Help on some tech math problems

1) you first need to find a couple equations so you can solve the system:

L = 6 + 2W

Perimeter = 48 = 2W + 2L

Then you can solve the system:

L = 6 + 48 - 2L

3L = 54

L = 18

Then you can plug L back into the second equation and find W:

48 = 2W + 2(18)

2W = 12

W = 6

So the solution is:

L = 18

W = 6

2) This looks like a physics formula for kinetic energy, but since you have the numbers it's just an algebra problem.

K = 1/2 *mv^2

460 = 0.5*m*(5.0)^2

Simplify:

460 =0.5*m*25

460 = 12.5*m

Solve:

m = 36.8

Are there any specific issues you're having with the concepts?
The other commenter did a really nice job explaining problem 1. I just want to add in another strategy.

Draw a picture of a generic rectangle.

Label two opposite sides x. This will be the width.

Label the remaining two opposite sides 6 + 2x. This will be the length.

Combine like terms by adding up all four sides of the rectangle. You should get 6x + 12. This is an expression for the perimeter.

Set the perimeter equal to 48. So we have 6x + 12 = 48.

Solve for x. We get x = 6.

Substitute the 6 back into the sides of the rectangle from your drawing and you’ll get the length and the width.

Edit: fixed an error

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