Consider the graph of the function f(x) shown above. It consists of two line segments, an arc of a semi-circle centered at (-4,0) with radius 3, and an arc of a quarter-circle centered at (1,0) with radius 2. Find the value of [tex]\int\limits^4_ {-7} \, f(x) dx[/tex]
Answers
The value of the integral is given as follows:
C. -7π/2.
How to obtain the result of the integral?The result of the integral is given by the total area of the figure.
From x = -7 to x = -1, the figure is a semi-circle of radius 3, below the y-axis, hence it's area is given as follows:
A1 = -0.5π x 3²
A1 = -4.5π.
From x = -1 to x = 1, with the line, the figure is a right triangle with sides 2 and 2, hence the area is given as follows:
A2 = 0.5 x 2 x 2
A2 = 2.
From x = 1 to x = 3, the figure is quarter circle with radius 2, hence the area is given as follows:
A3 = 0.25π x 2²
A3 = π.
From x = 3 to x = 4, the figure is a right triangle with sides 1 and 4, below the y-axis, hence the area is given as follows:
A4 = 0.5 x 1 x 4
A4 = -2.
Hence the total area, representing the integral, is given as follows:
A = A1 + A2 + A3 + A4
A = -4.5π + 2 + π - 2
A = -3.5π
A = -7π/2.
(the result of the integral is negative but the area is positive).
Meaning that the correct option is given by option C.
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Related Questions
Find the area of this irregular figure, all angles are right angles
Answers
The area of this irregular figure is 256 square inches
How to determine the area of the figureFrom the diagram shown, we can see that the figure is composite, holding two rectangles together.
We can see that both rectangles have the same length and width measurement.
It is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
Given that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFor Rectangle A
Area = 16(8)
multiply values
Area = 128 Inches square
Rectangle B
Area = 16(8)
Area = 128 Inches square
Area of figure = 128 + 128
Area =256Inches square
Hence, the value is 256Inches square
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if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is
Answers
we have distance from focus to its vertex =p, then distance between focus to directrix = p + p=2p
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.
Since the distance between the vertex and the focus is the same as the distance between vertex to directrix,
So, we have distance from focus to its vertex =p
then distance between focus to directrix = p + p=2p
The complete question is:-
if the distance from a parabola's focus to its vertex is p, then the distance from its focus to its directrix is equal to?
(a) p (b) 2p (c) p+1 (d) p/2.
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Is y = 1 over 4 x 0.5 a power function? Explain your reasoning.
Answers
The function y = 1 over 4 x 0.5 is not a power function
What is a function?A function can be described as a rule, equation or expression that tends to explain the relationship between two variables.
These variables are;
The independent variableThe dependent variableThe types of functions are;
Into – functionPolynomial functionLinear FunctionIdentical FunctionQuadratic FunctionPower functionA power function is a function single that has a term that is product of a real number, a coefficient, and a variable raised to an exponent.
Hence, y = 1/4 × 0.5 is not a power function.
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A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. What are the appropriate hypotheses for this test?
H0: p = 0.28 versus Ha: p < 0.28, where p = the proportion of all high school students who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p > 0.28, where p = the proportion of all high school students who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p < 0.28, where p = the proportion of high school students in the sample who work a part-time job during the school year.
H0: p = 0.28 versus Ha: p > 0.28, where p = the proportion of high school students in the sample who work a part-time job during the school year.
It is common knowledge that a fair penny will land heads up 50% of the time and tails up 50% of the time. It is very unlikely for a penny to land on its edge when flipped, so a probability of 0 is assigned to this outcome. A curious student suspects that 5 pennies glued together will land on their edge 50% of the time. To investigate this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student would like to know if the data provide convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The student tests the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met. The standardized test statistic is z = –0.80 and the P-value is 0.2119. What conclusion should the student make using the α = 0.10 significance level?
Because the test statistic is less than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Because the test statistic is less than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
Answers
The student is investigating whether the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
To test this claim, the student securely glues together 5 pennies and flips the penny stack 100 times. Of the 100 flips, the penny stack lands on its edge 46 times. The student will use the hypotheses H0: p = 0.50 versus Ha: p ≠ 0.50, where p = the true proportion of all flips for which the penny stack will land on its edge. The conditions for inference are met, as the sample size is large enough (n = 100) and the sample is randomly selected. The standardized test statistic can be calculated as z = (P - p)/(σ/√n) = (0.46 - 0.50)/(√(0.50*0.50/100)) = -0.80. The P-value can be calculated as P(z ≤ -0.80) = 0.2119. Since the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.
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Suppose you have 6 homework assignments to complete one night.
In how many different orders can you complete all of the assignments
Answers
There are a total of 6 homework assignments that need to be completed one night. The number of ways to arrange n items in a specific order is n! (n factorial).
How many different orders can you complete all of the assignments?Therefore, for 6 homework assignments, the number of different orders in which they can be completed is 6! = 720.
This means that there are 720 different ways in which you can complete these 6 assignments on one night. Each permutation represents a unique order in which the assignments can be completed, such as starting with assignment 1, then 2, then 3, and so on, or starting with assignment 4, then 5, then 6, and then 1, and so on.
It is worth noting that this formula is only applicable when the order of the assignments matters. If the order of the assignments does not matter, then we would use the formula for combinations, which is n! / (r!(n-r)!).
Multiplying all of these options together results in 6 x 5 x 4 x 3 x 2 x 1 = 720 possible ways to complete the assignments in a different order. This is known as the permutation formula, which states that the number of ways to arrange n items in a specific order is n! (n factorial).
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factor $(x^2 y^2-z^2)^2-4x^2y^2$ as the product of four polynomials of degree $1$, each of which has a positive coefficient of $x$.
Answers
The four polynomials are all of degree 1 and each has a positive coefficient of x.
Polynomials:
A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
The factorization of the following expression is $(x2 y2 z2)4x2y2. $ is equal to (x2 y2 z2 2xy) (x2 y2 z2 + 2xy).
It is possible to factor the first factor further into $(x2 y2 z2 2-2xy) = (xy-z)(x2y+xyz+z2)$.
The second factor can be factored into the equation $(x2 y2 z2 + 2xy) = (xy+z)(x2 y-xyz+z2)
$
As a result, the original expression can be factored as $(x2 + y2 + z2).
2-4x2y = (xy-z)(xy+z)(xy+z)(xy-z)(xy+z)(xy-z)(xy-z)(xy-z)(xyz+z)$
Each of the four polynomials has a positive coefficient of x and is of degree 1.
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Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+19y=0. separate your answers by commas.
Answers
For all values of k for which the function y=sin(kt) satisfies the differential equation y''+19y=0.
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable.
The given differential equation is
y'' + 19 y= 0
The following function satisfy the differential equation
y = sin(kt)
Differentiating twice with respect to t,
y'' = - k^2 sin(kt)
Putting the value in differential equation given above, we get
- k^2 sin(kt) + 19 sin(kt) = 0
k^2 = 19 ⇒ k = +/- sqrt(19).
points to know
(sin(at))'=acos(at)
and (cos(at))'=-asin(at)
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A student's course grade is based on one midem that counts as 10% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 50% of his final grade, and a final exam that counts as 15% of his final grade. His midterm score is 68, his project score is 95, his homework score is 93, and his final exam score 62. What his overall final score? What letter grade did he eam (A, C, D, or F) Assume that mean of 50 or above is an A, a mean least 80 but less than 90 is a B, and so on.
Answers
The overall final score of the student is 86.35 and he got B grade in the exam.
What is Percentage?
Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole.
Let the final score to be 'f'
According to the question :
midterm score = 10% 68 = 6.8
class project score = 25% 95 = 23.75
homework assignment = 50% 93 =46.5
final exam = 15% 62 = 9.3
So, the Overall final score = midterm score + class project score + homework assignment + final exam
= 6.8 + 23.75 + 46.5 + 9.3
= 86.35.
Hence, he got grade 'B' .
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I can’t figure it this problem out please help me
Answers
30.009
Change to fraction
Any numbers decided by 1 are always equal to the same number. So one fraction form is 30.009/1. But your teacher will beat you up if you write that. I know my teacher would, decimals and fractions should always be separated.
Looking at the image and the problem, we’ll need to convert it to a mixed fraction, meaning a whole number and a fraction.
The number given is 30.009. You already have a whole number. It’s 30. So you can put 30 in the left box. Now we’re left with 0.009. The number ends at the thousandths place, so the denominator will be 1,000. The numerator will be 9 because it’s 0.009, or 9 out of a thousand.
So the answer in mixed number is 30 9/1,000.
The fraction cannot be simplified further.
use the empirical rule. sketch the values and calculate the z scores. a) approximately what percentage of the observations fall between 32 and 48?
Answers
Approximately 95.45% of the observations fall between 32 and 48.
Using the Empirical Rule, we can calculate the Z scores for 32 and 48 to see what percentage of observations falls between these values.
First, calculate the Z score for 32:
Z = (32 - 40) / 4 = -2
Next, calculate the Z score for 48:
Z = (48 - 40) / 4 = 2
The Empirical Rule states that approximately 68% of the observations fall within 1 standard deviation of the mean, which is between 36 and 44 in this case. However, since the Z scores for 32 and 48 are both outside of this range, we need to calculate the percentage of observations that falls between these Z scores.
Using a standard normal distribution table, we can see that the percentage of observations between Z = -2 and Z = 2 is approximately 95.45%. This means that approximately 95.45% of the observations fall between 32 and 48.
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--The given question is incomplete; the complete question is
"Data are drawn from a normal distribution with a mean of 40. the standard deviation of 4. Use the Empirical Rule. SKETCH the values and calculate the Z scores. a) Approximately what percentage of the observations fall between 32 and 48?"--
If the measure of angle is 0 is 7pi/4, which statements are true?
The measure of the reference angle is 45°.
The measure of the reference angle is 30°.
tan(0) = -1
The measure of the reference angle is 60°.
cos(0) = -â2/2
sin(0) = -â2/2
Answers
The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
The measure of an angle is the amount of rotation from the starting position to the endpoint of the angle. In this problem, the measure of angle is 0 is 7π/4. This means that the angle has rotated 7π/4 radians from the start position, which is equivalent to 360° - (7π/4)*180/π = 315°.
Therefore, the measure of the reference angle is 45°, because the reference angle is the smallest angle that starts at the x-axis and terminates at the terminal side of the angle, which in this case is 315°. The reference angle is equal to the measure of the angle minus the multiple of 360°, so 45° = 315° - 360°.
The trigonometric functions of sine, cosine, and tangent can be used to evaluate the measure of an angle. The sine of an angle is equal to the ratio of the opposite side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, sin(0) = opposite/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The cosine of an angle is equal to the ratio of the adjacent side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, cos(0) = adjacent/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The tangent of an angle is equal to the ratio of the opposite side of the angle over the adjacent side of the angle. In this problem, tan(0) = opposite/adjacent = -1, since the angle is 7π/4 radians, or 315°.
In conclusion, the measure of angle is 0 is 7π/4, and the measure of the reference angle is 45°. The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
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The questions are in the image
Answers
The sampling method used was random sampling.
What was the sampling method used?This sample may not be representative of the entire class as it does not consider the individual characteristics of the students and only takes into account the row that they are seated on.
Additionally, there is a potential for bias as the sample size is quite small and may not accurately reflect the overall population. Therefore, it would be beneficial to use a larger sample size or use a stratified random sampling method to ensure a representative sample.
The sampling method used was random sampling.
This sample is likely to be representative, as it was chosen randomly and evenly from the seating chart. However, there could be potential issues if the student's Exam 1 scores are not evenly distributed among the rows.
For example, if all the higher scores are concentrated in one row, then the sample may not be representative of the entire class. To ensure an accurate estimation of the average Exam 1 score for the entire class, it may be better to use stratified sampling, where each row is given equal weight and students are selected from each row with the same probability.
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.An artist sells his paintings at a gallery. He charges a set price for each small painting K and
each large painting he sells. Last month, the artist sold 6 small paintings and 8 large
paintings and earned $670 in all. This month, he sold 12 small paintings and 10 large
paintings and earned $950 in all. How much does the artist charge for a small painting?
How much does he charge for a large painting?
I need this in system of equation form please.
Answers
The artist charges $25 for a small painting and $65 for a large painting.
How to substitute two equations?
To substitute one equation into another, you can replace one of the variables in the second equation with the expression from the first equation.
Let K be the price of small painting and L be the price of large painting.
From the information given, we know that:
Last month:
6K + 8L = $670 (1)
This month:
12K + 10L = $950 (2)
We have two equations and two unknowns, so we can use a system of equations to find the values of K and L.
Solving the system of equations:
From (1) equation, we have:
6K + 8L = $670
From (2) equation, we have:
12K + 10L = $950
Now we can solve for K (small painting) by multiplying equation (1) by 2 and equation (2) by -1 and adding the two equations together:
12K + 16L = $1340
-12K - 10L = -$950
0K + 6L = $390
Therefore, L = $390 / 6 = $65
Now we can substitute this value of L back into the first equation (1) and solve for K:
6K + 8($65) = $670
6K = $670 - 8($65) = $670 - $520 = $150
K = $150 / 6 = $25
So, the artist charges $25 for a small painting and $65 for a large painting.
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piece of material measures 38 inches Courtney cuts the piece of material into two pieces one piece measures 19 inches write an addition equation that could be used to find the length of the other piece of material
Answers
An addition equation that could be used to find the length of the other piece of material is,
38 = 19 + x.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
A piece of material measures 38 inches.
Courtney cuts the piece of material into two pieces.
One piece measures 19 inches.
Let x be the length of other pieces.
An addition equation that could be used to find the length of the other piece of material is,
38 = 19 + x
Therefore, 19 + x = 38 is an addition equation.
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three girls shared a piece of land. One got x/3y of the land. Another got x/6y of the land. What fraction of the land will the third girl get.
Answers
The third girl will recieve a land area equals to the fraction (2y-x)/2y.
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
The fractions are x/3y, x/6y and z(say)
so sum of all the fraction must be 1 so
x/3y + x/6y + z = 1
⇒z = (2y-x)/2y
The third girl recieve a land area equals to (2y-x)/2y.
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Pls help, OR ELSE a grotesque Dung Beatle will find its way into your coffee ☕
Question
In this figure, GH=10, GP=16, and FP=4.
What is EF?
Enter your answer in the box.
EF =
Answers
Answer: EF = 12 is the correct answer.
Step-by-step explanation: EF = GP - FP = 16 - 4 = 12Given that GH=10, GP=16, and FP=4. We have to find the value of EF. We can use this formula to find it:EF = GP - FP = 16 - 4 = 12So the value of EF is 12. In the given figure, ABCD is a rectangle and GP and GH are the diagonals. EF is the length of the rectangle.Therefore, EF = 12 is the correct answer.
Answer:Well i think EF would be 10 since it looks like the same length as GH
Step-by-step explanation:
2. fill in the exclusive and inclusive ranges for the following items. be sure to show your work below. high score low score inclusive range exclusive range 7 6 89 45 34 17 15 2 1 1
Answers
The inclusive range includes all numbers from 2 to 89, while the exclusive range includes all numbers from 3 to 88, excluding the two endpoints.
Inclusive Range: Low Score (2) = Low Score (7) + 1 = 7 + 1 = 8
High Score (89) = High Score (45) + 44 = 45 + 44 = 89
Exclusive Range: Low Score (3) = Low Score (7) + 1 = 7 + 1 = 8
High Score (88) = High Score (45) + 44 = 45 + 44 = 89
The inclusive range includes all values within a given set of numbers, including the endpoints. In this case, the low score is 7 and the high score is 45. Adding 1 to the low score gives us a low score of 8, and adding 44 to the high score gives us a high score of 89. This gives us an inclusive range of 8 to 89.
The exclusive range excludes the endpoints, so we add 1 to the low score and subtract 1 from the high score. This gives us a low score of 8 and a high score of 88, giving us an exclusive range of 8 to 88. This means that the range excludes the values of 7 and 89 from the set.
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The terms power and exponent are used interchangeably
True or False?
Answers
True, the terms power and exponent have the same meaning.
Help me ASAP math question.
Answers
The trip was 18 minutes and they travelled 6 miles.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From the given information we form system of equations
0.2x+1.5y+5=17.60..(1)
x-3y=0
x=3y..(2)
Plug 2 in equation 1
0.2(3y)+1.5y+5=17.6
0.6y+1.5y=12.6
2.1y=12.6
Divide both sides by 2.1
y=6
x=3(6)=18
Hence, the trip was 18 minutes and they travelled 6 miles.
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Jasmine has a bucket of $600 to spend on home renovations. She will spend $175 on a new sink and the remainder on countertops. The countertops cost 35 per square foot. What is the maximum number of square feet Jasmine can purchase ?
Answers
Answer: 12 square feet
600 - 175 = 425
425 / 35 per square foot = 12.14
The maximum number of square feet Jasmine can purchase is 12, because you can not purchase 0.14 of a square foot.
What is the slope of the given line?
Answers
Answer:
2
- ------
3
Step-by-step explanation:
The equation of slope is m = (y2-y1)/(x2-x1)
You can find it by finding two random points on the line. I'll use (3, -2) and (-3, 2)
Note: The line is going downwards, so the answer should be negative.
So plugging those two points into the equation...
(2-(-2))/(-3-3)
Simplifying this we get (2+2)/(-3-3)
(4)/(-6)
If we divide both sides by 2, we get our final simplified answer of. 2/-3, also known as -2/3
What is the average speed of the car during the first two hours of the trip? (2 p
O0 miles/hour
20 miles/hour
O40 miles/hour
80 miles/hour
Answers
Answer:
20
Step-by-step explanation:
first hour 40mph
second hr 0
so average = 20
Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
one half comma negative 5
one half comma 5
5 comma one half
negative 5 comma one half
Answers
The solution to the simultaneous equations is; 5 comma one half
How to solve Simultaneous Linear Equations?The simultaneous equations are;
y = -¹/₂x + 3 -------(1)
y = ¹/₂x - 2 -------(2)
Substitute ¹/₂x - 2 for y in eq 1 to get;
¹/₂x - 2 = -¹/₂x + 3
Add -¹/₂x to both sides using addition property of equality to get;
¹/₂x + ¹/₂x - 2 = 3
Add 2 to both sides using addition property of equality to get;
x = 3 + 2
x = 5
Thus;
y = ¹/₂(5) - 2
y = ¹/₂
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Answer:
Solve the system of linear equations by graphing.
y equals negative one half times x plus 3
y equals one half times x minus 2
Step-by-step explanation:
The drawing shows an isosceles triangle. 65° Work out the size of angle a. 23/196 a
Answers
In the isosceles triangle, the size of angle, a is 50°
What is isosceles triangle?An isosceles triangle is a type of triangle which has two sides that are equal in length.
This type of triangle has two angles which are the same and the third angle is different from the other two. It also has three sides, with two sides being equal and the third side being different.
The base of the isosceles triangle is the side that has two equal sides, and the sides that are equal are called the legs. The angles that are equal are called the base angles. The point at which the two equal sides meet is called the vertex.
The angles of the isosceles triangle add up to 180 degrees. The base angles are the same, while the third angle is different and can be greater or smaller than the other two angles. This type of triangle is very symmetrical, as the two equal sides create a mirror image of the triangle.
Isosceles triangles are very useful in many areas, such as mathematics, engineering and architecture. In mathematics, isosceles triangles are used to solve problems involving angles, area, and perimeter.
In engineering, they are used in many structures such as bridges. In architecture, they are used to create aesthetically pleasing designs for buildings and monuments.
Given, one side of angle is 65°
For isosceles triangle two sides of angles are equal.
A triangle always have 180°
a + b + c = 180°
a = 180° - 65° - 65°
a = 50°
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write v as a linear combination of u1, u2, and u3, if possible. (enter your answer in terms of u1, u2, and u3. if not possible, enter impossible.
Answers
The v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
To find the linear combination of u1, u2, and u3 that equals v, we can use the method of solving a system of linear equations.
The equation for v in terms of u1, u2, and u3 is:
v = a1u1 + a2u2 + a3u3
where a1, a2, and a3 are the coefficients of the linear combination.
Plugging in the given values for v, u1, u2, and u3:
(-1,7,2) = a1(3,2,8) + a2(1,-3,-1) + a3(-2,1,-3)
We can solve this system of equations by equating the corresponding entries of the two vectors:
-1 = 3a1 + a2 - 2a3
7 = 2a1 - 3a2 + a3
2 = 8a1 - a2 - 3a3
We can then use any method to solve the system of equations, such as substitution, elimination or Cramer's rule.
By solving the system of equations we get:
a1 = -(1/9), a2 = (5/3), a3 = -(4/3)
Therefore, v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
It is possible to write v as a linear combination of u1, u2, and u3.
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Tracey makes her muffin recipe with 2 1/2 cups flour, 1 1/4 sugar, and 1 3/4 cups oatmeal. How many more cups of flour and oatmeal does Tracey use than sugar? Explain.
Answers
Tracey used 1 1/4 cups more flour and 1/2 cup more oatmeal than sugar.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Tracey makes her muffin recipe with 2 1/2 cups flour, 1 1/4 sugar, and 1 3/4 cups oatmeal.
The number of cups of flour Tracey used than sugar is,
= 2 1/2 - 1 1/4.
= 5/2 - 5/4.
= (10 - 5)/4.
= 5/4.
= 1 1/4 cups of more flour.
The number of cups of oatmeal Tracey used than sugar is,
= 1 3/4 - 1 1/4.
= 7/4 - 5/4.
= 2/4.
= 1/2 cup more oatmeal.
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$40$ is $120\%$ of what number?
Answers
By replacing the given values in the formula, you get:
120 = 40
100 whole
Now cross-multiply:
120 × whole = 40 × 100
Then, divide both sides by 120 and get the whole:
whole = 40 × 100 = 33.3333333333
120
One step solution:
You can easily find the answer in one step, just multiplying the part by 100 then dividing the result by the percentage. So, 40 is 120% of = 40 × 100 = 33.3333333333
Which graph shows the new image of the rectangle after a translation of two units up?
Answers
The graph that shows the new image after a translation of two units up is:
The fourth graph.
(which is the third graph if we consider that the first is the original image).
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For this problem, we have a translation two units up, meaning that the x-coordinates of the figure remain constant, while two is added to each of the y-coordinates.
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Guys pls help me fast rapidly is of math:
Answers
For the given equation, the binomial factor is (5x² + 3).
In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y
How do binomial factors work?Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.
5x³ - 25x² + 3x - 15
Taking 5x² and 3 as common factors -
⇒ 5x² (x - 5) + 3 (x - 5)
GCF of 1 step is 5x²
⇒ (5x² + 3) (x - 5)
GCF of 2 step is 5x² + 3
Common binomial factor is (5x² + 3)
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Evaluate the expression using the given value of the variable:[ y + z - z ]; use [y = 6], and [z = 5] .
Answers
Answer:
( y + z - z )
given, y= 6 z=5
(6 + 5 - 5 )
Use DMAS rule
D=division M= multiplication A= addition S=subtraction
(11-5)
6 (ans)