Question

Please help

numbers 38, 39, 45, 47, 48​

Answer 1

Part 38)
`y-3=(3)/(4)(x-1)`

Part 39)
`y+1=(2)/(3)(x-4)`

Part 45) The system has infinity solutions

Part 47) Is a exponential growth, the percent rate of change is 20%

Part 48) Is a exponential decay, the percent rate of change is -60%

Explanation:

Part 38) Write an equation in point slope form of the line that pass through the given points

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

(1,3) and (-3,0)

substitute

`m=(0-3)/(-3-1)`

`m=(-3)/(-4)`

`m=(3)/(4)`

step 2

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=(3)/(4)`

`point\ (1,3)`

substitute

`y-3=(3)/(4)(x-1)`

Part 39) Write an equation in point slope form of the line that pass through the given points

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

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

substitute

`m=(-1+5)/(4+2)`

`m=(4)/(6)`

`m=(2)/(3)`

step 2

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=(2)/(3)`

`point\ (4,-1)`

substitute

`y+1=(2)/(3)(x-4)`

Part 45) Solve the system of linear equations using any method

`-5x-4y=-15` ----> equation A

`10x+8y=30` ----> equation B

Multiply the equation A by -2 both sides

`-2(-5x-4y)=-2(-15)`

`10x+8y=30` -----> equation C

Compare equation B and equation C

Line B and Line C are the same line

so

The system has infinity solutions

Is a consistent dependent system

Part 47) Determine whether the function represent exponential growth or exponential decay. Identify the percent rate of change

we have

`y=(1)/(4)(1.2)^t`

This is a exponential function of the form

`y=a(b)^x`

where

a is the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

If b < 1 ---> the function is a exponential decay

If b > 1 ---> the function is a exponential growth

In this problem we have

`a=(1)/(4)`

`b=1.2` ----> is a exponential growth

`r=b-1=1.2-1=0.2`

convert to percentage

`r=0.2*100=20\%`

Part 48) Determine whether the function represent exponential growth or exponential decay. Identify the percent rate of change

we have

`f(t)=70((2)/(5))^t`

This is a exponential function of the form

`y=a(b)^x`

where

a is the initial value or y-intercept

b is the base of the exponential function

r is the percent rate of change

b=(1+r)

If b < 1 ---> the function is a exponential decay

If b > 1 ---> the function is a exponential growth

In this problem we have

`a=70`

`b=(2)/(5)=0.4` ----> is a exponential decay

`r=b-1=0.4-1=-0.60` --->is negative because is a decreasing function

convert to percentage

`r=-0.60*100=-60\%`