On a piece of paper use a protractor to construct ABC with a m < A =30, and m AB
B. AC>BC
C. AC < BC
D. AC < AB
Answers
The statements about the right - triangle that are true are:
AC > BC (Option B) ;and AC < AB (Option D). This can be established using the open mouth theorem and the law of sines.
A right triangle is a type of triangle that has one angle measuring 90 degrees. The side opposite the right angle is the longest side and is called the hypotenuse.
The Open Mouth Theorem states that in any triangle, the side opposite the largest angle is the longest side. Therefore, in triangle ABC with angle measures of 90°, 60°, and 30°, the side opposite the 90° angle is the longest side.
Let the side opposite the 90° angle be labeled as c, the side opposite the 60° angle be labeled as b, and the side opposite the 30° angle be labeled as a. By the Open Mouth Theorem, we know that c is the longest side.
To show that b is longer than a, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides. That is,
a/sin(30°) = b/sin(60°) = c/sin(90°)
Since sin(30°) = 1/2 and sin(60°) = √3/2, we can write:
a/(1/2) = b/(√3/2) = c/1
Simplifying, we get:
a = c/2 and b = c√3/2
Therefore, we can see that b is longer than a since b = c√3/2 > c/2 = a√3.
Thus, we have shown that the side provided by the ∠90° is greater than the side provided by the ∠60°, and the side provided by the ∠60° is greater than the side provided by the ∠30°, using the Open Mouth Theorem and the Law of Sines.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
On a piece of paper, use a protractor to construct △ABC with m∠A = 30° , m∠B = 60°, and m∠C = 90°.
Which statements about the triangle are true?
A. AC > AB
B. AC > BC
C. AC < BC
D. AC < AB
Related Questions
amy asked alfred, an international student from denmark to participate in her survey. after alfred completed the survey, amy also asked alfred to introduce other international students who might be interested in participating in her survey. as a result, amy was able to collect enough data to conduct her analysis. what type of sampling method did amy use?
Answers
In conclusion, Amy used a snowball sampling method to collect data for her survey. This method is useful when the population is hard to locate or identify, and when other sampling methods are not possible
Amy used a snowball sampling method. Snowball sampling is a non-probability sampling method where the participants recruit other members of the population.
It is useful when the population is difficult to locate or identify, as it relies on word of mouth or referrals from already recruited participants. In this case, Alfred was able to introduce other international students who might be interested in participating in Amy's survey. This allowed Amy to collect enough data to conduct her analysis. Snowball sampling is useful when the sample size is not known, when time is limited, or when a random selection is not possible.
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A, B and C lie on a straight line. Given that angle y = 95° and angle z = 330°, work out x .
Answers
If A, B, and C lie on a straight line, the sum of angles y, x, and z will be 180 degrees:
y + x + z = 180
Substituting the values given in the problem:
95 + x + 330 = 180
Simplifying:
425 + x = 180
Subtracting 425 from both sides:
x = -245
Therefore, x is -245 degrees.
However, since x represents an angle on a straight line, we can add 180 degrees to get an equivalent angle:
x + 180 = -245 + 180 = -65
Therefore, x is -65 degrees.
Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6 years?
Give your answer to two decimal places.
Answers
Answer:
The required amount Ahmet needs to pay after 6 years is $1619.14.
What is compound interest?
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Principal = P rate= r Time =a , n = compounding frequency
Here,
From the given data,
P = 700, r = 15% and t = 6 (n =1)
Now,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 700(1 + 0.15)⁶
Amount = $1619.14
Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.
Step-by-step explanation:
If i walk 3. 5 miles in 2 hours. How far can i walk in 8 hours?
Answers
If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.
If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.
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Imagine a rectangle whose length is (0.5x+13) inches long and whose width is (2x+8) inches wide.
Part1) Write a polynomial for the perimeter of the rectangle
Part2) Write a polynomial for the area of the rectangle
Answers
The perimeter of the rectangle is (x² + 30x + 104) in² while The area of the rectangle is (x² + 30x + 104) in²
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The rectangle have a length of (0.5x + 13) and width of (2x + 8)
1) Perimeter = 2(length + width)
Perimeter = 2(0.5x + 13 + 2x + 8) = 2(2.5x + 21) = (5x + 42) inches
The perimeter of the rectangle is (x² + 30x + 104) in²
2) Area = length * width
Area = (0.5x + 13) * (2x + 8) = x² + 4x + 26x + 104
Area = (x² + 30x + 104) in²
The area of the rectangle is (x² + 30x + 104) in²
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Yuri's dad needs to fertilize the grass in the yard. The back yard measures 55 feet by 30 feet, while the front yard is a square with a length of 42 feet on each side
Answers
Answer: To find the total area of the grass that Yuri's dad needs to fertilize, we need to calculate the area of the back yard and the area of the front yard, and then add them together.
Area of the back yard:
The back yard measures 55 feet by 30 feet, so the area is:
55 feet x 30 feet = 1650 square feet
Area of the front yard:
The front yard is a square with a length of 42 feet on each side, so the area is:
42 feet x 42 feet = 1764 square feet
Total area:
To find the total area, we add the area of the back yard and the area of the front yard:
1650 square feet + 1764 square feet = 3414 square feet
Therefore, Yuri's dad needs to fertilize a total area of 3414 square feet.
Step-by-step explanation:
PLEASE HELPP Find a.
Answers
Answer:122
Step-by-step explanation:
sum of the interior angles of a rectangle is equal to 360 degrees. sum of neighbor angles is equal to 180 degrees. the if one of the neighbor angle is 90 then, other is 180-90=90.
a+76+72+90=360
a+238=360
a=122
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a number from the multiples of 4 between 20 and 40, inclusive The sample space is _______ (Use a comma to separate answers as needed. Use ascending order.) There are _____ outcome(s) in the sample space.
Answers
The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space. In this case, the sample space is {20, 24, 28, 32, 36, 40}.
The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.
To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.
Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.
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r of the alphabet if letters of the alphabet are selected at random, find the probability of getting at least letter . letters can be used more than once. enter your answer as a fraction or a decimal rounded to decimal places.
Answers
The probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1/1.
The reason for this is that if any letter of the alphabet is selected at random, the probability of getting an "r" is 1/26, or 0.0385. Since letters can be used more than once, this probability remains the same regardless of how many letters are selected. Thus, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1.
In summary, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1. This is because, when a letter is selected at random, each letter has an equal chance of being chosen (1/26), and since the probability of selecting an "r" remains the same regardless of how many letters are selected, the probability of getting at least one "r" is also 1.
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1. Jimmy volunteers at events at the hospital each year. He does not work for more than two events in a year. Over the past ten years, he attended exactly two events seven times, one event two times, and no events one time.
a. Define the random variable X.
b. What values dose X take on?
c. Fill in the following table ( where P(x) is the probability of x and u is the expected value). In addition, what are the expected value and standard deviation of X?
Answers
The expected value and standard deviation of x are 1.6 and 0.66, respectively.
The definition of the random variablesGiven that:
Jimmy volunteers at events at the hospital each year.
The random variable x is the number of hospital events Jimmy works at each year.
What values dose x take on?We understand that he does not work for more than two events in a year
So, x can take on the values 0, 1, or 2.
The table of probabilitiesFrom the question, we have:
Over the past ten years
He attended exactly two events seven timesOne event two timesNo events one timeSo, the table is
X P(X)
0 0.1
1 0.2
2 0.7
To find the expected value, we take the sum of the products of x and P(x)
So, we have
E(x) = 0(0.1) + 1(0.2) + 2(0.7)
E(x) = 1.6
To find the standard deviation, we need to first calculate the variance:
Var(X) = E(x^2) - [E(x)]^2
Where
E(x^2) = 0^2(0.1) + 1^2(0.2) + 2^2(0.7)
E(x^2) = 3
So, we have
Var(X) = 3 - (1.6)^2
Var(X) = 0.44
This means that
SD(x) = √0.44
SD(x) = 0.66
Hence, the standard deviation is 0.66
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One year, the population of a city was 252,000. Several years later it was 204,120. Find the percent decrease
Answers
The percentage decrease in the population after on year is found to be 19%.
The percentage decrease can be found by using the formula,
Percentage decrease = change in population/initial population x 100.
Now change in population in one year is given as final population - initial population.
Putting values, change in population = 252000 - 204120
Change in population = 47880
Now, putting all the value in the formula,
percentage decrease = 47880/252000 x 100
percentage decrease = 19%
So, the decrease in the population is found to be 19%.
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What is the slope of the line?
Answers
Answer:
Slope m = 1/3
Step-by-step explanation:
Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)
Find the difference in y coordinates, y2 - y1 (called rise)
Find the difference in corresponding x coordinates x2 - x1 (called run)
Rise/Run gives the slope
Two distinguishable points on the line graph are (0, 2) and (3, 3)
rise = 3 - 2 = 1
run = 3 - 0 = 3
Slope = 1/3
Prove that STV is congruent to TUW
Answers
Answer:
The picture shows that the side lengths and the angle are the same because of the lines
Step-by-step explanation:
The answer is given and VS=WT but add the line symbol above that
Elavate each expression when x is 4 and y is 6
Answers
Answer:
the answer to ur question is: 36
Mei and kara build computers from parts and sell them to make a profit mei can build a computer in 0. 8 hours
Answers
Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.
Let's use the following variables to represent the unknowns in the problem:
Let M be the number of computers Mei built
Let K be the number of computers Kara built
We can set up a system of equations based on the given information:
M + K = 17 (the total number of computers built is 17)
0.8M + K = 15 (the total time worked is 15 hours)
We can solve for one of the variables in terms of the other by using the first equation:
M = 17 - K
Now we can substitute this expression for M into the second equation:
0.8(17 - K) + K = 15
13.6 - 0.8K + K = 15
0.2K = 1.4
K = 7
So Kara built 7 computers. We can use the first equation to find how many computers Mei built:
M + 7 = 17
M = 10
Therefore, Mei built 10 computers.
Now we can find how long each girl worked by multiplying the number of computers by their respective build times:
Mei: 10 computers x 0.8 hours per computer = 8 hours
Kara: 7 computers x 1 hour per computer = 7 hours
Therefore, Mei worked 8 hours and Kara worked 7 hours.
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The complete question is :
Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?
Create tables to solve the problems, and then check your answers with the word problems.
During a basketball game, Jeremy scored triple the number of points as Donovan. Kolby scored double the number of points as Donovan.
If the three boys scored 36 points, how many points did each boy score?
Answers
Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.
Let's denote the number of points scored by Donovan as "D".
According to the problem, Jeremy scored triple the number of points as Donovan, so he scored 3D points.
Similarly, Kolby scored double the number of points as Donovan, so he scored 2D points.
We also know that the total number of points scored by all three boys is 36. So we can write an equation:
D + 3D + 2D = 36
Simplifying this equation, we get:
6D = 36
Dividing both sides by 6, we get:
D = 6
So Donovan scored 6 points.
Using the values we found for Donovan's score, we can find the scores of Jeremy and Kolby:
Jeremy scored 3D = 3(6) = 18 points
Kolby scored 2D = 2(6) = 12 points
Therefore, Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.
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pls answer this
it isnt add 3, it says its wrong when i press it
pls helpp meee
Answers
I think you are correct, I am not sure why. Maybe you ask your teacher and she or he made a mistake with this question.
find the length of side 3
answers
5x^3-4x^2+3x-4
5x^3-4x+3x-12
5x^3-4x^2+3x+4
5x^3=4x^2+3x+12
Answers
Answer:
Side 3 is: 5x^3 - 4x^2 +3x - 12
Note that the answer options do not include this result, but it is likely that the second option is simply missing the square term for the -4x, and it should read -4x^2.
Step-by-step explanation:
The perimeter is the sum of all three sides. To find Side 3, subtract Sides 1 and 2 from the perimeter:
5x^3 - 2x^2 +3x - 8 - (3x^2-4x-1) - (4x-x^2+5) = Side 3
Perimeter - Side 1 - Side 2 = Side 3
5x^3 - 2x^2 +3x - 8 - 3x^2+4x+1 - 4x+x^2-5 [Remove parentheses]
5x^3 - 3x^2 +x^2 - 2x^2 +3x +4x - 4x - 8 +1 -5 [Combine like terms]
5x^3 - 4x^2 +3x - 12 [Simplify] = Side 3
PLS HELP ME LESSON 12.03: PLOT TWISTS
1. Use the data set provided to create a line plot. i really need help
Answers
Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd satisfied with yοur line plοt, save it and distribute it as needed.
What is unitary methοd?The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.
a general methοd fοr prοducing a line plοt:
First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.
Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.
Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.
If yοu're satisfied with yοur line plοt, save it and distribute it as needed.
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Complete question:
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
Answers
The correct option to model the height is
h = cosine (StartFraction pi Over 6 EndFraction t) + 9.
Finding the equation to model the height:Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.
We will use the general form of a cosine function to model the height has a function of time t:
h = A cos(Bt) + CWhere A is the amplitude, B is the frequency and C is the vertical shift
Here we have
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Hence, the applitude A = [9+10]/2 = 0.5.
The period of a cosine function is given by 2π/B,
Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.
=> B = π/6.
The vertical shift is C = 9.
Thus, the equation that models the height h as a function of time t is:
h = 0.5 cos(π/6 t) + 9.
Therefore,
The correct option to model the height is
h = cosine (StartFraction pi Over 6 EndFraction t) + 9.
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need help with part a part b part c quick
Answers
Answer:
1. C.
2. D.
3. D.
Step-by-step explanation:
A. Round both dimensions the nearest whole number. 8 1/3 rounds to 8, 6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.
B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions and get 225/4. Convert to a mixed number, 56 1/4. Option D.
C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.
Solve for x in the triangle
Answers
The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.
According to the given question,
angle sum property of triangle-
20+21+29=180
70x=180
x=180/70.
Hence, With the angle sum property of triangle, x=180/70.
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Gethyn needs to drink 8 cups of water each day. Today he has consumed 48 fluid ounces. How many more cups does he need to drink today?
Answers
By the given parameters, Gethyn needs to drink 2 more cups of water today.
How many more cups does he need to drink today?From the question, we have the following parameters that can be used in our computation:
Amount = 8 cups
Today = 48 ounces
There are 8 fluid ounces in one cup.
So, to convert 48 fluid ounces to cups, we divide by 8:
48 fluid ounces / 8 fluid ounces per cup = 6 cups
Therefore, Gethyn has already drnk 6 cups of water today.
To reach his goal of 8 cups, he still needs to drink:
8 cups - 6 cups = 2 cups
So Gethyn needs to drink 2 more cups of water today.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C
Answers
To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:
Draw a line segment from each vertex of the triangle to the point P.
Measure the distance from each vertex to the point P and make note of the lengths.
Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).
Use the new endpoints of the line segments to draw the new triangle, A'B'C'.
For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:
AP = sqrt((3-1)² + (3-2)²) = sqrt(5)
BP = sqrt((3-3)² + (3-4)²) = 1
CP = sqrt((3-5)² + (3-2)²) = sqrt(5)
After rotating each vertex 90 degrees clockwise about P, we get:
A'(4,1)
B'(2,3)
C'(4,5)
Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C
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Which fractions have 20 as the LCD (lowest common denominator)?
Answers
The lowest common denominator, 20, can be used to represent any fraction that can be stated as a ratio of integers with factors of 2 and 5 in the denominator. eg. 1/4, 1/2, 2/5 and 7/10
To find all the fractions that have 20 as the lowest common denominator, we need to identify all the prime factors of 20, which are 2, 2, and 5.
Then, we can express each fraction with these prime factors in the denominator, by multiplying the numerator and denominator by the missing factors. For example, for the fraction 1/4, we need to multiply both the numerator and denominator by 5 to get:
1/4 = 5/20
Similarly, for the fraction 3/5, we need to multiply both the numerator and denominator by 2 to get:
3/5 = 6/10 = 12/20
By doing this for all fractions, we can express them with the same denominator of 20. Here are some examples:
1/4 = 5/20
3/5 = 12/20
1/2 = 10/20
2/5 = 8/20
7/10 = 14/20
Therefore, any fraction that can be expressed as a ratio of integers with factors of 2 and 5 in the denominator can be written with 20 as the lowest common denominator.
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Complete Question
Write any two fractions which have 20 as the LCD (lowest common denominator)?
x-15+2x+6
please help me with step by step explanation
Answers
Answer:
To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:
Group the x terms and the constant terms separately:
(x + 2x) + (-15 + 6)
Simplify the terms inside the parentheses:
3x - 9
So the simplified expression is 3x - 9.
Therefore, x - 15 + 2x + 6 equals 3x - 9.
Answer:
3(x-3)
Step-by-step explanation:
given : x-15+2x+6
factorize using like terms : x-15+3x+6 = 3x-9
= 3x - 9
=3(x-3)
Wilbur flew twice as fast as his brother Orville and therefore made the 852-ft flight in 6 seconds less time. What is each of their rates in feet per second and how many seconds is each of their flights.
Answers
Wilbur's flight took about 43.7 seconds.
How to find the time?Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.
We know that the distance traveled by both brothers is the same, which we can express with the equation:
distance = rate × time
For Orville:
distance = x * t
For Wilbur:
distance = 2x * (t - 6)
Since the distance is the same for both brothers, we can set the two equations equal to each other:
x * t = 2x * (t - 6)
Expanding and simplifying the right-hand side:
xt = 2xt - 12x
12x = xt
x = t/12
So, Orville's rate is x = t/12 feet per second.
Substituting this into one of the equations for distance, we can solve for t:
distance = x * t
852 = (t/12) * t
852 = t² / 12
t² = 12 * 852
t² = 10224
t ≈ 101.1 seconds (rounded to the nearest tenth)
So, Orville's flight took about 101.1 seconds.
Now we can use the equation for Wilbur's distance to find his rate:
distance = 2x * (t - 6)
852 = 2(2x) * (101.1 - 6)
852 = 4x * 95.1
x ≈ 5.64 feet per second (rounded to the nearest hundredth)
So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.
To find Wilbur's time, we can use the equation for distance again:
distance = 2x * (t - 6)
852 = 2(11.28) * (t - 6)
852 = 22.56t - 135.36
22.56t = 987.36
t ≈ 43.7 seconds (rounded to the nearest tenth)
So, Wilbur's flight took about 43.7 seconds.
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What are the domain and range of g of x equals the square root of the quantity x plus 4?
a. d: [4, [infinity]) and r: [0, [infinity])
b. d: (–4, [infinity]) and r: (–[infinity], 0)
c. d: [–4, [infinity]) and r: [0, [infinity])
d. d: (4, [infinity]) and r: (–[infinity], 0)
Answers
The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).
We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,
g(x) = √x + 4
We have to determine the domain and range of function g(x).
The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4
the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0
Subtracting the 4 from both sides
=> x + 4 -4 ≥ 0 - 4
=> x ≥ -4
The domain is x∈ [-4,+∞)
When x = -4, g(x) = 0
Therefore, The range is y∈ [0, 00)
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Help me please with this math assignment
Answers
The actual distance of 6 cm, given the scale of the map, would be 30 km .
The distance on the map, given the actual distance on the ground and the scale, would be 6 inches .
How to find the actual distance ?The scale is that for every 1 cm on the map, the actual distance is 5 kilometers. When given 6 cm therefore, the actual distance is :
= 6 x 5
= 30 km
The scale of the second map is such that 1 inch on the map is 3 actual kilometers so 18 km on the ground would be :
= 18 / 3
= 6 inches
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NI
Megan is taking out a loan for $6,000 with
an annual compound interest rate of 13%
for 6 years. Megan will not make any
additional deposits or withdrawals. What
will be the total balance paid at the end of 6 X
years?
Round your answer to the closest dollar
amount. Do not include $ symbol in answer
Answers
Steps:
1) The formula for compound interest is x=P(1+r/n)^nt. This means that the final amount (x) is equal to the initial deposit (P) times the result of 1 plus the interest rate (r) divided by the number of times the interest occurs in a given time period (n) to the power of n times the number of time periods (t).
2)Next we have to plug in our information from the problem. We know that the initial deposit (P) was 6000 and the interest rate (r) is .13 (13%), so we can start by plugging those two in. This will get us x=6000(1+.13/n)^nt. Since it occurs annually, we know that the number of times it occurs each year is n, and we also know that the number of years for which she will leave it (t). This gives us n = 1 (since it happens once per year) and t = 6 (since she is leaving it for 6 years). Plugging this in, we get x = 6000(1+.13/1)^1x6. We can simplify this to x = 6000(1+.13/1)^6 since 1x6 is 6.
3) Finally, we need to solve. If you can use a calculator, you may skip this part. However, if you can’t, it goes like this: First, we need to solve everything within the parentheses. .13/1 is still .13, and once we add in the 1 we get 1.13. This gives us x = 6000(1.13)^6. Next, we need to do the exponent. 1.13^6 is about 2.081952. We are unable to round this number yet in order to keep it accurate. After that, we get x = 6000x2.081952. Multiplying those together, we get 12491.712, which rounds to 12491.71.
Hope this helped