Is the following relation linear, quadratic, or cubic? If it is linear, find the equation. Explain your reasoning and include all of your work in your final answer.


1. Q = { (x,y) : (0,0), (1,2), (2,16), (3, 54), (4, 128), (5,250) }

2. R= { (x,y) : (2,3), (4,4), (6,5), (8,6) }

3. S = { (x,y), : (1,3), (2,9), (3,17), (4,27), (5, 39), (6,53) }

Answers

Answer 1

Answer:

Q = { (x,y) : (0,0), (1,2), (2,16), (3, 54), (4, 128), (5,250) } is cubic

R= { (x,y) : (2,3), (4,4), (6,5), (8,6) } is linear

S = { (x,y), : (1,3), (2,9), (3,17), (4,27), (5, 39), (6,53) } is quadratic

Equation of the linear relation is

y = 0.5x + 2

Step-by-step explanation:

A linear equation has the form y = mx + b where m is the slope and b is the y-intercept. Slope is a constant and growth of function is determined by x value

A quadratic equation has the general form y = ax² + bx + c where a b and c are constants. Growth of the function is mostly determined by the square of x

A cubic equation has the general form y = ax³ + bx² + cx + d where a, b and c are constants. The growth of the function is mostly determined by the cube of x value

Looking at the three relations

#1 is obviously cubic since the value of y appears to be determined by the cube of the value of x. Specifically, when x = 0, y = 0/. When x =1, y = 2 but when x =2, y =16 and 16 is 2x³ = 2(2³) = 2 x 8

Looking at x =3, 2(3³) = 2(27) = 54

So this is a cubic function

#2 is obviously a linear function When x increases by 2, y increases by 1 so it is a linear growth

#3 In this equation we can see that the y value appears to be controlled by the square of x. The specific equation is y = x² + 3x -1

For the linear equation, find the slope from the first two points

m = (4-3)/(4-2) = 1/2 = 0.5

So the equation is y = 0.5x + b

To find b, use the coordinates of any point. Let's choose (4,4)

At x = 4, y = 4 so

4 = (0.5)4 + b = 2+b yielding b = 2

So the equation is y = 0.5x + 2

Answer 2

Relation Q is not linear, relation R is linear with the equation y = (1/2)x + 2, and relation S is not linear.

1: Q = { (0,0), (1,2), (2,16), (3,54), (4,128), (5,250) }

To determine if this relation is linear, quadratic, or cubic,

Examine the differences between the y-values.

Calculate the differences for the given data:

Difference in y-values:

(2-0) = 2

(16-2) = 14

(54-16) = 38

(128-54) = 74

(250-128) = 122

Looking at the differences,

we can see that they are not constant.

In a linear relation, the differences between the y-values would be constant.

Therefore, we can conclude that this relation is not linear.

2: R = { (2,3), (4,4), (6,5), (8,6) }

Similar to the previous relation, let's calculate the differences:

Difference in y-values:

(4-3) = 1

(6-4) = 2

(8-6) = 2

In this case, the differences between the y-values are constant

(both are 2). This indicates a linear relation.

To find the equation, we can use the slope-intercept form (y = mx + b). Let's choose any two points from the relation, for example, (2,3) and (4,4):

Slope (m) = (4-3) / (4-2) = 1/2

m = 1/2

Now, let's plug in the values of one point (2,3) and the slope into the equation:

y = mx + b

3 = (1/2) x 2 + b

3 = 1 + b

b = 2

Therefore, the equation for this linear relation is y = (1/2)x + 2.

3: S = { (1,3), (2,9), (3,17), (4,27), (5,39), (6,53) }

Again, calculate the differences:

Difference in y-values:

(9-3) = 6

(17-9) = 8

(27-17) = 10

(39-27) = 12

(53-39) = 14

The differences between the y-values are not constant, indicating that this relation is not linear.

Hence,

Relation Q is not linear.

Relation R is linear, with the equation y = (1/2)x + 2.

Relation S is not linear.

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Related Questions

There are 3 red marbles, 2 blue marbles, and 7 black marbles if you choose one marble, what is the probability that it will be a red marble?

Answers

Answer:

3:12

Step-by-step explanation:

3 + 2 + 7 = 12

3 = red marbles

12 = total marbles

Answer:

Probability of both red =3(182)=3(18!2!16!)=3153

Step-by-step explanation:

Let Ai be the event in which the i-th ball you grab is red. For the first ball you choose, you have 3 red marbles out of a total of 18. Therefore,

P(A1)=318.

For the second marble you grab, given that you already took a red one, that is, given A1, you have 2 red balls out of a total of 17, then

P(A2∣A1)=217.

Finally,

P(A1∩A2)=P(A1)P(A2∣A1)=318217=151.

find the value of x (9x-3)​

Answers

9x^2-3x
mark me brainliest if the answer is correct, thank you in advance :)

The result of the multiplication is the value of x (9x-3)​ is:  9x² - 3x.

Here, we have,

given that,

the expression is:  x (9x-3)​

now we need to find the value of x (9x-3)​

we have,

x (9x-3)​

=> x × (9x-3)​

so, we have to multiply this two terms.

now, we get,

=> x × (9x) - x × 3

=> 9x² - 3x

Hence, The result of the multiplication is the value of x (9x-3)​ is:  9x² - 3x.

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Which compound inequality is graphed?

Answers

The answer is D hope this helps!!

If a circle has equation (x-3)^2 + (y+1)^2 = 49, what is it’s domain?
I’m forgetting everything from algebra

Answers

The domain of the circle is [-4, 10]

How to determine the domain of the circle?

The circle equation is given as:

(x - 3)^2 + (y + 1)^2 = 49

Express 49 as 7^2

So, we have

(x - 3)^2 + (y + 1)^2 = 7^2

The general circle equation is

(x - a)^2 + (y - b)^2 = r^2

Where the domain is

Domain = [a ± r]

So, we have

Domain = [3 ± 7]

Evaluate

Domain = [3 - 7, 3 + 7]

This gives

Domain = [-4, 10]

Hence, the domain of the circle is [-4, 10]

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How many shares does Whitney own at the end of the year

Answers

Answer:

who's Whitney? And im gonna say 47

Step-by-step explanation:

Answer: I think 43 If it is whitner bulger you actually talking about.

Step-by-step explanation:

Please help!! I don’t understand this :(

Answers

Answer:

1c

2b

Step-by-step explanation:  i think im not absolutly

shure

what is the solution to the following system? (picture)
a. (2,3,4)
b. (4,3,-2)
c. (4, 3, 2)
d. (6, 7, -2)

Answers

option C

PLS MAKE ME AS THE BRAINLIEST ANSWER

Juan and Maria walk dogs in their neighborhood. Maria walks 10 more than twice the number of dogs Juan walks. Together they walk 52 dogs.

Which system of equations models this situation if j represents the number of dogs Juan walks and m represents the number of dogs Maria walks?

Answers

Answer:

m=2j+10

m+j=52

Step-by-step explanation:

m = maria

j = juan

1. A television set costs ₱35 000.00 and a yearly cost of electricity of ₱572.00

Answers

Answer:

whats the question for this?

Step-by-step explanation:

Some help would be appreciated !!

Find the perimeter.

Answers

perimeter = 2(x - 6y) + 2(8x² - x - 4y)

2x - 12y + 16x² - 2x - 8y

= 16x² - 20y units

Math question help me

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Answer:

A

Step-by-step explanation:

Find the value of (7x+17) (8x+2)

Answers

Answer:

Step-by-step explanation:

7x+17+8x+2)

7x+17+8x+2

7x+8x+17+2

15x+19.

help me please I'm stuck ​

Answers

Answer:

I think its C

Step-by-step explanation:

B. Looks like the correct answer, tell me if I’m right

does the graph represent a function if its a triangle

Answers

obviously yes..........

HELP !
A small shop can manufacture 4 windows every
5 hours. At that rate, how long will it take to
manufacture 7 windows?
A) 8 hr
B) 8 hr 15 min
C) 8 hr 30 min
D) 8 hr 45 min

Answers

D would be the answer i think if you need me to explain i can

The answer is option D it will take 8 hours 45 minutes to manufacture 7 windows.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The time will be calculated as follows:-

4 windows ------->   5 hours

1 window   --------> 5 / 4 hours

7 window  --------> 7 x ( 5 / 4 )

7 window  --------> 8.75 ≅ 8 hours 45 minutes

Therefore the answer is option D it will take 8 hours 45 minutes to manufacture 7 windows.

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If you have 3.4 dozen eggs, how many eggs do you have?

Answers

Answer:

2 eggs

Step-by-step explanation:

A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoes is -4.8 meters. The equation 12+d=-4.8 represents the situation.

Answers

Answer:

i. The distance between the balloon and canoe is 16.8 meters.

ii. The situation can be represented by: -12 + d = 4.8

Step-by-step explanation:

Let the surface of the lake be zero. Then any position above it is taken to be positive, while any position below is taken as negative.

So that,

the balloon's vertical position = 12 meters

the sunken canoe's position = -4.8 meters

Given that the distance between the balloon and the canoes is d, then:

d = balloon's position - canoe's position

  = 12 - (-4.8)

  = 12 + 4.8

d  = 16.8

The distance between the balloon and canoe is 16.8 meters.

Thus,

d = 12 -(-4.8)

d = 12 + 4.8

-12 + d = 4.8

The situation can be represented by: -12 + d = 4.8

from the set ( 1,2,3,4,5), which values make n+1>4 true?

- (1,2)
- (4,5)
- (3,4,5)
- (1,2,3)

Answers

Answer:

(4,5)

Step-by-step explanation:

n+1>4

subtract 1 from both sides

n>3

that means n is greater than 3 so 3 is not a solution but everything higher than 3 is true.

Write the equation in slope intercept form y - 4=10(x-5)

Answers

Answer:

y= 10x - 46

Step-by-step explanation:

slope intercept form model: y=mx+b

Joyce paid $117.00 for an item at the store that was 35% off the original price. What was the original price? Round your answer to the nearest cent.

I just need the explanation.

Answers

Considering the definition of an equation and the way to solve it, the original price was $180.

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.

The solution of a equation means determining the value in which the equality must be true. To solve an equation, keep in mind:

When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Original price

Being "x" the original price, and knowing that:

Joyce paid $117.00 for an item at the store.The item was 35% (0.35 expressed as a decimal number) off the original price.

The original price  can be calculated through the equation:

x - 0.35x= 117

Solving:

(1 - 0.35)x= 117

0.65x= 117

x= 117 ÷ 0.65

x= 180

Finally, the original price was $180.

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Please help Expert and Above Only! I will double the points if you can explain it! Both questions please!

Answers

Problem 11

Answer:  339 square meters

---------------

Work Shown:

The surface area of a 3D sphere is 4pi*r^2. So a hemisphere has surface area 2pi*r^2 since we cut the surface area in half.

Plug in r = 6 (half of the diameter 12) and we get 2pi*r^2 = 2pi*6^2 = 72pi

Now consider the circle with radius r = 6. Its area is pi*r^2 = pi*6^2 = 36pi

Add the two areas and we get 72pi+36pi = 108pi

Lastly, use your calculator to get 108pi = 108*3.1415926535898 = 339.292006587699 which rounds to 339

======================================

Problem 12

Answer:  C) 19.5 mm

---------------

Explanation:

Look at where the "0" in the bottom sliding portion lines up with the number scale above. That "0" is between 19 and 20 mm. So you could argue that 19.2 and 19.5 are both valid answers, but I think 19.5 is the better answer since the tickmark seems to be right in the middle (more or less).

Step-by-step explanation:

surface area of hemisphere =3πr²

=3*3.14(6)²

=339.12m²

diameter of pipe= 19.5mm

Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family.
Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill
was $99, how many people ordered each dinner?

Answers

Answer:

We conclude that:

The number of people who ordered the chicken dinner = 1The number of people who ordered the steak dinner = 5

Step-by-step explanation:

Given that

Some order the chicken dinner for $14some order the steak dinner for $17.Total bill = $99

Let 'n' be the number of people who ordered the chicken dinner.Let '6-n' be the number of people who ordered the steak dinner.

Thus, the equation becomes

[tex]14n + 17(6-n) = 99[/tex]

[tex]14n + 102 - 17n = 99[/tex]

[tex]-3n = 99 - 102[/tex]

[tex]-3n = -3[/tex]

Divide both sides by -3

[tex]n = 1[/tex]

and

[tex]6-n = 6-1 = 5[/tex]

Therefore, we conclude that:

The number of people who ordered the chicken dinner = 1The number of people who ordered the steak dinner = 5

1. (8.2k - 6) - (4.5 – 9k)

2. (-3 + 2g) - (4 + 5g)


Answers

Answer:

a. [tex]= 17.2k - 1.5[/tex]

b.[tex]=-7 + 203g[/tex]

Step-by-step explanation:

Required

Simplify

[tex]1.\ (8.2k - 6) - (4.5 - 9k)[/tex]

Open bracket

[tex]= 8.2k - 6 - 4.5 + 9k[/tex]

Collect Like Terms

[tex]= 8.2k + 9k - 6 - 4.5[/tex]

[tex]= 17.2k - 1.5[/tex]

[tex]2.\ (-3 + 2g) - (4 + 5g)[/tex]

Open bracket

[tex]= -3 + 2g - 4 - 5g[/tex]

Collect Like Terms

[tex]=-3-4+2g - 5g[/tex]

[tex]=-7 + 203g[/tex]

A cash register must have at least $25 in change consisting of x dimes and y quarters. Write a linear inequality that represents the different numbers of dimes and quarters that can satisfy this requirement.

In addition, would 150 dimes and 40 quarters satisfy this requirement?

Answers

Answer:

150 has to be times 40

Step-by-step explanation:

150×40+25÷35=1

simplify (-63) divided by (-9)

Answers

Answer:

7

Step-by-step explanation:

-63/-9

7

5 1/2 x 1 1/2
using unit rate.
Simplify if possible.​

Answers

Answer:

2 3/4

Step-by-step explanation:

this is the answer

arianne is taking a geometry course and is working with the area of triangles. she knows the area and the height but needs to find the base. rearrange the following equation for b, where a is the area, b is the base, and h is the height of the triangle. a

Answers

Base is 2 times A over height= [tex](base)=\frac{2Area}{height}[/tex].

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure.

Area of a triangle is given by the formula;

                               [tex]A=\frac{1}{2} base * height[/tex]

Now, we need to solve for b. We multiply the right side, cross multiply,  and follow rules of algebra to isolate b. Shown below:

                         [tex]A=\frac{1}{2} base*height\\A=\frac{bh}{2} \\2A=bh\\b(base)=\frac{2A}{h}[/tex]

Thus, Base is 2 times A over height= [tex](base)=\frac{2Area}{height}[/tex].

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Answer:

The answer is B

Step-by-step explanation:

10 POINTS For which equation would x = 4 be a solution?

A.4x + 7 = 23
B.4x ÷ 8 = 8
C.8 - 5x = 1
D.7 + 3x = 18

Answers

A would be the correct answer
A would be the answer because you -7of both sides then it would leave 4x=16 so then divided both sides by 4 so x=4

thank god for creating this beauty

Answers

Answer:

yesss

Step-by-step explanation:

PLEASE HELP ME!!!!! PLEASE I WANT TO GET THIS RIGHT

What is the price per pound for Fuji apples?

What is the price per pound for Golden Delicious apples?

What is the price per pound for Macintosh apples?

Answers

Answer:

Step-by-step explanation:

Fuji Apples: 7/6 = $1.16

Golden Delicious Apples: 1/0.75 = 100/75 = $1.33

Macintosh Apples:  $2

Hope this helps!      :3

plz mark as brainliest!

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