The rate at which the area of the circle is increasing at the moment when the circumference of the circle is 27/2 inches is 9 inches squared per second.
derivative of the circle's area with respect to time.
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Given that the radius is increasing at a constant rate of 2/3 inches per second, we can express this as dr/dt = 2/3.
We are also given that the circumference of the circle is 27/2 inches. The formula for the circumference of a circle is C = 2πr.
Plugging in the given circumference value, we have 27/2 = 2πr. Solving for r, we get r = (27/4π) inches.
Now, we can differentiate the area formula with respect to time:
dA/dt = d/dt (πr^2)
= 2πr(dr/dt)
Substituting the values, we have:
dA/dt = 2π(27/4π)(2/3)
= (27/2)(2/3)
= 9 inches squared per second
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alejandra's tapas bar offers a menu consisting of savory and sweet dishes. you can also get a mix-and-match plate consisting of two different dishes on the menu. how many different mix-and-match plates can you get consisting of one savory and one sweet dish?
So, there are 20 different mix-and-match plates that can be created by combining one savory and one sweet dish from Alejandra's Tapas Bar's menu.
To determine the number of different mix-and-match plates that can be created from Alejandra's Tapas Bar's menu, we need to calculate the number of options for both the savory and sweet dishes and then multiply them together.
Let's assume that there are 5 savory dishes and 4 sweet dishes on the menu. To create a mix-and-match plate, we need to choose one savory and one sweet dish. The number of options for the savory dish is 5, and the number of options for the sweet dish is 4. Therefore, the total number of different mix-and-match plates that can be created is:
5 x 4 = 20
Customers can choose any combination they like and can enjoy a unique dining experience each time they visit the restaurant.
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the axis of symmetry is the imaginary line that goes through the vertex of a parabola and splits it into mirrored halves. question 1 options: true false
A parabola is a symmetrical U-shaped curve that can be defined as a set of points in a plane that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix). The axis of symmetry is always perpendicular to the directrix and passes through the focus and vertex of the parabola. In a quadratic equation, the coefficient of the x^2 term determines the direction of the opening of the parabola, and the vertex lies on the axis of symmetry.
True. The axis of symmetry is a line that passes through the vertex of a parabola and divides it into two identical halves.
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PLS ANSWER QUICK FIRST TO ANSWER RIGHT WILL GET BRAINLIEST!!!!
Answer:
xy=k
-2×4=k
k=-8
y=-8/x
PLSSSS HELPPP IM IN NEED AND I WILL GIVE BRAINLIEST!!!!
Answer:
a) 24/36 = 2/3 = w/6, so w = 4 inches
The maximum length of this postcard is 6 inches since the width is 4 inches.
b) 24/36 = 2/3 = w/11.5, so w = 7.67 inches
(won't work)
24/36 = 2/3 = 6.125/l, so
l = 9.1875 inches
The maximum width of this postcard is 6.125 inches since the length is 9.1875 inches.
Which expression can be used to find the value of 3/2 divided by 1/8
The value of 3/2 divided by 1/8 is 12 (or 12/1).
To find the value of 3/2 divided by 1/8, you can use the expression (3/2) ÷ (1/8). To solve this division problem, follow these steps:
Step 1: Rewrite the division as a multiplication problem by multiplying the first fraction (3/2) by the reciprocal of the second fraction (8/1). The expression becomes: (3/2) × (8/1).
Step 2: Multiply the numerators (the top numbers) of the fractions: 3 × 8 = 24.
Step 3: Multiply the denominators (the bottom numbers) of the fractions: 2 × 1 = 2.
Step 4: Write the result as a new fraction with the product of the numerators as the numerator and the product of the denominators as the denominator: 24/2.
Step 5: Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (in this case, 2): 24 ÷ 2 = 12 and 2 ÷ 2 = 1. The simplified fraction is 12/1.
Therefore, the value of 3/2 divided by 1/8 is 12 (or 12/1).
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4. Put the steps for deriving the formula for the arc length of a circle in the correct order. Please help me with this.
The formula for the arc length of the circle is L = ( θ/360° ) 2πr
Given data ,
Let the circle be represented as A
Now , The central angle of a circle formula is as follows.
Central Angle = ( s x 360° ) / 2πr
where s is the length of the arc
r is the radius of the circle
Central Angle = 2 x Angle in other segment
Write the circumference of the circle
C = 2πr
Find the angle ratio that represents a percentage of the circle using the central angle θ
θ/360°
Multiply the angle ratio times the circumference to get the arc length
Arc Length = ( θ/360° ) 2πr
Hence , the arc length of the circle is L = ( θ/360° ) 2πr
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What is the best next step in the construction of a line that passes through point C and is parallel to AB?
By constructing these arcs and connecting the appropriate points, we ensure that the newly drawn line passing through point C is parallel to line AB. Remember to use a straightedge to draw the lines accurately and ensure that the arcs intersect correctly.
To construct a line that passes through point C and is parallel to line AB, the best next step is to use a compass to mark an arc centered at point C that intersects line AB at two distinct points.
Here are the steps:
1) Take a compass and set its width to a convenient distance.
2) Place the compass point on point C and draw an arc that intersects line AB at two different points, let's call them D and E.
3) With the compass width still set, place the compass point on point D and draw an arc that intersects the previously drawn arc.
4) Without changing the compass width, place the compass point on point E and draw another arc that intersects the previous arc.
5) Label the point where the two new arcs intersect as F.
6) Draw a straight line passing through point C and point F. This line will be parallel to line AB.
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jenny reads a book with 92 pages. jenny's book has 13 more pages than the book macy reads. which equation could you solve to find how many pages, m, macy's book has?
Find half of the time that Arnold skied without falling, and write inequalities to compare it with the times others in the family skied without falling.
To find half of the time that Arnold skied without falling, we first need to know how much time he spent skiing in total and how many times he fell. Let's assume that Arnold skied for a total of T minutes and fell F times. Then the time that Arnold skied without falling is (T - F * f), where f is the average time it takes Arnold to get up and start skiing again after a fall.
To find half of the time that Arnold skied without falling, we can simply divide (T - F * f) by 2. Let's call this value H. Then we have:
H = (T - F * f) / 2
To compare Arnold's skiing time with that of other family members who did not fall, we need to make some assumptions. Let's assume that each family member skied for a total of T minutes, and that some of them did not fall at all. Let's call the time that each family member skied without falling Ti.
Then we can write the following inequalities to compare Arnold's skiing time with that of others:
Arnold's skiing time without falling (H) is greater than or equal to the skiing time without falling of any family member Ti who fell at least once:
H >= Ti
Arnold's skiing time without falling (H) is less than or equal to the skiing time without falling of any family member who did not fall at all:
H <= T.
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10 c and 10 d plsssssssssssssssss
Answer:
10c a - 3; b = 4
10d See below
Step-by-step explanation:
10c
The problem asks about
3² × 4² = 12²
The given rule is
a² × b² = (a × b)²
Match each number in the problem to each variable or expression in the given rule.
a = 3; b = 4; a × b = 3 × 4 = 12
Answer: a = 3; b = 4
10d
Let's use two sets of number for the formula.
a = 2; b = 5
a² × b² = (a × b)²
2² × 5² = 4 × 25 = 100
(2 × 5)² = 10² = 100
100 = 100
a = 6; b = 8
a² × b² = (a × b)²
6² × 8² = 36 × 64 = 2304
(6 × 8)² = 48² = 2304
2304 = 2304
The formula works every time.
The formula shows you that if you have to multiply the squares of two numbers, you can also multiply the numbers first, then square the product. The result is the same.
the length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches.
The width of a rectangular frame with a total area of 140 square inches, we set up an equation using the expressions for the length and width, simplify it, solve for x, and substitute the value of x into the expression for the width.
To solve for the width of a rectangular frame with a total area of 140 square inches, we first need to set up an equation using the given expressions for the length and width.
The formula for the area of a rectangle is length x width. Therefore, we can write:
(2x + 10)(2x + 6) = 140
We can then simplify this equation by expanding the expressions in the parentheses:
4x^2 + 32x + 60 = 140
Next, we can move all the terms to one side and simplify further:
4x^2 + 32x - 80 = 0
Now, we can solve for x by factoring or using the quadratic formula. After finding the value of x, we can substitute it into the expression for the width (2x + 6) to get the final answer.
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3.a coin is tossed, and a die is rolled.(a) what is the probability the outcome consists of a head and an even number?
To find the combined probability of both events occurring, multiply the individual probabilities: (1/2) * (1/2) = 1/4.
Therefore, the probability of getting a head and an even number is 1/4 or 25%.
The probability of flipping a head on a coin is 1/2. The probability of rolling an even number on a die is 1/2, since there are three even numbers (2, 4, 6) out of a total of six possible outcomes. Therefore, the probability of getting both a head and an even number is (1/2) x (1/2) = 1/4. In other words, there is a 25% chance that the outcome will consist of a head and an even number.
It's important to note that the outcome of the coin toss and the die roll are independent events. This means that the outcome of one event does not affect the outcome of the other event. So even if you flip a tail on the coin, there is still a 1/2 chance of rolling an even number on the die.
Overall, the probability of getting a head and an even number is relatively low at only 1/4. However, it's important to remember that probability is simply a measure of likelihood, and even events with low probability can still occur.
The probability of an outcome consisting of a head and an even number when a coin is tossed and a die is rolled can be determined by finding the individual probabilities and multiplying them.
For the coin, there are two possible outcomes: heads (H) and tails (T). The probability of getting a head is 1/2.
For the die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. The even numbers are 2, 4, and 6. The probability of rolling an even number is 3/6 or 1/2.
Now, to find the combined probability of both events occurring, multiply the individual probabilities: (1/2) * (1/2) = 1/4.
Therefore, the probability of getting a head and an even number is 1/4 or 25%.
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Find the volume of the pyramid. Round your answer to two decimal places. 4in, 5in, and 3in.
If f(x) = x² + 5x - 4, then what is the remainder when f(x) is divided by
x-8?
Answer:
100-------------------------
The Remainder Theorem states that:
if you divide a polynomial f(x) by x - c, the remainder is equal to f(c).Identify the value of c in the divisor x - 8. In this case, c = 8.
Plug the value of c into the function f(x).
f(8) = (8)² + 5(8) - 4Calculate the remainder.
f(8) = 64 + 40 - 4 f(8) = 100So, the remainder is 100.
bubba decides to put an extra coat of paint on his barn. he buys 3 gallons of paint. the paint is applied with a thickness of 0.0552 mm. a gallon is the same as 3.78 liters volume. how large of an area cam bubba paint with a single coating of this paint if he manages a uniform thickness?
Bubba can paint an area of approximately 205,797.10 square meters with a single coating of the 3 gallons of paint, assuming he manages a uniform thickness.
The area that Bubba can paint with a single coating of the 3 gallons of paint, we need to first convert the volume of the paint into liters. As given, 1 gallon is the same as 3.78 liters.
3 gallons x 3.78 liters/gallon = 11.34 liters
Now, we need to use the thickness of the paint to calculate the area that can be covered with this amount of paint. The thickness of the paint is given as 0.0552 mm. We need to convert this to meters so that it is in the same units as the area. 1 mm is equal to 0.001 meters, so:
0.0552 mm x 0.001 meters/mm = 0.0000552 meters
The thickness of the paint in meters. Now we can use the volume and thickness of the paint to calculate the area that can be covered. The formula for this is:
Area = Volume / Thickness
Area = 11.34 liters / 0.0000552 meters
Area = 205,797.10 square meters
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1. Expand: (4x - 1)(x-3)
O4x² - 2x +3
O4x²+3
O4x²-13x-3
O4x²-13x +3
Answer:
The correct answer is option D: 4x² - 13x + 3.
Step-by-step explanation:
To expand the expression (4x - 1)(x - 3), we use the distributive property of multiplication.
Let's multiply each term of the first expression (4x - 1) by each term of the second expression (x - 3):
(4x - 1)(x - 3) = 4x(x) - 4x(3) - 1(x) - 1(-3)
Now, simplify each term:
= 4x^2 - 12x - x + 3
Combining like terms:
= 4x^2 - 13x + 3
Therefore, the expanded form of (4x - 1)(x - 3) is 4x^2 - 13x + 3.
The correct answer is option D: 4x² - 13x + 3.
You are given the following information obtained from a random sample of 4 observations 25, 47, 32, 56. You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.) a. State the null and the alternative hypotheses b. Determine the test statistic. c. Determine the p-value; and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 48. Give your conclusion.
Based on the given sample data, we do not have sufficient evidence to conclude that the population mean is significantly different from 48.
The null hypothesis (H0): The population mean is equal to 48.
The alternative hypothesis (Ha): The population mean is not equal to 48.
b. To determine the test statistic, we can use the t-test since the population standard deviation is unknown. The formula for the t-test statistic is:
t = (sample mean - hypothesized mean) / (sample standard deviation / √n)
Given:
Sample mean () = (25 + 47 + 32 + 56) / 4 = 40
Hypothesized mean (μ0) = 48
Sample standard deviation (s) = √[( (25 - 40)^2 + (47 - 40)^2 + (32 - 40)^2 + (56 - 40)^2) / (4 - 1)] = √[242] ≈ 15.56
Sample size (n) = 4
Substituting these values into the formula, we get:
t = (40 - 48) / (15.56 / √4) = -8 / 7.78 ≈ -1.028
c. To determine the p-value, we need to find the probability of observing a t-value as extreme or more extreme than the calculated test statistic under the null hypothesis. This can be done using a t-distribution table or statistical software.
For a two-tailed test at the 5% level of significance, we divide the significance level by 2, resulting in an alpha of 0.025. Degrees of freedom (df) = n - 1 = 4 - 1 = 3.
From the t-distribution table or software, we find that the p-value for a t-value of -1.028 with 3 degrees of freedom is approximately 0.381.
Since the p-value (0.381) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to suggest that the population mean is significantly different from 48 at the 5% level of significance.
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Jo has 5 sweaters. He needs to take 3 sweaters on a vacation. In how many different ways can he choose 3 sweaters out of 5?
40
30
20
10
Answer:
10 is the answer. Hope this helps!
Vik is constructing a spherical model of Earth
for his science fair project. His model has a
radius of 24 inches. Since roughly 75% of
Earth's surface is covered by water, he wanted
to paint 75% of his model blue to illustrate
this fact. Approximately how many square
inches on his model will be painted blue?
Answer:
5,428.67 inches^2
Step-by-step explanation:
for finding the surface area of a sphere, the formula is:
A = 4(pi)r^2
r = 24 in
we just fill in the equation and get a total surface area of around 7238.23 inches^2
next, we find one percent of this by dividing by 100.
7238.23 / 100 = 72.3823
multiply this by 75
72.3823 x 75 = 5428.6725
so the answer is this rounded to be approximately 5,428.67 inches^2
a bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (ml) and standard deviation 6 ml. the fill volumes are normally distributed. what proportion of bottles have volumes less than 1,015 ml? 0.6293
Proportion of bottles with volumes less than 1,015 ml, we can use the concept of standard deviation and the properties of the normal distribution.
In this case, we have a normally distributed population of bottle volumes with a mean of 1,007 ml and a standard deviation of 6 ml. We want to find the proportion of bottles that have volumes less than 1,015 ml.
The first step is to calculate the z-score, which measures how many standard deviations a value is from the mean. We can use the formula:
z = (x - μ) / σ
where x is the value we are interested in (1,015 ml), μ is the mean (1,007 ml), and σ is the standard deviation (6 ml).
Substituting the values into the formula, we get:
z = (1,015 - 1,007) / 6
Simplifying the equation:
z = 8 / 6
z ≈ 1.33
Next, we need to find the proportion of bottles with volumes less than 1,015 ml. We can use a standard normal distribution table or a calculator to find the corresponding cumulative probability for a z-score of 1.33.
Looking up the value in the table or using a calculator, we find that the cumulative probability for a z-score of 1.33 is approximately 0.9088.
This means that approximately 90.88% of the bottles have volumes less than 1,015 ml.
The correct answer is not 0.6293, but approximately 0.9088 or 90.88%.
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Brad and Allison have three girls. Brad tells Allison that he would like one more child because they are due to have a boy. What do you think of​ Brad's logic?
Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents
. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.
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write the equation of a line that is perpendicular to x =3 and that passes theough the point (0,-4).
When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank? Write your answer in the order of the sample answer: 5 nickels, 6 pennies. PLEASE GIVE AN ACTUALLY ANSWER! Thank you!
Answer:
90 nickels, 72 pennies
Step-by-step explanation:
0.05n+0.01p= 5.22
n+p=162
0.05(162-p)= 5.22
p= 72
n+72= 162
n=90
a box is full of tokens. each token has an integer printed on it, from 0 to 60. if drawn at random, how many tokens must you draw to be certain you get at least one that is odd?
Drawing 31 tokens ensures that you have at least one odd token, by the Pigeonhole Principle.
To be certain you get at least one token that is odd, you need to draw enough tokens to ensure that you exhaust all possible even numbers. Since there are 30 even numbers between 0 and 60, it follows that you must draw 31 tokens to be certain you get at least one that is odd.
This is known as the Pigeonhole Principle, which states that if there are n pigeonholes and n+1 pigeons, then at least one pigeonhole must contain more than one pigeon. In this case, the even numbers represent the n pigeonholes and the odd numbers represent the n+1 pigeons.
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Use the graph of y=Ca to determine C and a.
C= 1
a=
CIT
Help me solve this View an example Get more help
[-10, 10] [-10, 10]
Xscl=1 Yscl=1
Aу
Clear all
Answer:
C = 1a = 4Step-by-step explanation:
You want the values of C and 'a', given the graph of y = C·a^x.
Values of yWhen x = 0, ...
y = C·a^0 = C·1 = C
The graph shows y = 1 when x = 0, so C = 1.
When x = 1, ...
y = C·a^1 = C·a = 1·a = a
The graph shows y = 4 when x = 1, so a = 4.
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The value of the variable are; C = 1 and a = 4
If we know that the function crosses the x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
We want the values of C and 'a', given the graph of y = C·a^x.
To find the Values of y
When x = 0, y = C·a^0 = C·1 = C
The graph shows that y = 1 when x = 0, so C = 1.
When x = 1, then y = C·a^1 = C·a = 1·a = a
The graph shows that y = 4 when x = 1, so a = 4.
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You are on a game show and are playing a game to try to win a trip to Orlando. There are 7 tiles in a bag, each with a letter of the city on it. You must pull the tiles out in the correct order to spell Orlando. What is the probability you will win the trip?
The probability that you will win the trip to Orlando would be = 1
How to calculate the probability of the given event?To calculate the probability that you will win the trip to Orlando the formula for probability should be used and this is given below;
Probability = possible outcome/sample space.
The total small space = 7
For first Letter;
Possible outcome = 1
probability = 1/7. This will be done for the total number of letters used to spell Orlando = 1/7+1/7+1/7+1/7+1/7+1/7+1/7 = 7/7 = 1
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Write a recursive formula for an,the nth term of the sequence 3,-12,48,-192
The recursive formula for the sequence is a(n) = -4*a(n-1) . where a(1) = 3.
To find the recursive formula for the sequence 3,-12,48,-192, we need to look at how each term relates to the previous term.
Starting with the first term, we have a(1) = 3.
To get to the second term, we multiply the first term by -4. So we have a(2) = -4*a(1) = -4*3 = -12.
To get to the third term, we multiply the second term by -4. So we have a(3) = -4*a(2) = -4*(-12) = 48.
To get to the fourth term, we multiply the third term by -4. So we have a(4) = -4*a(3) = -4*48 = -192.
So we can see that each term is obtained by multiplying the previous term by -4.
Therefore, the recursive formula for the sequence is:
a(n) = -4*a(n-1)
where a(1) = 3.
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Xsquare_2x_ysquare +4y_3 hcf
The HCF of the given expression is (x + 2y).
To find the highest common factor (HCF) of the given expression, [tex]X^2 + 2xy^2 + 4y^3[/tex], we need to factorize it. However, the given expression seems to contain some typographical errors or inconsistencies, as it is not a valid mathematical expression.
If you meant to write the expression as , [tex]X^2 + 2xy^2 + 4y^3[/tex]we can proceed with finding the HCF.
The expression can be factored as follows:
[tex]X^2 + 2xy^2 + 4y^3 = (x + 2y)(x^2 - 2xy + 2y^2)[/tex]
To find the HCF, we look for the common factors among the terms. In this case, the common factor is (x + 2y). Therefore, the HCF of the given expression is (x + 2y).
Please note that if there was an error in the original expression you provided, and it differs from what was assumed here, please correct it so that a more accurate response can be given
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Note the full question is ;
Xsquare_2x_ysquare +4y_3
hcf of the given term is ?
Rank the following methods of timekeeping from least precise to most
precise.
A clock with only an hour hand
A clock with an hour and minute hand
A calendar
A clock with an hour, minute, and second hand
The required, methods have been arranged according to the rank from least precise to most precise.
Ranking the methods of timekeeping from least precise to most precise:
A clock with only an hour hand - This clock is the least precise, as it can only measure time in hour increments.A calendar - A calendar is more precise than a clock with only an hour hand, as it can measure time in days and months, but not precise to measure hours, minutes or seconds.A clock with an hour and minute hand - This clock is more precise than a calendar, as it can measure time in hours and minutes.A clock with an hour, minute, and second hand - This clock is the most precise, as it can measure time in hours, minutes, and seconds.Therefore, methods have been arranged according to the rank from least precise to most precise.
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Will make brainiest if 2 people answer :D
Polygon ABCD with vertices at A(1, 1), B(3, 1), C(3, 2), and D(1, 2) is dilated to create polygon A′B′C′D′ with vertices at A′(4, 4), B′(12, 4), C′(12, 8), and D′(4, 8).
Determine the scale factor used to create the image.
1/4
1/2
4
2
Answer:
(c) 4
Step-by-step explanation:
You want the scale factor that dilates point A(1, 1) to point A'(4, 4).
DilationDilation about the origin multiplies each coordinate value by the scale factor. That factor is ...
k = A'/A = (4, 4)/(1, 1) = 4
The dilation scale factor is 4.
__
Additional comment
You will notice the same scale factor can be computed from any corresponding pair of points:
k = A'/A = B'/B = C'/C = D'/D = 4
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