Write the coordinates of the vertices after a dilation with a scale factor of 1/3 considered at the origin

Write The Coordinates Of The Vertices After A Dilation With A Scale Factor Of 1/3 Considered At The Origin

Answers

Answer 1

The coordinates of the vertices after a dilation with a scale factor of 1/3 considered at the origin include:

Q' (-3, -3).

R' (1, -3).

S' (3, 3).

T' (-1, 3).

What is a dilation?

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

In this scenario and exercise, we would dilate the coordinates of the vertices by applying a scale factor of 1/3 that is centered at the origin as follows:

Coordinate Q (-9, -9) → Q' (-9 × 1/3, -9 × 1/3) = Coordinate Q' (-3, -3).

Coordinate R (3, -9) → R' (3 × 1/3, -9 × 1/3) = Coordinate R' (1, -3).

Coordinate S (9, 9) → S' (9 × 1/3, 9 × 1/3) = Coordinate S' (3, 3).

Coordinate T (-3, 9) → T' (-3 × 1/3, 9 × 1/3) = Coordinate T' (-1, 3).

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Related Questions

In isosceles triangle the length of a base is 10 cm and the length of a leg is 13 cm. What is the radius of a circle inscribed in this triangle?

Answers

Answer:

4 cm

Step-by-step explanation:

Step: 1

Consider a circle inscribed in an isosceles triangle with legs of length 13cm and a base length of 10cm.

Step: 2

Draw-in altitude AD will pass through the center  O and bisects the base into two segments each in 5cm length.

So the triangle is isosceles so the segment BD is 6cm.

Draw in radius OB and radius OA  and length of  OD as h.

Refer to the attachment for step 3 and step 4

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a real estate company reviewed last year purchases to determine trends in sizes of homes purchased. the results are shows in the table. what are the probabilities for the size of homes that future buyers will desire



homes purchase percentage

2BR 10%

3BR 35%

4BR,,,,,,,,,,,,,,,,,,,,,,30%

5BR 15%'

6BR,,,,,,,,,,,,,,,,,,,,,,,,,,,,10%

Answers

The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

We have,

To determine the probabilities for the size of homes that future buyers will desire, we can use the information provided in the table.

Let's calculate the probabilities for each size of home:

Probability of purchasing a 2BR home: 10%

Probability of purchasing a 3BR home: 35%

Probability of purchasing a 4BR home: 30%

Probability of purchasing a 5BR home: 15%

Probability of purchasing a 6BR home: 10%

To find the probabilities, we divide each percentage by 100:

Probability of purchasing a 2BR home: 10% / 100 = 0.10

Probability of purchasing a 3BR home: 35% / 100 = 0.35

Probability of purchasing a 4BR home: 30% / 100 = 0.30

Probability of purchasing a 5BR home: 15% / 100 = 0.15

Probability of purchasing a 6BR home: 10% / 100 = 0.10

Therefore,

The probabilities for the size of homes that future buyers will desire are as follows:

2BR: 0.10 or 10%

3BR: 0.35 or 35%

4BR: 0.30 or 30%

5BR: 0.15 or 15%

6BR: 0.10 or 10%

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PLEASE HELP
Which of the following values for X will make relation A shown below, a function?


A=(5,3),(4,9),(7,2),(x,6)


3

4 (I know 4 is wrong)

5

7

Answers

The value of x that makes the relation a function is 3.

Option A is the correct answer.

We have,

A = (5, 3), (4, 9), (7, 2), (x, 6)

Given the points (5, 3), (4, 9), (7, 2), and (x, 6), we need to ensure that x does not repeat in the relation.

If we substitute the given values of x (3, 4, 5, 7) into the relation, we find:

For x = 3: (3, 6)

For x = 4: (4, 6)

For x = 5: (5, 6)

For x = 7: (7, 6)

Now,

A function can not have the same output for the same input.

So,

(4, 6) and (4, 9) are not possible.

(5, 6) and (5, 3) are not possible.

(7, 6) and (7, 2) are not possible.

And,

(3, 6) is possible

Thus,

The value of x that makes a function is 3.

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the total cost of bowling is proportional to the number of games played. this relationship can be modeled by the equation y = 3.25x. select all of the tables that represent this relationship

Answers

Answer:

A C E

Step-by-step explanation:

judging by the fact that every game is $3.25 2 games is $6.50 3 is 9.75 and so on

Use percentages to work 4 Mujib has $40 and Prakash has $120. Each of them spends $24. Work out the percentage of their money that each of them has spent.

Answers

The Mujib spent 60% of his money, while Prakash spent 20% of his money.The Mujib spent 60% of his money ($24 out of $40), and Prakash spent 20% of his money ($24 out of $120). Understanding percentages is an important skill, as it allows us to analyze and compare data in a meaningful way.

To work out the percentage of money each person has spent, we first need to determine the amount spent by each person. Both Mujib and Prakash spent $24 each. Now, let's calculate the percentage of money spent by each person.

Mujib had $40 initially and spent $24, so his total spending is $24. To find the percentage, we divide his spending by his initial amount and multiply by 100: ($24 / $40) * 100 = 60%. Therefore, Mujib spent 60% of his money.

Prakash had $120 initially and also spent $24, resulting in a total spending of $24. Similarly, we calculate the percentage of Prakash's spending by dividing his spending by his initial amount and multiplying by 100: ($24 / $120) * 100 = 20%. Hence, Prakash spent 20% of his money.

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Answer the questions below to find the total surface area of the can.

Answers

Answer:

[tex]\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}[/tex]

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

First, we can calculate the area of the circular base:

[tex]A_{\text{circle}} = \pi r^2[/tex]

[tex]A_{\text{base}} = \pi (0.75 \text{ in})^2[/tex]

[tex]A_{\text{base}} = 0.5625\pi \text{ in}^2[/tex]

Next, we can calculate the area of the rectangular side:

[tex]A_\text{rect} = l \cdot w[/tex]

[tex]A_\text{side} = (4\text{ in}) \cdot C_\text{base}[/tex]

Since the width of the side is the circumference of the base, we need to calculate that first.

[tex]C_\text{circle} = 2 \pi r[/tex]

[tex]C_\text{base} = 2 \pi (0.75 \text{ in})[/tex]

[tex]C_\text{base} = 1.5 \pi \text{ in}[/tex]

Now, we can plug that back into the equation for the area of the side:

[tex]A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})[/tex]

[tex]A_\text{side} = 6\pi \text{ in}^2[/tex]

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

[tex]SA = 2( A_{\text{base}}) + A_\text{side}[/tex]

[tex]SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2[/tex]

[tex]\boxed{SA = 7.125\pi \text{ in}^2}[/tex]

[tex]\boxed{SA \approx 22.4 \text{ in}^2}[/tex]

2. The Michaels family records their grocery
bill each week. What is the range of the cost of
their family grocery bill?
$108.55, $86.20, $135.13, $176.97, $57.06
TL
Range:

Answers

The range of the cost of their family grocery bill is $119.91.

The range of the cost of the Michaels family grocery bill can be calculated by finding the difference between the highest and lowest values.

In this case, the highest value is $176.97, and the lowest value is $57.06.

Range = Highest value - Lowest value

Range = $176.97 - $57.06

Range = $119.91

Therefore, the range of the cost of their family grocery bill is $119.91.

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A classroom is rectangular in shape. If listed as ordered pairs, the corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9). What is the perimeter of the classroom in feet?

45 feet
90 feet
252 feet
504 feet

Answers

The perimeter of the classroom in feet is 90 feet.

We are given that;

The corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9).

Now,

Using the given coordinates, we can find the length and width of the rectangle. The length of the rectangle is the difference between the y-coordinates of two opposite corners, which is 15 - (-9) = 24 feet. The width of the rectangle is the difference between the x-coordinates of two opposite corners, which is 9 - (-12) = 21 feet.

P = 2(24 + 21) = 90 feet

Therefore, by the perimeter the answer will be 90 feet.

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Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids will he need to make a perfect cube? What will be the dimensions of the cube?..... pls tell dimension of cube too.​

Answers

Answer:

Step-by-step explanation:

To find out how many cuboids of dimension 5 cm x 5 cm x 3 cm are needed to form a cube, we need to calculate the volume of both the cuboid and the cube.

The volume of the cuboid is:

5 cm x 5 cm x 3 cm = 75 cubic cm

To form a perfect cube, the volume of the cube should be a multiple of the volume of the cuboid. The smallest cube that can be formed using a multiple of 75 cubic cm is a cube with a volume of 75 x 8 = 600 cubic cm.

To find the dimensions of this cube, we need to find the cube root of 600 cubic cm:

cube root of 600 = 8.66 cm

So, the dimensions of the cube are 8.66 cm x 8.66 cm x 8.66 cm.

To find how many cuboids are needed to form this cube, we need to divide the volume of the cube by the volume of the cuboid:

Volume of the cube = 8.66 cm x 8.66 cm x 8.66 cm = 658.39 cubic cm

Number of cuboids required = 658.39 cubic cm ÷ 75 cubic cm = 8.78

Since we can't use a fraction of a cuboid, Anuj will need 9 such cuboids to make a perfect cube.

The graph below is the graph of which inequality?

Answers

Answer: D (√x < 2)


Explanation: In interval notation, it reads:

0 < x < 4

It goes from 0 to 4.

A is the point (7,12) and B is the point (2,-1) find the length of AB

Answers

Answer:

[tex]\huge\boxed{\sf |AB|\approx 13.9 \ units}[/tex]

Step-by-step explanation:

Point 1 = (x₁, y₁) = (7, 12)

Point 2 = (x₂, y₂) = (2, -1)

So,

x₁ = 7

y₁ = 12

x₂ = 2

y₂ = -1

Using distance formula to solve the question.

Solution:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\D=\sqrt{(2-7)^2+(-1-12)^2} \\\\D=\sqrt{(-5)^2+(-13)^2} \\\\D = \sqrt{23+169} \\\\D=\sqrt{194} \\\\|AB|\approx 13.9 \ units\\\\\rule[225]{225}{2}[/tex]

HELP EXPLAIN THIS PLEASE

Answers

Step-by-step explanation:

a)   x = riders     y = racers       ( that is just what I picked...YMMV)

b)   x+y = 321        <======given

c)  25 x + 15 y =  6935    <=====given

Now just graph the two equations.....where they cross is the solution.

Graph below:

A cereal company puts coupons for a free movie ticket in 20% of their boxes,
a free drink in 30% of their boxes, and a free popcorn in 40% of the boxes.
Luke designs a simulation with the spinner. He lets the numbers 0-1
represent a movie ticket coupon, 2-4 represent a drink coupon, and 5-8
represent a popcorn coupon. He spins the spinner and records the results.
His results are shown. Based on the simulation, what is the probability that
Luke gets all three prizes in three boxes of cereal? Explain.
716
796
176
262
730
742
639
450
634
292
822
415
020
462
383
678
117
926
312
635
714

Answers

To determine the probability of Luke getting all three prizes in three boxes of cereal, we need to find the probability of each individual event happening and then multiply those probabilities together.

The probability of getting a movie ticket coupon is 20% or 0.2.

The probability of getting a drink coupon is 30% or 0.3.

The probability of getting a popcorn coupon is 40% or 0.4.

Since Luke spins the spinner three times, the probability of getting all three prizes is calculated by multiplying the probabilities together:

P(all three prizes) = P(movie ticket) * P(drink) * P(popcorn)

= 0.2 * 0.3 * 0.4

= 0.024 or 2.4%

Therefore, based on the simulation, the probability that Luke gets all three prizes in three boxes of cereal is 2.4%.

Write the expression for the following statement without
any spaces: the sum of x squared and 17 can be
expressed as

Answers

The expression x² + 17 represents the sum of x squared and 17.

The sum of x squared and 17 we have to write in expression

x squared is the term x² represents x squared.

It means that the variable x is being multiplied by itself.

If x = 3, then x² would be 3 squared, which is 9.

Similarly, if x = -2, then x² would be (-2) squared, which is 4.

The term + 17 represents the constant value 17 being added to x squared. Regardless of the value of x, 17 will always be added to the result of x squared.

By combining these two terms using the addition operator (+), we express the sum of x squared and 17 as a single mathematical expression, which is x² + 17

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I need a lot of help in this! I’m not the best at graphs. Thank you so much! : )

Answers

The option that shows the inverse's graph (with the correspondent domain and range) is option a.

Which is the graph of the inverse?

Remember that for a function:

f(x) = y

The inverse f⁻¹(x) is defined as:

f⁻¹(y) = x

Here the original function is defined by the relation:

x: -1,  1,  3, 5, 7

y: 4, 2, 1, 0, 1

Then for the inverse function, the domain and range are:

x: 4, 2, 1, 0, 1

y: -1, 1, 3, 5, 7

Then the domain is 0 ≤ x ≤ 4

And the range is -1 ≤ y ≤ 7

the option with these two is a, so that is the correct option.

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Mr Mbhalati predicted that his water bill will decrease in Polokwane.he estimates that he will also use an average of 50kl of water per month.
By using Table 1.calculate if Mr Mbhalati is correct.

Answers

Answer:

Step-by-step explanation:

Jennifer drives on the highway, averaging 54 1/2 miles per hour for 3 hours. Then she turns off the highway onto a smaller route, where she drives at an average rate of 34.25 miles per hours for 3 hours. How many miles has she driven after 6 hours? A. 266.25 miles B. 200 miles C. 80.75 miles D. 275 miles

Answers

Answer:

To solve this problem, we can use the formula distance = rate x time.

For the first part of the trip on the highway, Jennifer travels at an average rate of 54 1/2 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = (54 1/2) x 3

distance = (109/2) x 3

distance = 327/2

distance = 163.5 miles

For the second part of the trip on the smaller route, Jennifer travels at an average rate of 34.25 miles per hour for 3 hours, so the distance she covers is:

distance = rate x time

distance = 34.25 x 3

distance = 102.75 miles

The total distance Jennifer has driven after 6 hours is the sum of the distances she covered on both parts of the trip:

total distance = 163.5 + 102.75

total distance = 266.25 miles

Therefore, the answer is (A) 266.25 miles.

Find the surface area of the square pyramid. (All the triangular faces are
congruent.)
15 m
10 m
10 m

Answers

To determine the area of the figure accurately, we need more information or a description of the figure. The measurements provided (4 cm, -3 cm, 8 cm, 6 cm) do not provide enough details to calculate the area. Please provide additional information or a description of the figure so that I can assist you in finding the closest measurement to its area.

Randall has been practicing his conversions. He said 40 cm is 400 m. Use reasoning to explain why his conversion is incorrect.

Answers

Randall's conversion is incorrect because centimetre value cannot be less than the meter value for an equivalent measurement.

Length Conversion

Both meters and centimeters are used to measure the length of distances or objects. As distances becomes longer, the use of meters would be more preferable as they can represent this distances with smaller values than centimeters.

100 cm = 1 m

Therefore,

40 cm = (40/100) m

40cm = 0.4 m

This shows that centimeters values cannot be greater than equivalent meter values .

Hence, Randall is incorrect .

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Find the distance between the points A and F

Answers

Answer:

7

Step-by-step explanation:

What is the meaning of "predicates"?

Answers

Predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

In logic and linguistics, a predicate is a term used to describe or assert something about a subject. It is a fundamental concept in predicate logic, which is a formal system for reasoning about statements and their relationships.

In a logical statement, a predicate is typically a function or a relation that takes one or more arguments and returns a truth value (either true or false) when those arguments are substituted into it. The arguments of a predicate are usually referred to as its subjects.

For example, in the statement "Socrates is mortal," the predicate is "is mortal," which asserts the property of being mortal about the subject "Socrates." In this case, the predicate is a unary relation since it takes only one argument.

Predicates can also take multiple arguments. For instance, in the statement "John loves Mary," the predicate is "loves," which relates the subject "John" to the object "Mary." In this case, the predicate is a binary relation.

In general, predicates are used to express statements, properties, or relationships between entities in a formal and systematic way, allowing for logical reasoning and analysis. They are an essential component of predicate calculus, which is a branch of mathematical logic.

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5. The revenue, in dollars, from selling x units of a product is given by R(x) = 25x-0.003x². Use
the definition of derivative to find the marginal revenue when 20 units are sold.

Answers

The marginal revenue when 20 units are sold is approximately $24.877.

To find the marginal revenue when 20 units are sold, we need to calculate the derivative of the revenue function with respect to the number of units (x) and then evaluate it at x = 20.

The revenue function is given by R(x) = 25x - 0.003x^2.

The definition of the derivative of a function f(x) is:

f'(x) = lim(h->0) [f(x+h) - f(x)] / h

Let's apply this definition to find the derivative of the revenue function:

R'(x) = lim(h->0) [R(x+h) - R(x)] / h

Substituting the revenue function R(x) = 25x - 0.003x^2:

R'(x) = lim(h->0) [(25(x+h) - 0.003(x+h)^2) - (25x - 0.003x^2)] / h

Expanding and simplifying the expression inside the limit:

R'(x) = lim(h->0) [25x + 25h - 0.003x^2 - 0.003h^2 - 0.006xh - 0.003h] - 25x + 0.003x^2) / h

Canceling out the common terms:

R'(x) = lim(h->0) (25h - 0.003h^2 - 0.006xh - 0.003h) / h

Factoring out h from the numerator:

R'(x) = lim(h->0) h(25 - 0.003h - 0.006x - 0.003) / h

Canceling out h:

R'(x) = lim(h->0) 25 - 0.003h - 0.006x - 0.003

Taking the limit as h approaches 0:

R'(x) = 25 - 0.006x - 0.003

Simplifying:

R'(x) = -0.006x + 24.997

Now, to find the marginal revenue when 20 units are sold, we substitute x = 20 into the derivative:

R'(20) = -0.006(20) + 24.997

Calculating:

R'(20) = -0.12 + 24.997

R'(20) ≈ 24.877

Therefore, the marginal revenue when 20 units are sold is approximately $24.877.

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help please
What is the measure of


∠xstart color #11accd, angle, x, end color #11accd?
Angles are not necessarily drawn to scale.






=
∠x=start color #11accd, angle, x, end color #11accd, equals


Answers

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Tourists standing on a 100-m-tall viewing tower often drop coins into the
fountain below. The height of a coin falling from the tower after t
seconds is given by h(t)=100-5t^2. Find the instantaneous velocity
v(t) of the coin at 2 seconds.

Answers

The instantaneous velocity of the coin, from the first derivative of the height function of the coin, is; v(2) = -20 m/s

What is a derivative of a function?

The derivative of a function is the rate at which the function is changing with regards to the input variable, at a point within the domain of the function.

The height of the tower = 100 m

The function for the height of the coin is; h(t) = 100 - 5·t²

The instantaneous velocity of the coin is the rate of change of the height with respect to time, which is obtained from the derivative of the height function as follows;

The instantaneous velocity; v(t) = h(t)/dt = d(100 - 5·t²)/dt = -10·t

The instantaneous velocity for the coin at t = 2 seconds is therefore;

v(2) = -10 × 2 = -20

The instantaneous velocity of the coin after 2 seconds is -20 m/s

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Please help explain this problem.

Answers

a) h(t) = 200 - 4.9t²

b) it takes 6.39 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of -62.62 m/s.

d) It would take 14.37 seconds.

(a) The height of the stone, h(t), at time t can be determined using the formula for the position of an object under constant acceleration:

h(t) = h0 + v0t + (1/2)gt²

Here initial height= 200 m

initial velocity = 0 m/s

g= -9.8 m/s², and t is the time in seconds.

So, the equation becomes:

h(t) = 200 + 0t + (1/2)(-9.8)t²

h(t) = 200 - 4.9t²

(b) To find the time it takes for the stone to reach the ground, we set h(t) = 0 and solve for t:

0 = 200 - 4.9t²

4.9t² = 200

t² = 200/4.9

t² ≈ 40.82

t ≈ √40.82

t ≈ 6.39 seconds

Therefore, it takes 6.39 seconds for the stone to reach the ground.

(c) The velocity of the stone just before it strikes the ground can be found using the formula for final velocity:

v(t) = v0 + gt

In this case, the initial velocity (v0) is 0 m/s and the acceleration due to gravity (g) is -9.8 m/s². So:

v(t) = 0 + (-9.8)t

v(t) = -9.8t

v(6.39) = -9.8 * 6.39

v(6.39) ≈ -62.62 m/s

Therefore, the stone strikes the ground with a velocity of -62.62 m/s (negative sign indicates it is moving downward).

(d) If the stone were thrown downward with a speed of 7 m/s,

the initial velocity (v0) would be -7 m/s (

We can use the same formula as in part (b) to find the time it takes to reach the ground:

0 = 200 - 7t + (1/2)(-9.8)t²

9.8t² - 7t - 200 = 0

t ≈ 14.37 seconds

t ≈ -1.42 seconds (extraneous solution, as time cannot be negative in this context)

Therefore, it would take 14.37 seconds for the stone to reach the ground if thrown downward with a speed of 7 m/s.

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Find the volume of the pyramid above
Find the surface are of the pyramid above pls help

Answers

The volume of the pyramid is 18069333.33 cubic units

The area of the surface is 313280 square units

How to find the volume of the pyramid

The volume of the pyramid is solved using the formula

= 1/2 * base area * height

Where

base area = 440 * 440 = 193600

height = 280

volume of the pyramid = 1/3 * 193600 * 280

volume of the pyramid = 18069333.33 cubic units

The surface area

The surface area is calculated using the formula

= 4 *  area of the triangles

= 4 * 1/2 * 440 * 356

= 313280 square units

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A patient is prescribed Allegra 60 mg by mouth twice a day. How many tablets the patient need for seven days if the medication available is 30 mg tablets

Answers

Answer:

28

Step-by-step explanation:

2 30 mg pills for 60 mg

Twice a day is 4 pills and 7 days a week

So 4x7=28

4x7=28 4 pills 7 days in a week is 28

an algebraic expression and simplify if possible: the product of −3 and 15.

Answers

The Algebraic expression -3 * 15 simplifies to -45.

The product of -3 and 15 can be represented algebraically as (-3) * 15.

To simplify this expression, we can perform the multiplication operation:

(-3) * 15 = -45

Therefore, the product of -3 and 15 simplifies to -45.

In the given expression, we have multiplied -3 by 15, resulting in a negative value since one of the factors is negative. Multiplying a negative number by a positive number yields a negative product.

So, the algebraic expression -3 * 15 simplifies to -45.

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Which of these could be the value of x in
the triangle below?
42°
C
A 5
B 6
38
53
A
85
© 8
10
26
B

Answers

In the given triangle, we have a right triangle where one angle is 90 degrees (marked as a square symbol). To find the value of x, we can use the trigonometric ratios sine, cosine, or tangent.

Looking at the triangle, we can see that the side adjacent to the angle x is 8 cm, and the hypotenuse of the triangle is 10 cm.

Using the cosine ratio, which is defined as the adjacent side divided by the hypotenuse, we can set up the equation:

cos(x) = adjacent/hypotenuse

cos(x) = 8/10

To find the value of x, we can take the inverse cosine (arccos) of both sides:

x = arccos(8/10)

Using a calculator, we can determine the approximate value of x:

x ≈ 36.87 degrees

Therefore, the value of x in the given triangle is approximately 36.87 degrees.

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Answers

The relation that represents a function is: ((- 6, 5), (- 3, 2), (1, 2), (6, 5))

A relation represents a function if each input (x-value) is associated with only one output (y-value).

1. {(0, 3), (2, 4), (0, 6)}:

This relation is not a function because the input 0 is associated with two different outputs, 3 and 6.

2. ((- 7, 5), (- 7, 1), (- 10, 3), (- 4, 3)):

This relation is not a function because the input -7 is associated with two different outputs, 5 and 1.

3. ((- 6, 5), (- 3, 2), (1, 2), (6, 5)):

This relation is a function since each input is associated with a unique output.

4. {(2, 0), (6, 2), (6, - 2)}:

This relation is not a function because the input 6 is associated with two different outputs, 2 and -2.

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