Question

Help me please! All questions answer. Step by step explain it please....!!!

Answer 1

Answer:

Part 1) Option A. The graph of g(x) has the lesser y-intercept

Part 2) Option B. (2,4)

Part 3) Option B. 62.5 miles per hour

Part 4) Option A. The functions will intersect at x=-2 and at x=1

Step-by-step explanation:

Part 1)

Let

x ----->the number of years

g(x) ----> the expected value in dollars of televisions

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

In the function g(x)

The slope is

$m=-\ 90\ per\ year$ ---> is negative because is a decreasing function

The y-intercept is

$b=\ 360$

substitute

$g(x)=-90x+360$

Find the x-intercept (value of x when the value of the function is equal to zero)

For g(x)=0

$0=-90x+360$

$x=4$

The x-intercept is the point (4,0)

The y-intercept is the point (0,360)

Function f(x)

we have

$f(x)=100(-x+4)$

$f(x)=-100x+400$

Find the x-intercept (value of x when the value of the function is equal to zero)

For f(x)=0

$0=-100x+400$

$x=4$

The x-intercept is the point (4,0)

The y-intercept is the point (0,400) (value of f(x) when the value of x is zero)

Compare the intercepts both functions

The y-intercept is the same in both functions

The y-intercept is greater in the function f(x)

therefore

The graph of g(x) has the lesser y-intercept

Part 2) we have the equation of the line

$4x-3y=-4$

Remember that

If a ordered pair is on the given line, then the ordered pair must satisfy the given line

Verify each case

a) (4,4)

Substitute the value of x and the value of y in the equation and compare the result

$4(4)-3(4)=-4$

$4=-4$ ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

b) (2,4)

Substitute the value of x and the value of y in the equation and compare the result

$4(2)-3(4)=-4$

$-4=-4$ ---> is true

so

the ordered pair satisfy the equation

therefore

the ordered pair is on the line

c) (2,-4)

Substitute the value of x and the value of y in the equation and compare the result

$4(2)-3(-4)=-4$

$20=-4$ ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

d) (4,-4)

Substitute the value of x and the value of y in the equation and compare the result

$4(4)-3(-4)=-4$

$28=-4$ ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

Part 3) we know that

The formula to calculate the average rate of change using the graph is equal to

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

$f(a)=f(2)=75\ mi$  

$f(b)=f(4)=200\ mi$

$a=2\ h$

$b=4\ h$

Substitute

$\frac{200-75}{4-2}=125/2=62.5 mi/h$

Part 4) we know that

The solution of the equation

f(x)=g(x)

are the x-coordinates of the intersection points both graphs

In this problem

If the solutions are x=-2 and x=1

then

The functions will intersect at x=-2 and at x=1