if the numerator of a certain fraction is a quarter of the value of the whole fraction, what is the value of the denominator of that fraction?

5 and 25

A single counterexample to any conjecture that states that something will always be true immediately disproves the statement.

Conjecture

Conjecture is a statement or conclusion that is offered with little to no proof. The conclusion given in the question has no mathematical proof to support the idea; thus, it is conjecture. Conjecture is often easy to disprove.

Counterexamples are examples that follow the conditions of a statement (or conjecture) but do not meet the same conclusion. The conditions of the conjecture given are "an odd number plus another odd number". So, a counterexample must also meet these conditions. The conclusion of the conjecture is that this sum " will always be divisible by 4". Thus, the counterexample should not be divisible by 4.

Counterexample

At first, the conjecture may seem to be true because of pairs like 13+15 or 21+23. However, because the conjecture includes the word "always", it only takes one counterexample to completely disprove the statement.

I know that 30 is not divisible by 4, so I can find 2 odd numbers that sum to 30. I pair I chose was 5+25, but there are other possibilities like 13+17 or 1+29. No matter which you choose, it's clear that the conjecture is not true.

Answer:

Step-by-step explanation: This week, I had a question in math class about the different types of angles, such as alternate interior angles theorem, alternate exterior angles, same-side interior angles, same-side exterior angles, corresponding angles, concurrent lines, perpendicular lines, and a few more types of angles about lines and knowing what matches to what type of angle. Yes, I did ask a few questions when I was confused about certain lines and how they have this angle, such as a concurrent line. Yes, my question was answered. I actually enjoy asking questions because if I don't learn what I'm confused about, how will I know how to improve and avoid making the same mistakes? Yes, I had someone else ask the same question I had before, whether it was something new learned in class or something confusing or difficult to learn. It made me feel relieved and grateful because I'm glad I wasn't the only one who was confused, and it makes it easier when someone else doesn't understand the same step, and challenges when learning new things. The questions we ask lead to new discoveries. Questions lead us to answers we never considered before we asked the question. Of course, one cannot simply ask question after question without considering possible answers. Many people, on the other hand, are afraid that by asking questions, they will appear weak, ignorant, or unsure. They are afraid that asking questions will place them in a negative light. Lastly, some people are so eager to get things done that they don't stop to ask questions because it might slow them down.

The solution to the equation 5 – 6x = 8x + 17 is x = -6.

Using the general solution for linear equations, we can rewrite the given equation as x = (a - d)/(c + b). This means that the solution for x is equal to the fraction (a - d) divided by (c + b).

Now let's use this general solution to solve the equation 5 – 6x = 8x + 17. First, we need to identify the values of a, b, c, and d in the equation. From the given equation, we can see that a = 5, b = -6, c = 8, and d = 17.

Next, we can substitute these values into the general solution and simplify:

x = (a - d)/(c + b)

x = (5 - 17)/(8 - 6)

x = -12/2

x = -6

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Answer:-6/7

Step-by-step explanation: got it right on ed

Answer:

24.13

Step-by-step explanation:

Answer:

A) 1.7m, 1.78m, 1.8m, 1.82m, 1.86m, 1.88m, 1.9m

B) The median is 1.82

C) There is a 3/7 chance that the player will be taller than 1.85m

Step-by-step explanation:

The solution is, (a) 1.7m < 1.78m < 1.8m < 1.82m< 1.86m< 1.88m < 1.9m,  the heights in order from smallest to largest.

(b)  1.8 the median height.

(c) A player is picked at random, 3/7 is the probability that he is over 1.85m.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

given that,

The heights of seven footballers are listed below.

1.9m, 1.82m, 1.78m, 1.8m, 1.88m, 1.86m, 1.7m

now we have to Arrange the heights in order from smallest to largest.

we get,

(a) 1.7m < 1.78m < 1.8m < 1.82m< 1.86m< 1.88m < 1.9m,  the heights in order from smallest to largest.

now, the median = 1.7 + 1.9/ 2

                            = 1.8

(b)  1.8 the median height.

again,

(c) the total no. of outcome = 7

no. of event that he is over 1.85m = 3

so, the probability that he is over 1.85m = 7/3

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Answer:

3cos²x

Step-by-step explanation:

sinx = 3cosx [1]

(sinx)(cosx) [2]

sub 1 into 2:

(3cosx)(cosx)

= 3cos²x

Answer:

3/10?

Hope it's correct. :)

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.

given

We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.

The wider circle's circumference is 132 feet.

2πR = 132

R = 21

The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:

R - r = diameter of the circle

21 - r = diameter of the circle

r = 18

The smaller circle therefore has a radius of 18 feet.

Inside the arc of the path, there is:

R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

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Answer:

he has 39 lunch boxes left

Step-by-step explanation:

26 + 15 + 17 gives you 58 and when you subtract 19 from 58 that leaves you with 39 left

Answer: $5232.15

Step-by-step explanation:

990 x 5.7% = 1046.43

1046.43 x 5 years = 5232.25

After 6 weeks, the size of the bacteria is 1600, and after 15 weeks, the size of the bacteria is 12800

Let N₀ be the initial number of bacteria in a population and r be the growth rate of the bacteria.

The doubling time t doubles the population after each time interval t, hence:

Nt = N₀ × 2^(t/t) Nₜ

= N₀ × 2^(t/d)Nt/N₀

= 2^(t/d)ln(Nₜ/N₀)

= (t/d)ln2ln(Nₜ) - ln(N₀)

= (t/d)ln2ln(Nₜ/N₀)

= (t/d)ln2t/d

= ln(Nt/N₀) / ln2

Now, we can calculate the time required for the population to double in size as

t = d × ln2/ln(Nₜ/N₀)

Now, let's substitute the values given and solve:

a) After 6 weeks, t = 3 weeks (since doubling time is 3 weeks)

So, Nₜ/N₀ = 2^(t/d)

= 2^(6/3)

= 2^2 = 4

Nt = N₀ × 4

= 100 × 4

= 400.

After 6 weeks, the size of the bacteria is 400.

b) After 15 weeks,

t = d × ln2/ln(Nₜ/N₀)ₜ

= 3 × ln2/ln(128)

= 3 × 0.9983/7.1554

= 0.4186 weeks

So, Nₜ/N₀ = 2^(t/d)

= 2^(15/3)

= 2^5

= 32Nₜ

= N₀ × 32 = 100 × 32

= 3200

After 15 weeks, the size of the bacteria is 3200.

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A rectangular flag is 29ft long and 17ft wide. if a triangle is cut out of the center of the flag that has a base of 9ft and a height of 2ft, So the remaining area of the flag is 484 ft².

The data we get from the question is,

        Length of rectangular flag = 29 ft

        Width of rectangular flag = 17 ft

        Base of triangle = 9 ft

        Height of triangle = 2 ft

  We need to find the remaining area of the flag when a triangle is cut out of the center of the flag. 

  We know that the area of the rectangle is given by:

                       Area of rectangle = length × breadth

                       Area of rectangle = 29 × 17

                                                     = 493 ft²

  The area of the triangle is given by:

                                       Area of triangle = (1/2) × base × height

                                       Area of triangle = (1/2) × 9 × 2

                                                                  = 9 ft²

   The remaining area of the flag will be the area of the rectangle minus the area of the triangle.

The remaining area of the flag = Area of the rectangle - Area of the triangle

                                                   = 493 - 9

                                                   = 484 ft²

         Therefore, the remaining area of the flag is 484 ft².

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The answer of the given question based on the linear function the answer is option b) g(x) = 3x + 8 is linear and for linear function graph the explanation is given below,

In mathematics,  function is  relationship between two sets of values, where each element in  first set (called domain) is paired with exactly one element in the second set (called range).

1) Among the given functions, only g(x) = 3x + 8 is linear. A linear function is one whose graph is a straight line, and it has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

The function f(x) = x²+2x-3 is a quadratic function because its graph is a parabola, not a straight line. Similarly, the function h(x) = 4 is a constant function because its graph is a horizontal line with a constant y-value of 4, not a straight line.

2) To graph the function f(x) = 2x - 7, we can first identify its slope and y-intercept. The slope of the line is 2, which means that for every increase of 1 in x, the value of y increases by 2. The y-intercept is -7, which means that the line crosses the y-axis at the point (0, -7).

Using this information, we can plot the y-intercept at (0, -7) and then use the slope to find other points on the line. For example, if we increase x by 1, y will increase by 2, so we can plot the point (1, -5). We can continue this process to find other points on the line, and then draw a straight line through them to graph the function.

To graph the function f(x) = -2/5x+1, we can follow the same process. The slope of the line is -2/5, which means that for every increase of 1 in x, the value of y decreases by 2/5. The y-intercept is 1, so the line crosses the y-axis at the point (0, 1).

Using this information, we can plot the y-intercept at (0, 1) and then use the slope to find other points on the line. For example, if we increase x by 5, y will decrease by 2, so we can plot the point (5, -1). We can continue this process to find other points on the line, and then draw a straight line through them to graph the function.

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Johnson has a scoring percentage of 46.57% while Clarence has a scoring percentage of 53.84%. Clarence has the higher scoring percentage.

A percentage is a way of expressing a number as a fraction of 100. It is often used to represent a part of a whole or a comparison between two quantities.

To calculate the scoring percentage, we divide the number of shots made by the number of shots attempted and then multiply by 100. For Johnson, the scoring percentage is

For Clarence, the scoring percentage is

Therefore, Clarence has the higher scoring percentage.

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To calculate the number of days it will take Ivan to read both books, we need to divide the total number of pages by the number of pages Ivan can read per day.

The first book has c pages, and the second book has d pages, so the total number of pages is c + d. If Ivan reads eight pages per day, then he will read a total of 8[tex]*[/tex]n pages in n days. Therefore, the number of days it will take Ivan to read both books can be calculated as: n = (c + d) / 8

This formula tells us that we need to divide the total number of pages by the number of pages Ivan can read per day, which is eight. The result of this division will give us the number of days it will take Ivan to read both books.

For example, if the first book has 100 pages and the second book has 200 pages, then the total number of pages is 300. plugging this into the formula, we get: n = (100 + 200) / 8 = 37.5 Since Ivan can't read a fraction of a day, we round up to the nearest whole number. Therefore, it will take Ivan 38 days to read both books.

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Disha is not correct, as the area of the larger circle is actually four times the area of the smaller circle, not double.

Circumference is the distance around the edge of a closed curved shape, such as a circle. In the case of a circle, it is the distance around the circle, or the perimeter of the circle.

Let "r" denote the smaller circle's radius. Then the circumference of the smaller circle would be 2πr, and the area would be πr².

If the circumference and area of the larger circle are both double the circumference and area of the smaller circle, then:

Circumference of larger circle = 2(2πr) = 4πr

Area of larger circle = 2(πr²) = 2π(r²)

Let "R" represent the larger circle's radius. Then the circumference of the larger circle would be 2πR, and the area would be πR².

If the circumference and area of the larger circle are both double the circumference and area of the smaller circle, then:

Circumference of larger circle = 2(2πr) = 4πr = 2πR

Area of larger circle = 2(πr²) = 2π(r²) = πR²

We may see from the equations above that:

R = 2r

Substituting this value of R in the equation for the area of the larger circle, we get:

Area of larger circle = πR² = π(2r)² = 4πr²

But we already know that the area of the larger circle is 2π(r²). This means that Disha is not correct, as the area of the larger circle is actually four times the area of the smaller circle, not double.

Therefore, Disha's statement is incorrect.

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Systematic sampling is the term used to describe the sampling method portrayed in the scenario.

Systematic sampling is a form of probability sampling technique in which a researcher randomly selects a beginning point before selecting every nth item from the target population. The researcher is choosing one consumer at each table in this case, which can be interpreted as choosing every nth customer, where n is the average number of customers per table.

When the researcher wants to select a sample from a pre-defined list and the target population is broad and diverse, systematic sampling is a beneficial strategy. Because it takes less time and resources to choose the sample, it is also a more effective strategy than simple random sampling.

It is crucial to remember that systematic sampling might induce bias if the process of selection follows a pattern or is regular. For instance, bias could be introduced if the researcher only chooses consumers at tables with even numbers, producing a non-representative sample. To eliminate bias and get a representative sample, it is crucial to ensure that the selection procedure is truly random.

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the right option is B.) a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

The corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (1,25), (3,19), (4,16) and (7,7)

Time(in days)    -    Number of boxes

1                                  25

3                                  19

4                                   16

7                                    7

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=--3x+28

Putting x=0, we get

y=-3(0)+28=28

Putting x=2, we get

y=-3(2)+28

y=22

hence,. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

The diagram is attached below.

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Answer: 1.5

Step-by-step explanation:

The interquartile range (IQR) is a measure of statistical dispersion and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). For the given dot plot data of the toddler's heights, the data would first be arranged in ascending order, then divided into two halves below and above the median to determine the first and third quartiles.

To find the interquartile range (IQR) in the dot plot data of the toddler's heights at Mrs. Orlando's daycare, we first need to understand what the IQR represents. The Interquartile Range is a measure of where the bulk of the values lie in a data set. It's computed by subtracting the first quartile (Q1) from the third quartile (Q3).

As a first step, you would arrange the data points in ascending order. The median would give us the second quartile (Q2). The data set is then divided into two halves, below and above the median. The first quartile (Q1) is the median of the lower half and the third quartile (Q3) is the median of the upper half. Finally, subtract Q1 from Q3 to find the IQR.

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Opioids are a class of drugs that include both prescription painkillers, such as oxycodone, hydrocodone, and fentanyl, and illegal drugs, such as heroin.

Opioids are highly addictive and can lead to physical dependence and addiction with prolonged use. They can also cause a range of negative side effects, including drowsiness, confusion, constipation, nausea, and respiratory depression, which can be life-threatening in high doses.

Opioid addiction has become a major public health crisis in many countries, including the United States, where it has been linked to a dramatic increase in overdose deaths.

The numbers that match the phrases are;

1 - j

2 - c

3 - b

4 - a

5 - i

6 - d

7 - e

8 - f

9 - j

10 - h

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The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.

The burning of fossil fuels is not an example of a human activity that directly threatens the biodiversity of species. While burning fossil fuels can contribute to climate change, which can have indirect impacts on biodiversity, such as changing habitats or altering migration patterns, it is not a direct threat to individual species or their populations.

On the other hand, the picking of flowers, overexploitation of resources, introduction of invasive species, and destruction of habitats are all examples of human activities that directly threaten the biodiversity of species. For example, overexploitation of resources such as fishing can lead to the depletion of fish populations, while the introduction of invasive species can outcompete and displace native species. The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.

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The equation given as |x-1| + |x-2| = -3 has no solution while the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3

Given that

|x-1| + |x-2| = -3

The above equation has the sum of absolute expressions

As a general rule, the sum of absolute expressions is always positive

The solution -3 is negative

So, the equation has no solution

On the other hand, we have

|x-1| + |x-2| = 3

Assume x = 0, we have

|0-1| + |0-2| = 3

1 + 2 = 3 --- true

Assume x = 3, we have

|3-1| + |3-2| = 3

2 + 1 = 3 --- true

Hence, the solutions of |x-1| + |x-2| = 3 are x = 0 and x = 3

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Chance is 1/10

Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.

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The 0.05(x+4)+0.10(x) = $1.25 equation could be used to determine the number of dimes, x, in his pocket.

An equation is a mathematical expression containing an equal sign that states the equality of two expressions. It is essentially a statement of balance, showing that two expressions are equal in value. Equations are used to solve a wide variety of problems in mathematics, science, and engineering. For example, the equation x+2=4 expresses the fact that when 2 is added to any number x, the result is 4.

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The new coordinates of point s after the dilation are (12x, 12y)

A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.

The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.

The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.

To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:

New x-coordinate = 12 × x

New y-coordinate = 12 × y

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The function that could not be true is , f(-1) = 4.option b, f(3) = 30 is not correct.

To find f(2), we simply substitute 2 for x in the function f(x):

[tex]f(2) = (2 + 1)^2 = 9[/tex]

Therefore,

[tex]f(2) = 9.[/tex]

Now, to determine which of the following statements could not be true if f(x) is a function and f(1) = 5, we need to check whether they violate any properties of functions. Here are the statements:

f(1) = 5

means that y = 5x

so when y = 1

x = 5

Therefore, option b, f(3) = 30 is not correct.

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Complete question:

Find f(2) if f(x) = (x + 1)2.

If f(x) is a function and f(1) = 5, then which of the following could not be true?

f(10) = 50

f(3) = 30

f(2) = 10

f(7) = 35

To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.

where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.

P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.

Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.

After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.

Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.

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Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

After the triangle is dilated by a scale factor of 1/4, the coordinates of point C' are (10, -14).

We can use the following formula to find the coordinates of point C' after the triangle has been dilated by a scale factor of 1/4:

C' = (1/4)(C - center) + center

where C denotes the original coordinate of point C and centre denotes the dilation center (which is not specified in the problem).

However, because this is the most common choice and is not explicitly stated, we can assume that the center of dilation is the midpoint of line segment AB. Line segment AB's midpoint is:

((8+8)/2, (-24-8)/2) = (8, -16)

So, in the formula, we can substitute this value for Centre:

C' = (1/4)(C - (8, -16)) + (8, -16)

All that remains is to plug in the coordinates of point C and simplify:

C' = (1/4)((16, -8) - (8, -16)) + (8, -16)

= (1/4)(8, 8) + (8, -16)

= (2, 2) + (8, -16)

= (10, -14)

As a result, the coordinates of point C' after the triangle has been dilated by a factor of 1/4 are (10, -14).

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Step-by-step explanation:

Since the three horizontal lines are parallel, you can set up a simple ratio:

71 is to 79    as   x is to 81

71/79 = x/81

x = 71/79 * 81 = 73 units   ( rounded to two S.D.)