that each step needs to be documented and the source of the information should be clearly indicated.
In terms of sources, it is important to only select reliable websites, textbooks and journals approved by experts in the field. Examples of these are the American Mathematical Society, the Johns Hopkins University, and the Massachusetts Institute of Technology.
Finally, the expression needs to be scrutinized to ensure that all steps have been taken correctly and the outcome is what was expected. Once this has been completed, the answer can be documented and the paper/article can be published.
In conclusion, the expression (5x-2y)(a-b)-(2x-y)(a-b) can be evaluated through an organized approach involving the use of the fundamental principles of algebra and reliable sources for validating the findings.
(a-b) (3x - y)
Step by step explanation:
First, we can simplify the expression by factoring out the common factor of (a-b):
(5x-2y)(a-b)-(2x-y)(a-b) = (a-b) [(5x-2y) - (2x-y)]
Expanding the brackets, we get:
(5x-2y) - (2x-y) = 5x - 2y - 2x + y = 3x - y
Substituting this back into the simplified expression, we get:
(5x-2y)(a-b)-(2x-y)(a-b) = (a-b) (3x - y)
Therefore, the final simplified expression is:
(a-b) (3x - y)
four times the sum of two consecutive even integers is 40. what is the greater of the two even integers?
Answers
The greater of the two even integers is 6. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often referred to as "arithmetic operations",are said to be able to describe all real numbers. The four mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
Let the consecutive integers be 'x' and 'x+2'.
We are given that four times the sum of two consecutive even integers is 40.
So,
4 (x + x +2) = 40
On solving this, we get
⇒4 (2x +2) = 40
⇒2x + 2 = 10
⇒2x = 8
⇒x = 4
The next integer will be 6.
Hence, the greater of the two even integers is 6.
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which hypothesis states that a mean difference between two groups is due to sampling error? group of answer choices null hypothesis alternative hypothesis directional hypothesis nondirectional hypothesis
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The hypothesis that states that the mean difference between two groups is due to sampling error is the null hypothesis.
What is a hypothesis?
A hypothesis is a theory or idea that is proposed and tested to see if it can be proven to be true. It is used to explain a phenomenon and make predictions. A null hypothesis is a type of hypothesis that assumes that there is no significant difference between two groups or variables being studied. It is the default hypothesis that researchers assume to be true unless proven otherwise
If the null hypothesis is proven to be false, it means that there is a significant difference between the groups or variables being studied. In such a case, an alternative hypothesis is formulated.The hypothesis that states that the mean difference between two groups is due to sampling error is the null hypothesis. It assumes that the difference between the groups is due to chance or random sampling errors rather than a real effect. The null hypothesis is tested using statistical tests to see if the results are significant or not. If the results are not significant, it means that there is no evidence to reject the null hypothesis, and the difference between the groups is due to sampling error.
If the results are significant, it means that there is enough evidence to reject the null hypothesis, and the difference between the groups is real and not due to chance or sampling error. Therefore, the null hypothesis is an essential tool in hypothesis testing, and it helps researchers to determine whether the results are meaningful or not.
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Find the radius of a hemisphere with a volume of 2,712. 3 in3
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[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{2\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=2712.3 \end{cases}\implies 2712.3=\cfrac{2\pi r^3}{3}\implies (3)(2712.3)=2\pi r^3 \\\\\\ \cfrac{(3)(2712.3)}{2\pi }=r^3\implies \sqrt[3]{\cfrac{(3)(2712.3)}{2\pi }}=r\implies 10.90\approx r[/tex]
Need help with these problems
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1) A nonagon is a polygon with nine sides.
To find the sum of the interior angles of a nonagon, we can use the formula:
aggregate of interior angles = (n - 2) × 180°
where n stands for the number of sides of the polygon.
Substituting n = 9 for a nonagon, we get:
sum of interior angles = (9 - 2) × 180° = 7 × 180°
Thus, the aggregate of the interior angles of a nonagon is:
sum of interior angles = 1260°
2)
To find the sum of the interior angles of a 17-gon, we can use the formula:
aggregate of interior angles = (n - 2) × 180°
where n stands for the number of sides of the polygon.
Substituting n = 17 for a 17-gon, we get:
sum of interior angles = (17 - 2) × 180° = 15 × 180°
Thus, the aggregate of the interior angles of a 17-gon is:
sum of interior angles = 2700°
3)
It is correct to state that a hexagon can be defined as a polygon with six sides.
To find the sum of the interior angles of a hexagon, we can use the formula:
aggregate of interior angles = (n - 2) × 180°
where n refers to the number of sides of the polygon.
Replacing n = 6 for a hexagon, we get:
sum of interior angles = (6 - 2) × 180° = 4 × 180°
Therefore, the sum of the interior angles of a hexagon is:
sum of interior angles = 720°
4)
To find the sum of the interior angles of a regular 20-gon, we can use the formula:
aggregate of interior angles = (n - 2) × 180°
where n refers to the number of sides of the polygon.
Substituting n = 20 for a 20-gon, we get:
sum of interior angles = (20 - 2) × 180 degrees = 18 × 180°
Thus, the sum of the interior angles of a regular 20-gon is:
sum of interior angles = 3,240°
5)
A regular octagon is a polygon with eight sides that are all congruent and eight angles that are all congruent.
To find the measure of each exterior angle of a regular octagon, we can use the formula:
dimensions of each exterior angle = 360° ÷ number of sides
For a regular octagon, the number of sides is 8. Replacing this value into the formula, we get:
measure of each exterior angle = 360° ÷ 8
Simplifying this expression, we get:
the dimensions of each exterior angle = 45°
Therefore, the dimensions of each exterior angle of a regular octagon is 45°.
6)
A regular 24-gon is a polygon with 24 sides that are all congruent and 24 angles that are all congruent.
To find the measure of each exterior angle of a regular 24-gon, we can use the formula:
mensuration of each exterior angle = 360° ÷ number of sides
For a regular 24-gon, the number of sides is 24. Replacing this value into the formula, we get:
measure of each exterior angle = 360° ÷ 24
Simplifying this expression, we get:
The measure of each exterior angle = 15°
Therefore, the measure of each exterior angle of a regular 24-gon is 15°
7)
The sum of the interior angles of any pentagon can be calculated using the formula:
Aggregate of interior angles = (n - 2) × 180°
where n refers the number of sides of the polygon.
For a pentagon, n = 5, so we have:
Aggregate of interior angles = (5 - 2) × 180° = 3 × 180° = 540°.
We can use this fact to set up an equation using the given expressions for the interior angles:
(5x + 2) + (7x - 11) + (13x - 31) + (8x - 19) + (10x - 3) = 540
Simplifying and solving for x, we get:
43x - 62 = 540
43x = 602
x = 14
Therefore, x = 14.
8)
The sum of the exterior angles of any polygon is always 360 degrees. Therefore, we can add the six exterior angles of the hexagon to get:
(11x-30) + 5x + 50 + (2x+60) + (6x-10) + 50 = 360
Simplifying and solving for x, we get:
24x + 120 = 360
24x = 240
x = 10
Therefore, x = 10.
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In a voter survey (February 2022), the Center Party had 5.2% sympathizers out of 1972 people interviewed. In a corresponding survey in January 2022, 6.0% of 2189 interviewees sympathized with the Center Party.
Form a 95% confidence interval for the difference in the proportion of Center Party members at the two survey times.
Answer only with the statistical margin of error and enter this as a number between 0 and 1 to 3 correct decimal places.
Answers
0.0247
To form a 95% confidence interval for the difference in the proportion of Center Party members at the two survey times, one needs to use the following formula: CI = (p1 - p2) ± z (SE), where p1 and p2 are the sample proportions for February 2022 and January 2022, respectively. To calculate the standard error (SE), use the following formula: SE = √ [(p1 (1-p1))/n1 + (p2 (1-p2))/n2], where n1 and n2 are the sample sizes for February 2022 and January 2022, respectively.The statistical margin of error is the term used to describe the range of error that is expected for a statistical estimate or survey. This range of error is expressed as a percentage of the estimate or survey result, and it is typically denoted as a plus or minus sign before the percentage value. Thus, the statistical margin of error can be calculated by taking the product of the standard error and the z-score corresponding to the desired level of confidence. In this case, the level of confidence is 95%, and the corresponding z-score is 1.96. Therefore, the formula for the margin of error is: ME = z × SE, where z = 1.96. So, let's now calculate the confidence interval for the difference in the proportion of Center Party members at the two survey times.CI = (p1 - p2) ± z (SE)CI = (0.052 - 0.06) ± 1.96 (SE)SE = √ [(p1 (1-p1))/n1 + (p2 (1-p2))/n2]SE = √ [(0.052 (1-0.052))/1972 + (0.06 (1-0.06))/2189]SE = 0.0126ME = z × SE = 1.96 × 0.0126ME = 0.0247Therefore, the 95% confidence interval for the difference in the proportion of Center Party members at the two survey times is (-0.057, -0.029), and the statistical margin of error is 0.0247 (rounded to 4 decimal places).Answer: 0.0247
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Then lengths of the sides of a square are 9 meters. Find the length of the of the diagonal of the square.
? square root of ?
Answers
Answer:
12.73 meters
Step-by-step explanation:
Let d be the length of the diagonal, and let s be the length of each side of the square. Then, we have:
d^2 = s^2 + s^2 (by the Pythagorean theorem)
d^2 = 2s^2
d = sqrt(2s^2) = sqrt(2) * s
Substituting s = 9 meters, we get:
d = sqrt(2) * s = sqrt(2) * 9 meters
d ≈ 12.73 meters
Therefore, the length of the diagonal of the square is approximately 12.73 meters
The arm span and foot length were measured (in
centimeters) for each of the 19 students in a statistics
class. The results are displayed in the scatterplot.
Arm Span vs. Foot Length
Foot Length (cm)
29
27
23
21
●
●
19
155 160 165 170 175 180 185 190 195
Arm Span (cm)
The equation ý = -7.61 +0.19x is called the least-
squares regression line because it
O passes through each data point.
Ominimizes the sum of the squared residuals.
Omaximizes the sum of the squared residuals.
O is least able to make accurate predictions for the
data.
Answers
Answer: The correct answer is:
The equation ý = -7.61 +0.19x is called the least-squares regression line because it minimizes the sum of the squared residuals.
Explanation:
The least-squares regression line is a line that represents the best linear approximation of the relationship between two variables. It is called "least-squares" because it minimizes the sum of the squared residuals, which are the differences between the observed values and the predicted values from the regression line.
In this case, the scatterplot shows the relationship between arm span and foot length for 19 students in a statistics class. The equation ý = -7.61 +0.19x is the equation of the least-squares regression line for this data set. This means that it is the line that best fits the data by minimizing the sum of the squared residuals.
Therefore, the correct answer is that the equation ý = -7.61 +0.19x is called the least-squares regression line because it minimizes the sum of the squared residuals.
Step-by-step explanation:
Which term gives the horizontal length of one cycle of a periodic function?
amplitude
period
frequency
phase shift
Answers
Period gives the horizontal length of one cycle of a periodic function as [tex]2\pi[/tex].
Given that,
To determine which term gives the horizontal length of one cycle of a periodic function.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the periodic function 1 period is consist of 2π on the horizontal axis, so, the period represents the horizontal length of the periodic function.
Thus, Period gives the horizontal length of one cycle of a periodic function as 2π.
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Which of the following is an example of a function with a domain (-∞ + ∞ )and a range (-∞,+ ∞)?
A. f(x)-(2x)10
B. f(x)-(2x)
C. f(x)=(2x)/4
D. f(x)-(2x)/2
Answers
Option A is an example of a function with a domain (-∞, +∞) and a range (-∞, +∞). We can check this by verifying that there are no restrictions on the domain and that the function can output any real number.
What is a domain?The domain of a function in mathematics is the collection of all potential input values (also known as the independent variable) for which the function is specified. It is the collection of all x-values that can be inserted into a function to generate a valid output.
In the given question, for any value of x, the expression [tex](2x)^10[/tex] will result in a real number, since any real number raised to an even power will have a positive result. Therefore, there are no restrictions on the domain.
Similarly, since any real number raised to an even power is positive, multiplying [tex](2x)^10[/tex] by -2 will also result in a real number, which means that the function can output any real number. Therefore, the range is also (-∞, +∞).
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(31 points!)
A password consists of four different letters of the alphabet, where each letter is used only once.
(a) How many different passwords are possible?
(b) If the numbers 1 through 10 are also available to be chosen only once in addition to the alphabet, how many more passwords are possible?
Answers
Using permutation and combination concept, there are 358,800 different passwords that are possible and the number of more passwords available through this combination is 1054920
How many different passwords are possible?(a) To find the number of different passwords that are possible, we can use the permutation formula. Since there are 26 letters in the alphabet and we are choosing 4 letters without repetition, we can write:
Number of possible passwords = P(26, 4)
= 26 x 25 x 24 x 23
= 358,800
Therefore, there are 358,800 different passwords that are possible.
(b) If the numbers 1 through 10 are also available to be chosen only once in addition to the alphabet, we can use the same permutation formula to find the number of different passwords that are possible. Since there are now 36 characters to choose from (26 letters + 10 numbers), and we are choosing 4 characters without repetition, we can write:
Number of possible passwords = P(36, 4)
P(36, 4) - P(26, 4) = 1054920
The number of more passwords available through this combination is 1054920
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again ignore the erased stuff
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The image contains the answer to the questions.
Find the area under the standard normal curve to the left of z =-2.77 and to the right of z--2.22. Round your answer to four decimal places. if necessary. Answer Tables Keypad If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key Normal Table-" to-z Normal Table-a to z
Answers
The area under the standard normal curve to the left of z=-2.77 and to the right of z=-2.22 is 0.0167-0.0033 = 0.0134. This answer is rounded to four decimal places, so the answer is 0.0134.
What is area?Area is a two-dimensional measurement, defined as the amount of two-dimensional space taken up by a shape or object. It is measured in units such as square meters, square kilometers, or square feet.
The area under the standard normal curve to the left of z=-2.77 and to the right of z=-2.22 can be calculated using the normal tables. The normal table shows the area under the standard normal curve from 0 up to the given z-value. Using the normal table, the area to the left of z=-2.77 is 0.0033 and the area to the right of z=-2.22 is 0.0167.
The normal table is a useful tool for calculating the area under the standard normal curve for different z-values. The table is organized such that the row headers are the z-values and the column headers are the area under the curve from 0 up to the given z-value. By looking up the z-values in the table, we can calculate the area under the standard normal curve for any given area. This makes it easy to calculate the area under the standard normal curve for any given set of z-values.
Using a standard normal table, the area to the left of z = -2.77 is 0.0028 (rounded to four decimal places), and the area to the right of z = -2.22 is 0.0139 (rounded to four decimal places).
Therefore, the area under the standard normal curve to the left of z = -2.77 and to the right of z = -2.22 is:
0.0028 + 0.0139 = 0.0167 (rounded to four decimal places)
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What is the inverse relation of the function f(x)=−72x+4?
Answers
The inverse relation of the function f(x)=−72x+4 is f⁻¹(x) = 4 - y / 72.
What is inverse function?A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted on the line y = x. This graph's line traverses the origin and has a slope value of 1.
The given function is:
f(x)=−72x+4
Substitute the value of f(x) = y:
y = -72x + 4
Isolate the value of x:
y - 4 = -72x
x = 4 - y / 72
Now, let the value of x be written as f⁻¹(x), thus:
f⁻¹(x) = 4 - y / 72
Hence, the inverse relation of the function f(x)=−72x+4 is f⁻¹(x) = 4 - y / 72.
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Answer:
The correct answer is
please help with all three !!!!
Answers
Answer:
1. A'(3,2), B'(1,7), C'(-6,1)
Step-by-step explanation:
I only know 1. because you are reflecting from the y-axis so that being said
A' - intend of moving it to the left 3 you will move it to the right 3 and move up 2.
B' - intend of moving it to the left 1 you will move it to the right 1 and move up 7.
C' - intend of moving it to the right 6 you will move it to the left -6 and move up 1.
and were is the reflecting line happing at with Qs, 2 and 3.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1035 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 8 degrees At some later time, the crew measures the angle of elevation from point B to be 5 degrees . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer: Let's assume that the distance between the lighthouse and point B is x. Then, we can use the tangent function to set up an equation involving the angles of elevation:
tan(8°) = (height of lighthouse) / (distance from A to lighthouse)
tan(5°) = (height of lighthouse) / x
Since the height of the lighthouse is the same in both equations, we can set them equal to each other:
tan(8°) = tan(5°) * (distance from A to lighthouse) / x
Solving for x:
x = (tan(5°) * 1035) / tan(8°)
x ≈ 14416
So the distance from point A to point B is approximately 14,416 feet.
Step-by-step explanation:
Please answer the questions below
Answers
Step-by-step explanation:
First one
5,5√5,25
Second one
-3,12,-48
Need some assistance in Math
Answers
The cοrrect answer is "Yes, because angle A will still have the same degree measurement in the same pοsitiοn."
What is translatiοn?In mathematics, translatiοn is a geοmetric transfοrmatiοn that invοlves mοving an οbject in a straight line withοut changing its size, shape, οr οrientatiοn. This mοvement can be in any directiοn and at any distance.
The cοrrect answer is "Yes, because angle A will still have the same degree measurement in the same pοsitiοn." This is because an angle is defined by its degree measurement and the twο rays that fοrm it. When an angle is translated (mοved) in sοme way, its degree measurement and the pοsitiοn οf its rays dο nοt change, sο it remains an angle.
Hοwever, if the angle is rοtated οr scaled, its degree measurement and/οr the pοsitiοn οf its rays will change, and it may nο lοnger be an angle in its οriginal fοrm. Translatiοn οnly changes the lοcatiοn οf an οbject, nοt its fοrm οr shape, sο the image οf angle A will still be an angle with the same degree measurement and pοsitiοn οf rays as the οriginal angle A.
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The 3 lines x = 3, y – 2. 5 =-(x – 0. 5), and y – 2,5 = x – 3. 5 intersect at point P.
Find the coordinates of P. Verify algebraically that the lines all intersect at P.
Answers
All three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).
To find the coordinates of point P where the three lines intersect, we need to solve the system of equations formed by the three lines:
x = 3 (equation 1)
y - 2.5 = -(x - 0.5) (equation 2)
y - 2.5 = x - 3.5 (equation 3)
From equation 1, we know that x = 3. substituting this into equations 2 and 3, we get:
y - 2.5 = -2.5 (from equation 2)
y - 2.5 = -0.5 (from equation 3)
Simplifying these equations, we get:
y = 0 (from equation 2)
y = 2 (from equation 3)
So the coordinates of point P are (3, 2).
To verify that the lines all intersect at this point, we can substitute these coordinates into each of the original equations and check that they hold:
For equation 1: x = 3 holds when x = 3.
For equation 2: y - 2.5 = -(x - 0.5) becomes y - 2.5 = -(3 - 0.5) = -2 holds when x = 3 and y = 2.
For equation 3: y - 2.5 = x - 3.5 becomes y - 2.5 = 3 - 3.5 = -0.5 holds when x = 3 and y = 2.
So all three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).
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(Find the LCM of): (a - b)² + 4ab, (a + b)³ - 3ab(a+b) ,a² + 2ab + b²
Answers
Answer:
[tex](a+b)^2(a^2-ab+b^2)[/tex]
Hi, can you please help with math, I think the exercise solving is probably with x and y. Thank u very much:)
1. Two identical jars of cottage cheese and 3 buns of the same type cost 10 euros. A jar of cottage cheese is 2 euros more expensive than a bun. How much is a jar of cottage cheese and how much is a bun?
Again, Thank u!
Answers
Answer:
Cost of jar of cottage cheese = € 3.20
Cost of a bun = € 1.20
Step-by-step explanation:
Framing and solving system of linear equations:Let the cost of 1 jar of cottage cheese = x
Let the cost of 1 bun = y
Cost of 2 jar of cottage cheese = 2x
Cost of 3 bun = 3y
Cost of 2 jars of cottage cheese + cost of 3 buns = € 10
2x + 3y = 10 ------------------(I)
Cost of a jar of cottage cheese = 2 + cost of a bun
x = 2 + y ----------------(II)
Substitute x = 2 + y in equation (I),
2*(2+y) + 3y = 10
Use distributive property,
2*2 + 2*y + 3y = 10
4 + 2y + 3y = 10
Combine like terms,
4 + 5y = 10
Subtract 4 from both sides,
5y = 10 - 4
5y = 6
Divide both sides by 5
y = 6 ÷ 5
[tex]\boxed{\bf y = 1.20}[/tex]
Substitute y = 1.2 in equation (II),
x = 2 + 1.2
[tex]\boxed{\bf x = 3.20}[/tex]
Answer:
A jar of cottage cheese is €3.20
A bun is €1.20
Step-by-step explanation:
Let
x = Cost of a jar of cottage cheese (euros)
y = Cost of a bun (euros)
Step I:
Translate the statements mathematically:
2 jars of cottage cheese cost = [tex]2x[/tex] euros
3 buns cost = [tex]3y[/tex] euros
∴ Total cost = [tex]2x + 3y = 10[/tex] euros
A jar of cottage cheese is 2 euros more expensive than a bun: [tex]x = 2 + y[/tex]
Step II:
A system of linear simultaneous equations:
[tex]x = 2 + y[/tex] ——(equation i)
[tex]2x + 3y = 10[/tex] ———-(equation ii)
Step III:
Solve the linear simultaneous equations either by the substitution, elimination or graphical method
Substitution method:
Substitute (equation i) into (equation ii) and solve for y:
[tex]2(2 + y) + 3y = 10[/tex]
Expand the parenthesis and make y the subject of the equation:
[tex]4 + 2y + 3y = 10[/tex]
[tex]2y + 3y = 10 - 4[/tex]
[tex]5y = 6[/tex]
[tex]y = \frac{6}{5}[/tex]
∴y = Cost of a bun = €1.20 (One euro and 20 cents)
Substitute this value of y in any of the equations to solve for x:
[tex]x = 2 + 1.20[/tex]
∴x = Cost of a jar = €3.20(Three euros and 20 cents)
You are rolling two dice. Find the probability of rolling two fives.
A. 1/6
B. 1/36
C. 1/18
D. 1/24
Answers
Since we are rolling two dice, the probability of rolling two fives is the product of the probability of rolling a five on each die, which is:
(1/6) x (1/6) = 1/36
Therefore, the answer is B: 1/36.
Answer:
B. 1/36
Step-by-step explanation:
A dice has 6 sides, we are looking to roll a 5, which is just one number, hence 1/6. If you roll two, to find the probability of two independent events (meaning they do not affect each other), you multiply the two together.
1/6 x 1/6 = 1/36
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answers
Therefore, the equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are: 2.3p – 10.1 = 6.4p – 4 and 23p – 101 = 65p – 40 – p.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.
Here,
To rewrite the given equation using properties, we can simplify both sides by combining like terms and then isolate the variable term on one side of the equation:
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p - 6.5p + 0.01p = -4 + 10.1
-4.19p = 6.1
p = -6.1/4.19
To check which equations have the same solution, we can substitute this value of p into each equation and see if both sides are equal:
2.3p – 10.1 = 6.4p – 4
2.3(-6.1/4.19) - 10.1 = 6.4(-6.1/4.19) - 4
-9.84 = -9.84
This equation has the same solution as the original equation.
23p – 101 = 65p – 40 – p
23(-6.1/4.19) - 101 = 65(-6.1/4.19) - (-6.1/4.19)
-63.64 = -63.64
This equation also has the same solution as the original equation.
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Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of days, d, that Natalie can take classes and stay within her budget?
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The light from the Cape Florida Lighthouse in Key Biscayne is visible for a distance of 15 mi. If the beam of light sweeps in an arc of 270°, what is the area covered by the beam?
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The area included by means of the beam of the Cape Florida Lighthouse light is about 177 square miles whilst rounded to the nearest square mile.
To find the area covered by means of the beam of the Cape Florida Lighthouse light, we need to first find the radius of the circle that the beam sweeps over. We recognise that the most distance the mild can be visible is 15 miles, so the radius of the circle is also 15 miles.
Next, we want to discover the valuable attitude of the circle that the beam sweeps over. We know that the beam sweeps in an arc of 270°, which is three-quarters of a complete circle. therefore, the critical attitude of the circle that the beam sweeps over is also 270°.
Now, we are able to use the formula for the area of a sector of a circle to discover the area covered through the beam:
area of sector = (central angle/360°) x π x radius^2
Substituting the given values, we get:
area of sector = (270°/360°) x π x 15^2area of sector = (three/4) x π x 225area of sector = 176.71 square milesThus, the area included by means of the beam of the Cape Florida Lighthouse light is about 177 square miles whilst rounded to the nearest square mile.
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from the top of a building, a man observes a car moving toward him. as the car moves 100 ft closer, the angle of depression changes from 15 to 33 o o . find the height of the building.
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When a man on top of a building sees a car approaching him and as the car moves 100 ft closer, the angle of depression changes from 15 to 33 degrees, the height of the building is 159.8 feet.
To solve the problem, we can use the tangent function. Let x be the distance between the man and the building, then we have:
tan(15) = h / x ...........(1) and tan(33) = h / (x - 100) ...........(2)
Dividing (2) by (1), we get:
tan(33) / tan(15) = (x - 100) / x
Simplifying the expression, we have:
(x - 100) / x = 2.22
Solving for x, we get:
x = 100 / 1.22 ≈ 81.97
Using equation (1), we can solve for the height of the building:
h = x * tan(15)
h ≈ 159.8
Therefore, the height of the building is approximately 159.8 feet.
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4.02 Lesson Check Arithmetic Sequences (5)
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The explicit formula of each arithmetic sequence is given as follows:
35, 32, 29, 26, ...: [tex]a_n = -3n + 38[/tex].-3, -23, -43, -63, ...: [tex]a_n = -20n + 17[/tex]9, 14, 19, 24, ...: [tex]a_n = 4 + 5n[/tex]7, 9, 11, 13, ...: [tex]a_n = 5 + 2n[/tex]What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_1[/tex] is the first term of the arithmetic sequence.
For each sequence in this problem, the first term and the common difference are obtained, then substituted into the equation, which is simplified.
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PLS HELP ASAP MARKING BRAINLEIST
Answers
Answer: 21
Step-by-step explanation: The 8 is equivilent to the unknown number (a) therefore the answer is all of the numbers added and u would get 21
Answer:
22.4
Step-by-step explanation:
To find the missing side length:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]8^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]
64 + 25 = [tex]c^{2}[/tex]
89 = [tex]c^{2}[/tex]
[tex]\sqrt{89}[/tex] = [tex]\sqrt{c^{2} }[/tex]
9.4 ≈ c
Perimeter is the distance around the triangle, so we add the sides
8 + 5 + 9.4 = 22.4
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