The graph of a function contains the points (6, 7) and (10, 13). Which of these statements is correct based on this information?

A. If the graph also contains the point (4, 4) then the function must not be linear.
B. If the graph also contains the point (12, 16) then the function must not be linear.
C. If the graph also contains the point (1, 2) then the function could be linear.
D. If the graph also contains the point (8, 10) then the function could be linear.

Answers

Answer 1

Answer:

The true statements are:

B and D.

Step-by-step explanation:

First, a linear function can be written as:

y = a*x + b

Such that a is the slope, and b is the y-intercept.

If we know that the graph of the function passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have a function that passes through the points (6, 7) and (10, 13), then if this function is linear, the slope is:

a = (13 - 7)/(10 - 6) = 6/4 = 3/2

Then the function will be something like:

f(x) = (3/2)*x + b

Knowing that the function passes through (6, 7), this means that:

f(6) = 7

Then:

(3/2)*6 + b = 7

3*3 + b = 7

9 + b = 7

b = 7 - 9 = -2

The function, if linear, is:

f(x) = (3/2)*x  - 2

Now let's read the statements:

A)  If the graph also contains the point (4, 4) then the function must not be linear.

If the point is a solution of the equation, then the function is linear.

If the point is not a solution of the equation, then the function is not linear.

f(4) = 4 = (3/2)*4  - 2

        4 = 3*2 - 2

        4 = 6 - 2 = 4

Then (4, 4) is a solution, so if the graph also contains the point (4, 4) the function can be linear. Then the statement "A" is false.

Now let's do the same analysis for the other statements:

B)  If the graph also contains the point (12, 16) then the function must not be linear.

F(12) = 6 = (3/2)*12 - 2 = 3*6 - 2 = 18 - 2 = 16

           6 = 16

(12, 16) is not a solution, so if the graph contains this point, the function is not a linear function, the statement is true.

C) If the graph also contains the point (1, 2) then the function could be linear.

f(1) = 2 = (3/2)*1 - 2 = 3/2 - 2 = -1/2

The point (1, 2) is not a solution, so if the graph contains this point, then the function can't be linear, so the statement is false.

D) If the graph also contains the point (8, 10) then the function could be linear.

f(8) = 10 = (3/2)*8 - 2

        10 = 3*4 - 2 = 12 - 2

        10 = 10

The point (8, 10) is a solution of the linear equation, so if the graph contains this point, the function could be linear, so the statement is true.


Related Questions

HELP PLS/GEOMETRY
20 POINTS
WHAT IS THE HEIGHT?

Answers

Answer:

8 ft is correct

Step-by-step explanation:

How much would you pay for a boat that costs $35,000 if you buy it on
sale for 15% off (excluding tax)?

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Answer:

$29,750

Step-by-step explanation:

Hey guys, hope your day is going well, can you plz help me with is question thank you, i will give 10 pts.

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theres not picture so like i cant help u with that

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Answer:

that looks good

Step-by-step explanation:

Hi, here it is!

1 pizza ————5$
X pizzas ——— 90$

X= 90x1/5 =18 pizzas

May you give me the answer to this please ?

Answers

Answer:

using pythagoras theorem

H^2=P^2+B^2

here h=MN ,opposite(P) be 15 and adjacent(B) be 16

(MN)2=15^2+16^2

(MN)^2=225+256

MN=[tex]\sqrt{481}[/tex]

MN=21.93

after rounding off MN=21.9

Step-by-step explanation:

What is total surface area of the rectangular prism shown 10m 10m 8m​

Answers

Answer: 800

10 x 10 x 8= 800

Multiplication problem

Answer this question to get marked as brainliest!!!!!!

Answers

That is all correctly answer good job

Amari claims that a rectangle is sometimes a parallelogram but a parallelogram is always a
rectangle. Is she correct? Explain if you agree or disagree with her and why.

Answers

Answer:

The statement is false.

Step-by-step explanation:

A parallelogram is a figure of four sides, such that opposite sides are parallel

A rectangle is a four-sided figure such that all internal angles are 90°

Here, the statement is:

"A rectangle is sometimes a parallelogram but a parallelogram is always a

rectangle."

Here if we found a parallelogram that is not a rectangle, then that is enough to prove that the statement is false.

The counterexample is a rhombus, which is a parallelogram that has two internal angles smaller than 90° and two internal angles larger than 90°, then this parallelogram is not a rectangle, then the statement is false.

The correct statement would be:

"A parallelogram is sometimes a rectangle, but a rectangle is always a parallelogram"

pls help i dont know this

Answers

Answer:1 1/5

Step-by-step explanation:

1/5 x 6/1 = 6/5

6/5 is improper so it would be changed to 1 1/5

hope this helps!

Answer:

[tex]\frac{6}{5}[/tex]

Step-by-step explanation:

We can express 6 as [tex]\frac{6}{1}[/tex] , then

[tex]\frac{1}{5}[/tex] × 6

= [tex]\frac{1}{5}[/tex] × [tex]\frac{6}{1}[/tex]

= [tex]\frac{1(6)}{5(1)}[/tex]

= [tex]\frac{6}{5}[/tex]

If the height of the parallelogram shown is increased by 1 cm and the base is increased by 2 cm, what is the area of the new parallelogram?

A parallelogram with a base of 9 centimeters and a height of 4 centimeters.
28 cm2
39 cm2
55 cm2
60 cm2

My main problem: The base isn't at the top, so therefore I am confused. It should be on top of the shape but it is not. If it was I could figure it out.

Answers

So sorry I messed it up I let you down :(

Answer:

55 cm²

Step-by-step explanation:

In a parallelogram, the top base is equal to the bottom base (and the sides are equal to each other too!)

So the top and bottom base are both 9, and the left and right sides are both 5.

So, to solve, we need to use the equation:

(4 + 1) * (9 + 2) = 5 * 11 = 55 cm²

Help if you can thank you

Answers

Answer:

D $175

Step-by-step explanation:

HELP PLEASE!!! i’ll mark BRAINLEST.

Answers

Answer:

3

Step-by-step explanation:

I need answer Immediately pls!!!!!!

Answers

Given:

Total number of students = 27

Students who play basketball = 7

Student who play baseball = 18

Students who play neither sports = 7

To find:

The probability the student chosen at randomly from the class plays both basketball and base ball.

Solution:

Let the following events,

A : Student plays basketball

B : Student plays baseball

U : Union set or all students.

Then according to given information,

[tex]n(U)=27[/tex]

[tex]n(A)=7[/tex]

[tex]n(B)=18[/tex]

[tex]n(A'\cap B')=7[/tex]

We know that,

[tex]n(A\cup B)=n(U)-n(A'\cap B')[/tex]

[tex]n(A\cup B)=27-7[/tex]

[tex]n(A\cup B)=20[/tex]

Now,

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

[tex]20=7+18-n(A\cap B)[/tex]

[tex]n(A\cap B)=7+18-20[/tex]

[tex]n(A\cap B)=25-20[/tex]

[tex]n(A\cap B)=5[/tex]

It means, the number of students who play both sports is 5.

The probability the student chosen at randomly from the class plays both basketball and base ball is

[tex]\text{Probability}=\dfrac{\text{Number of students who play both sports}}{\text{Total number of students}}[/tex]

[tex]\text{Probability}=\dfrac{5}{27}[/tex]

Therefore, the required probability is [tex]\dfrac{5}{27}[/tex].

Becky found a tennis ball outside a tennis court. She picked up the ball and threw it over the fence into
the court. The path of the tennis ball can be represented by h = -16t2 + 80t, where h represents the
height of the tennis ball in feet and t represents the time in seconds.
31. Find the maximum height of the tennis ball.
32. How long will it take for the tennis ball to hit the ground?

Answers

Answer:

31). Maximum height = 100 feet

32). Time to hit the ground = 5 seconds

Step-by-step explanation:

31). Equation modeling the height 'h' of the ball is,

     h = -16t² + 80t

     For the maximum height of the ball,

     Find the derivative of 'h' with respect to time 't' and equate it to zero.

     [tex]\frac{dh}{dt}=\frac{d}{dt}(-16t^2+80t)[/tex]

          [tex]=-32t+80[/tex]

     [tex]\frac{dh}{dt}=0[/tex]

     [tex]-32t+80=0[/tex]

     [tex]t=\frac{80}{32}[/tex]

     [tex]t=2.5[/tex] seconds

     That means after 2.5 seconds ball will reach the maximum height.

     By substituting [tex]t=2.5[/tex] in the equation,

     [tex]h=-16(2.5)^2+80(2.5)[/tex]

     [tex]h=100[/tex] feet

     Therefore, maximum height achieved by the ball is 100 feet.

32). If the ball follows the parabolic path,

      Time taken by the ball to reach the maximum height = Time taken by  the ball to come back to the ground from the maximum height.

      Time taken by the ball to hit the ground = 2(2.5) = 5 seconds

i need the answer now please

Answers

Answer:

180/147

Step-by-step explanation:

We need to find the additive inverse of the given numbers.

For finding it we may simply out -1 as multiplication in front of the terms .

SOLUTION 1 :-

→ 3/-7 - 11/21

→ -3/7 -11/21

→ 3×-3 - 11 /21

→ -9-11/21

→ -20/21

SOLUTION 2 :-

→ 9/5 ÷ 7/5

→ 9/5 × 5/7

9/7

→ Product of nos . = -20/21 × -9/7

Ans = 180/147

It took Lorinda 45 minutes to drive from her house to the airport. It took her 10 minutes to find a parking space and 25 minutes to walk to the terminal and check in. Then it took her 20 minutes to walk to the gate and board the plane. She boarded the plane at 11:10 A.M. At what time did Lorinda leave her house?

Answers

Answer:

9:30am

Step-by-step explanation:

To find what time simply add all of the minutes together and subtract. All of the steps take 100 minutes to do. 11.10 am is 670 minutes. So 670 - 100 = 570 then divide by 60 to get the time ie 9:30 am

What is the slope of the line that is parallel to the line 8x – 2y = 6?

Answers

if it’s parallel it has the same slope. so we just need to put the equation into y=mx+b form to find out.
8x-2y=6 turns into y=4x-3. so the slope would be 4

Tom has some marbles in two bags. In one bag he has 3 yellow, 2 green and 1 red marble. In the other bag he has 3 yellow, 3 green and 3 red marbles. If Tom takes one marble out of each bag, how probable is it that neither one is yellow? Include a chart of all the data you have.

Answers

Answer:

1 / 3

Step-by-step explanation:

Bag 1 :

Yellow = 3

Green = 2

Red = 1

Total = 3 + 2 +1 = 6

Bag 2 :

Yellow = 3

Green = 3

Red = 3

Total = 3 + 3 + 3 = 9

P(not yellow from bag 1) = (green + red) / total = 3 /6 = 1/2

P(not yellow from bag 2) = (green + red) / total = 6/9 = 2 /3

P(neither is yellow) = 1/2 * 2/3 = 2 / 6 = 1/3

Rearrange 3x - 6y = -2 to the form y=mx + c

Answers

3x - 6y = -2

-6y = -3x - 2, divide through by -1

6y = 3x + 2, divide through by 6

y = 3x/6 + 2/6

y = x/2 + 1/3

Answer:

y = 1/2x - 1/3

Step-by-step explanation:

subtract 3x from each side first to get:

-6y = -3x - 2

divide each side by -6 to get:

y = 3/6x - 2/6

simplify:

y = 1/2x + 1/3

What is the area of this composite figure?
4 cm
7.5 cm
15.5 cm
18 cm
135 cm?
O 207 cm?
249 cm?
O 279 cm?

Answers

Answer:

249cm or the third option

Step-by-step explanation:

I got it right on the test.  Good luck to you!

Use substitution to solve the
following system of equations.
- 2x + 4y = -18AND x = y + 3

Answers

the anwser is (-6,-9)

Hellpppppppppp pleaseee​

Answers

b and c

give me brainliest plsss

The area of a triangle is 169 square meters. The base of the triangle is twice the height. Find the base and height.

I would like the answer and how to get it (show work).

Thanks!

Answers

Answer:

The base of the triangle has a length of 26 meters, and the height of the triangle has a length of 13 meters.

Step-by-step explanation:

Equation to find the height: [tex]\frac{2x*x}{2} = 169[/tex] ⇒ [tex]x^2=169[/tex] ⇒ [tex]x=13[/tex] meters.

Which graph represents the following piecewise defined function?

Answers

Answer:

A on Edge

Step-by-step explanation:

Just took the test and got a 100

The graph that represents the following piecewise defined function is of f(x) = x; x <-2 , -2; -2 < or = to x < or = to 1, x-3; x> or = to 1 is the first graph (Image attached)

What is a piecewise function?

A piecewise function is known to be a function that has been formed from pieces of a lot of functions over a lot of intervals.

An example, we can say a piecewise function f(x) where f(x) = -7 when -7 < x ≤ -4, f(x) = 4 when -4 < x ≤ -1, and f(x) = -5 when -1 <x ≤ 7.

The option that best explain the piecewise defined function is the image attached.

Learn more about piecewise defined function from

https://brainly.com/question/26145479

WILL MARK BRAINLIEST HELP ASAP ASAP EASY POINTS 20 POINTS

Answer choices are
4
5
6
7
8

Answers

Answer:

5

Step-by-step explanation:

which aniaml traveled at a rate of 1.5 meter per minute

Answers

Answer:

A turtle.

Step-by-step explanation:

a turtle they slow ash

What is the volume of this rectangular prism?
2
cm
2
cm
5
cm
5

Answers

Answer:

The volume is 8

Step-by-step explanation:

Volume=abc

V=(2/5)(2/5)(2/5)

V=8

William bought 114 juice boxes for his party. At the end of the party, he had 23 juice boxes left over. How many juice boxes did people drink at William's party? *

Answers

Answer:

Number of juice boxes people drank at Williams party = 91

Step-by-step explanation:

Total juice boxes Williams bought = 114

Juice boxes left over at the party = 23

How many juice boxes did people drink at William's party?

Number of juice boxes people drank at Williams party = Total juice boxes Williams bought - Juice boxes left over at the party

= 114 - 23

= 91

Number of juice boxes people drank at Williams party = 91

A sphere has a diameter of 24 units. What is its volume in cubic units?

Answers

Answer:

Okay done

Step-by-step explanation:

(2x + 3y = 12 (5x - 2y=11​

Answers

Answer:

[tex]x=\frac{23}{7}- \frac{y}{7}[/tex]

Step-by-step explanation:

2x + 3y = 12

5x - 2y = 11

2x + 3y + 5x - 2y = 11 + 12

7x + y = 23

[tex]x=\frac{23}{7}- \frac{y}{7}[/tex]

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