Write the rule for the linear function. Remember a function rule is written using f(x)

Write The Rule For The Linear Function. Remember A Function Rule Is Written Using F(x)

Answers

Answer 1

Answer:

The rule for the linear function will be:

[tex]f(x) = -2x+5[/tex]

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

(1, 3)(2, 1)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)[/tex]

[tex]m=\frac{1-3}{2-1}[/tex]

[tex]m=-2[/tex]

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - 3 = -2 (x-1)[/tex]

[tex]y-3 = -2x+2[/tex]

adding 3 to both sides

[tex]y-3+3 = -2x+2+3[/tex]

[tex]y = -2x+5[/tex]

or

[tex]f(x) = -2x+5[/tex]

Therefore, the rule for the linear function will be:

[tex]f(x) = -2x+5[/tex]


Related Questions

1. Which expressions are equivalent
to 16?
Select each correct expression.

Answers

Answer:

1^16

8^2

16^1

Step-by-step explanation:

These are the answers because they equal up to 16 like the question asks.

1x16= 16  (1^16)

8x8= 16 (8^2)

16x1= 16 (16^1)

The local newspaper has letters to the editor from 10 people. If this number represents 5% of all the newspaper's readers, how many readers does the newspaper have?

The newspaper has ___ readers.

Answers

Don’t know if I’m right but 50%

Answer:

200 readers

Step-by-step explanation:

question is:  5% of what number is 10

is  =  percent

of           100

is = 10

of = unknown (call is 'n')

5% = 5/100

10  =  5  

x        100

now, cross-multiply:  5x = 1000

divide each side by 5

x = 200

helpppppppppppppppppp​

Answers

y+9=-4(x+2)
y+9=-4x-8


Final answer: 4x+y=-17

Simplify each of the expressions below. Which of the expressions have a value between 0 and 10? Select all that apply.

Answers

Answer:

A and B

Step-by-step explanation:

A euqlas 4, B equals 5, c is -3 and d is -11

What is the general form of the equation 2x+3y=9

Answers

Answer:
y=-2x/3+3

Explanation:
2x+3y=9
-2x -2x

3y=-2x+9
3y/3= -2x/3+9/3
y=-2x/3+3

Hope this helps!!

sean has to face a big problem but he becomes stronger as a result which saying best summarizes the change in Sean?
A.A switch in tie saves nine
B.be careful what you wish for
C.pride comes before a fall
D.every cloud has a silver lining
Please help me I WILL give brainless <33

Answers

Answer: D. every cloud has a silver lining

The cloud represents a dark, scary, or sad moment. This is in contrast to the sun which metaphorically represents energy and happiness. The cloud sometimes covers up the sun to cover up those happy moments so to speak.

Despite the cloud being present, there's a silver lining to the cloud which represents some positive aspect a person didn't expect to happen. In this case, the problem allows Sean to get stronger. So this is an opportunity for his growth.

PLEASE HELP I NEED IT I WILL MARK BRAINLIEST

Answers

Answer:

y = (1/12)x^2

Step-by-step explanation:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus.  Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

Have  a good day!

-Millie

Pls help and show workings

Answers

The equation for line r is
y=-1/3x+5
Perpendicular slope would be 3 and passes through (3,-6)
-6=3(3)+b
-6=9+b
-9. -9
-15=b
y=3x-15
Plug in the x value of the point to see if it’s true
y=3(3)-15
y=9-15
y=-6
So the equation is y=3x-15 so the answers is c
3x-y=15
-3x. -3x
-y=-3x+15
Divide everything by -1
y=3x-15

i have no idea what the answer, please help me

Answers

Answer:

43°

Step-by-step explanation:

-the interior angle of a triangle always adds up to 180°

- angles that form a straight line always adds up to 180°

- the angle at 75° has the angle of 105° to add up to 180°

- the triangle needs a full degree of 180, but only affs up to 137° (105° + 32°) so you have to subtract the 137° from the total amount you need(180°) which gives you the answer of 43°

Answer:

Step-by-step explanation:

it cant be 73° then it would look about the same size as 75°

and it cant be 15° cause it would look smaller than 32°.

so in my Opinion it looks like it would be 43°.

sorry if its wrong

NEED HELP ASAP!!!
Carlos and his family are driving to California for vacation. The trip is 1,146 miles and they drive at an average speed of 56 mph. Which equation would give the number of miles remaining until they reach their destination, M, in terms of h, the number of hours they have driven? А. M= 1,146 + 56h
B. M= 56 - 1,146h
C. M= 56 + 1,146h
D. M= 1,146 - 56h​

Answers

Answer:

D. M = 1,146 - 56h

Step-by-step explanation:

I beleive that this answer is the most reasonable because we arent adding miles to the trip we are taking away. Also subtracting from 56 would result in a negative answer and that really doen't make sense because they still have more miles to travel before they reach their destination.

When building a car, you can choose from 3 colors, 3 interiors, 3 sound systems, 3 kinds of tires, and 3 seat coverings. How many combinations are possible if you are making two distinct cars?

Answers

There are 455 combinations possible

Find the slope of the line graphed below.

Answers

Answer:

Slope: -3/5

Step-by-step explanation:

Answer:

-3/5 would be the slope

Explanation

The increase in pressure (P) is a linear function of the depth (d) to which a scuba diver descends. This is the function: P(d)=0.445d + 14.7.
1.) What does the initial value represent?
2.) What does the rate of change represent?​

Answers

Answer:

Initial value = 14.7

Rate of change = 0.445

Step-by-step explanation:

Given the linear function :

P(d) = 0.445d + 14.7

The linear equation above takes the general. Form of a slope - intercept equation :

y = mx + c

Where ; m = slope or gradient = rate of change in y per unit change in x

c = intercept , which is the intial value of y when x = 0

Thus using the above information ;

Initial value = intercept value = 14.7

The rate of change is the slope value = 0.445

anyone know this? cuz i'm confused

Answers

Answer:

y =37

x=12

z=131

Step-by-step explanation:

The angles of the left triangle are 59, 84 , y

They sum to 180

59+ 84+ y = 180

143 +y = 180

y = 180-143

y =37

The angles of the right triangle are 104,64,x

They sum to 180

104+64+x

168+x=180

x = 180-168

x=12

The angles of the middle triangle are x,y,z

They sum to 180

x+y+z

12+37+z = 180

49+z =180

z = 180-z

z=131

You know that the total measure of the angles in a triangle is 180 degrees.

You can use this to find angles x and y.

The angles of one of the triangles are x, 104, and 64. This means x would be 12.

104+64+x = 180

x = 180-104-64

x = 12

Use this same method to find y. The angles of the triangle y is in are 84, 59, and y. This means y is 37.

84+59+y = 180

y = 180-84-59

y = 37

Now you have x and y. The angles x, y, and z share one triangle. You can use this to find z.

x+y+z = 180

You know that x is 12 and y is 37.

12+37+z = 180

z = 180-12-37

z = 131

So...

x = 12

y = 37

z = 131

Please solve it I will give you 30 points

Answers

Answer:

1. (2x^2+x-1)

Step-by-step explanation:

expanding (2x^2-1)^2. multiplying (x-2) (1-2x)

= 4x^2-4x+1. = x-2x^2-2+4x

= -2x^2+5x-2

(4x^2-4x+1-2x^2+5x-2)

=2x^2+x-1

Answer:

1.) (2x - 1)(x + 1)

2.) a = 6 ; b = -1

4.a.) x = all rational numbers excluding (-2÷3)

4.b.) x = -1

4.c.) Yes. x = 1÷2

Step-by-step explanation:

E(x) = (2x - 1)² + (x - 2)(1 - 2x) F(x) = ax²-bx-2

F(1) = 5 ; F(-2) = 20

a-b=7 ; 4a+2b=22

3.Answer) Q(x) = 6x² + x - 2

= 6x² + 4x - 3x - 2

= (3x + 2)×(2x - 1)

Hence verified!

P(x) = E(x) ÷ Q(x)

= (x + 1)÷(3x + 2)

Here, x belongs to,

[tex]( - \infty \: to \: - 2 \div 3) union( - 2 \div 3 \: to \: \infty )[/tex]

Means, except x = -2÷3 , all real numbers are valid excluding complex numbers.

P(x) = (x + 1)÷(3x +2) = 0

= > x = -1

Could someone pls help me if you know it thank you!:)

Answers

Answer:

30

Step-by-step explanation:

The full pie chart will equal 100%

So we can add all the percentages together and then subtract that percentage from 100 and whatever's left is the parentage that they attend school.

12+3+5+10+5+35

70

100-70

30

They spend 30% attending school

Don't be afraid to reach out for further assistance. Hope this helps!

Carla is going on a boat tour. The boat will travel a total distance of 40 kilometers during the 10 hour tour. If the boat travels at a constant speed during the​ tour, what distance in kilometers should the boat travel in 7 ​hours? Choose the correct answer below.

Answers

Answer:

Distance cover in 7 hour = 28 kilometer

Step-by-step explanation:

Given:

Distance = 40 kilometers

Time taken =  10 hour

Find:

Distance cover in 7 hour

Computation:

Distance cover in 7 hour = (40/10)7

Distance cover in 7 hour = (4)7

Distance cover in 7 hour = 28 kilometer

Andre shot three arrows and they landed at (-5,4),(-8,7),and(1,6). What is his Total score? Explain your reasoning

Answers

I've attached the graph showing the colored regions of the archery target.

The scores for the colored regions are;

Yellow: 10 points

Red: 8 points

Blue: 6 points

Green: 4 points

White: 2 points

Answer:

16

Step-by-step explanation:

From the graph, At coordinate of (-5,4), the colored region is blue which means a score of 6 points.

From the graph, At coordinates of (-8,7), the colored region is red which means a score of 8 points

From the graph, At coordinates of (1,6), the colored region is white which means a score of 2 points

Thus, total score = 6 + 8 + 2 = 16

Step-by-step explanation:

Here are the scores for landing an arrow in the colored regions of the archery target.  

Yellow: 10 points

Red: 8 points

Blue: 6 points

Green: 4 points

White: 2 points

Andre shot three arrows and they landed at (-5,4),(-8,7),and(1,6). What is his Total score? Explain your reasoning

A. 14

B.16

C. 5

D 12

Answer: the answer is A. 14 i took the test and i got it wrong because i put B. 16 because of the answers of this question but the correct answer is A. 14

please correct me if i am wrong

Which is the constant of proportionality for the relationship shown in the graph?

Answers

Answer:

COP: 2X

Step-by-step explanation:

K= Y/X

K= 4/2

K= 8/4

K= 12/6

K=16/8

29.8 ft
what’s the area

Answers

Answer:

The area is 888.04 square ft

Solve for
x
2
(
x

7
)
=
x

2

Answers

first you distribute the 2 to the x and -7 so that would equal 2x and -14. then you subtract x by both sides. then you would have x-14=-2 you want to get rid of the -14 on the left side so you would need to add it to both sides and you would get x=12

For each offspring genotype in the Punnett square you just completed, determine the phenotype. In other words, what is the predicted fur color and eye color of the offspring? Using your Punnett square from the last step, fill in the predicted fraction for each phenotype in the data table below. (other ppl got it wrong, so here is the answer)

answer:
(predicted fractions)
16/16
0/16
0/16
0/16

(predicted percentage)
100%
0%
0%
0%

Answers

Answer:

(predicted fractions)

16/16

0/16

0/16

0/16

(predicted percentage)

100%

0%

0%

0%

How many solutions does the system have?
y=3x-1
y=-2x+4

Answers

Answer:

This system has one answer.

Step-by-step explanation:

This system only has one answer which are: x=1  y=2

Hope this helped! :)

Answer:

(y,x) =(14,5)

Step-by-step explanation:

im in 10th grade

Given that f(x) = x2 + 4x – 45 and g(x) = x + 9, find f(x) = g(x) and
express the result in standard form.

Answers

2x + 4x - 45 = x + 9 --> (simplified) 6x - 45 = x + 9

you need to get x on one side. im gonna put it to the left since its easier (which side you move it to doesn't matter that much).

so you need to cancel out the x on the right (x + 9). we do this by subtracting x (or 1x) on both sides. our equation now looks like 5x - 45 = 9.

now we need to move our non-variable to the right. we do this by adding 45 on both sides. our equation now looks like 5x = 54.

we need to divide 54 by 5 so that x is alone. 54/5 = 10.8. x = 10.8

hiiiiiii help me thanks!

Answers

Would the answer be one isosceles triangle sorry if you get it wrong I’m kinda slow 10-9=1
You have the correct answer I believe

What is the solution to the system of equations? Two-thirds x minus one-third y = negative 2 Negative 2 x + y = negative 6 There is no solution. There are infinitely many solutions. There is only one solution, (2, –2). There is only one solution, (–2, –10).

Answers

Answer:

there no solution

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

One number is 1 more than 7 times the other number. If their sum is 73 more than
twice the smaller number. Find the numbers.​

Answers

Answer:

[tex]\boxed{\boxed{\pink{\bf The \ two \ numbers \ are \ 12 \& \ 85 . }}}[/tex]

Step-by-step explanation:

Given that , One number is 1 more than 7 times the other number. If their sum is 73 more than

twice the smaller number. And we need to find the numbers. So let us take the

First Number be x .Second number be 7x+1 .

[tex]\underline{\red{\boldsymbol{ According \ to \ the \ Question :- }}}[/tex]

[tex]\bf\implies 2( Small \ no.) + 73 = Bigger \ no. + Smaller \ no.\\\\\bf\implies 2x + 73 = x + 7x + 1\\\\\bf\implies 2x + 73 = 8x + 1 \\\\\bf\implies 8x - 2x = 73-1 \\\\\bf\implies 6x = 72 \\\\\bf\implies x =\dfrac{72}{6} \\\\\bf\implies \boxed{\red{\bf x = 12 }}[/tex]

Hence the smaller number is 12 and the bigger number will be :-

[tex]\bf \implies Number_{bigger} = 7x + 1 \\\\\bf\implies Number_{bigger} =7(12)+1\\\\\bf\implies Number_{bigger} = 84 + 1 \\\\\bf\implies \boxed{\red{\bf Number_{bigger}=85 }}[/tex]

Hence the bigger number is 85 and the smaller number is 12.

Step-by-step explanation:

let us say the number: x

7x+1=y

x+y=73+2x

y-73=2x-x

y-73=x or

x=y-73

then, 7x+1=y

x=y-73

then after,we'll substitute

7x+1=y

7(y-73)+1=y

7y-511+1=y

7y-510=y

7y-y=510

6y=510

y=510/6

y=85

x=y-73

x=85-73

x=12

Therefore y=85 & x=12

A dump truck bar 1/3 of a ton of rocks on the 1st beat trip when half of a ton on the 2nd trip and forfeits of a tone on the 3rd trip what was the total way of the rock.

Answers

Answer: 1/30

Step-by-step explanation:

Here's the correct question:

A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?

To calculate the the total weight of the rock left at the construction site goes thus:

= 1/3 + 1/2 - 4/5

The lowest common multiple of 3,2 and 5 is 30. Therefore, we'll make the fractions have a common denominator.

= 1/3 + 1/2 - 4/5

= 10/30 + 15/30 - 24/30.

= 1/30

HELP I WILL MARK U BRAINLIEST!!

Answers

Y-7 is your answer. You welcome

Answer:

Y-7 is the answerr

Step-by-step explanation:

Because there's is a minus sign behind of the y

You just found out you have to have a cavity filled! UGH! The dentist
office informs you that a filling usually costs $150, but that sometimes it
can vary but that it will only vary AT MOST $20. What is the range of cost
you can expect to pay for your filling?

Answers

Answer:

It could be anywhere from $130-$170

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