Question

I need some help with two of my math problems.

The side length of a cube can be represented by the expression 2x^5. If the side length is doubled, write an expression to represent the new volume of the cube.


The area of a triangle can be represented by the expression 14x^5 + 63x^2. If the base is 7x^2, write an expression to represent its height.

Answer 1

My mind broke so like..... @snowflake0531 @carmelle

Answer 2

The side length of a cube can be represented by the expression 2x^5. If the side length is doubled, write an expression to represent the new volume of the cube.

the original side length is 2x^5. doubling it gives us 2 * 2x^5 or simply 4x^5. from there, the volume is simply the new side length cubed, or (4x^5)^3. simplify.

Answer 3

The area of a triangle can be represented by the expression 14x^5 + 63x^2. If the base is 7x^2, write an expression to represent its height.

area of a triangle = (1/2)bh

so 14x^5 + 63x^2 = (1/2)(7x^2)*h

solve for h. first multiply both sides by 2 to eliminate the fraction, then factor out 7x^2 from the left side, then divide both sides by 7x^2. the remaining expression on the right is your height.

Answer 4

yup good

Answer 5

starting with: 14x^5 + 63x^2

if we factor out 7, we divide whole expression by 7 to get 2x^5 + 9x^5, then we write 7 outside the parentheses

14x^5 + 63x^2 = 7(2x^5 + 9x^2)

(think of this like the opposite of applying the distributive property)

factoring out x^2 using the same logic

14x^5 + 63x^2 = 7(2x^5 + 9x^2) = 7x^2(2x^3 + 9)

Answer 6

from there:

area = 7x^2(2x^3 + 9) = (1/2)(7x^2)*h

should be straightforward to solve for h from here, cross out the 7x^2 from both sides, multiply both sides by 2

Answer 7

so it would be h=4x^3+18?

Answer 8

yup good