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numbers 38, 39, 45, 47, 48​

Please help numbers 38, 39, 45, 47, 48​-example-1

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Answer:

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\%

User Ahmad Hammoud
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