Hi I’m so I need a lot of assistance with my math homework as soon as possible

Question

1.) The value of y varies directly with x, and y = 343 when x = 49. Find y when x = 8.

A.) 56

B.) 1/7

C.) 7

D.) 49

 

 

2.) Write the inverse variation function given that y varies inversely with x, and y = 5 when x = 5.

A.) y = x

B.) y = 5x

C.) 

D.)

   

   

 

3.) Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.

A.) y = 0.3x

B.) x = 0.3y

C.) y = 3x

D.) y = 0.25x

hi please explain and solve and help thanks

Answer 1

1. Initial statement: y ∝ x

To convert to an equation, multiply by 'k', the constant of variation

y=kx

We find k next given: y=343 and x= 49

k= y/x

k= 343/49= 7

The equation is: y=7x

When x=8, what is y?

y=7*8= 56

So the answer is A

2.Initial statement: y ∝ 1/x

To convert to an equation, multiply by 'k', the constant of variation

y=1/x*k

y=k/x

Given y=5 and x=5

5=k/5

k=25

The inverse variation function is: y=25/x

So the answer is D

3.Initial statement: y ∝ x

To convert to an equation, multiply by 'k', the constant of variation

y=kx

Given y=1.5 and x=5

1.5=k*5

k=0.3

y=0.3x

So the answer is A

Answer 2

1) A, 56 343= 49k k= 343/49 = 8 y=8x when x = 7 y = 8(7) = 56

2) D, y=25/x y=k/x 5=k/5 k=25

3) A y=0.3x y=kx 1.5=5k k=1.5/5 = 3/10 = 0.3