The amount y of your friend's allowance if the amount she receives is $77 more than the amount x you receive.

what is the rate of change for the linear relationship modeled in the table? x y −1 10 1 9 3 8 5 7 -1/2 0 1/2 2

Vesnalui [34]

Answer:

Rate of change for the linear relationship modeled is $\dfrac{-1}{2}$

Step-by-step explanation:

As the there is a linear relationship in the points, so all these points will be on a single straight line. Hence the slope will be same throughout all the points.

We know that, the slope of the line joining (x₁, y₁) and (x₂, y₂) is,

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Putting the points as (-1, 10) and (1, 9), we get

$m=\dfrac{9-10}{1-(-1)}$

$=\dfrac{9-10}{1+1}$

$=\dfrac{-1}{2}$

Rate of change is the slope of the line joining all these points.

7 0

3 years ago

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Ella purchased a game that was on sale for 12% off. The sales tax in her county is 6%. Let y represent the original price of the

sdas [7]

Let y represent the original price of the game. Write an expression that can be used to determine the final cost of the game.

(1 - 0.12) y (1 + 0.06)

4 0

3 years ago

Find an expression for the function f(x) whose graph is a line passing through the points (8,-5) and (-9,2). f(x)=

kolbaska11 [484]

Answer: f(x) = - 7x/17 - 29/17

Step-by-step explanation:

The expression for the function f(x) would be represented in the slope-intercept form, y = mx + c

Where

c represents the y intercept.

m represents the slope of the line.

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent

change in the value of y = y2 - y1

Change in value of x = x2 -x1

The line passes through (8, - 5) and (- 9, 2),

y2 = 2

y1 = - 5

x2 = - 9

x1 = 8

Slope,m = ( 2 - - 5)/(- 9 - 8) = 7/- 17 =

- 7/17

To determine the intercept, we would substitute x = 8, y = - 5 and m = - 7/17 into

y = mx + c. It becomes

- 5 = - 7/17 × 8 + c

- 5 = - 56/17 + c

c = - 5 + 56/17

c = - 29/17

The equation becomes

f(x) = - 7x/17 - 29/17

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3 years ago

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Wane went on a 4-kilometer run he took a break at four third kilometers he took a drink of water at ten third kilometers show Wa

otez555 [7]

Answer:

Given,

The total distance covered = 4 km,

Since, initially he would be in rest,

So, his starting point would be 0.

Now, his first break = $\frac{4}{3}$ km,

Second break = $\frac{10}{3}$ km,

Also, we can write,

$4=\frac{4\times 3}{3}=\frac{12}{3}$

Drawing number line:

Step 1: Draw a line.

Step 2: Make 12 marks in same distance.

Step 3: Starts from 0, then 1/3, 2/3, 3/3 and so on.

Thus, we can show Wayne's bike on a number line as below.

6 0

3 years ago

The m6 = (11x + 8)° and m7 = (12x – 4)° What is the measure of 4? m4 = 40° m4 = 48° m4 = 132° m4 = 140°

bezimeni [28]

M< 6 = m< 7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m< 6 = 11x + 8
m< 6 = 11(12) + 8
m< 6 = 132 + 8
m< 6 = 140

m<4 = 180 - m<6
m<4 = 180 - 140
m<4 = 40

answer

m<4 = 40

7 0

3 years ago

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The amount y of your​ friend's allowance if the amount she receives is ​$77 more than the amount x you receive.

The amount y of your friend's allowance if the amount she receives is $77 more than the amount x you receive.