Kathy is 33 years old. She is 7 years younger than 5 times her daughter's age. The equation, 5x-7= 33, where x equals her daughter's age, can be used to find the age of Kathy's daughter. How
old is Kathy's daughter?

Kathy's daughter is 8 years old

Step-by-step explanation:

What we know:

Kathy is 33 years old.

That is 7 years younger than 5 times her daughter's age.

With that, the equation 5x - 7 = 33 can be used to find x.

Step 1:

Move "- 7" to the right side of the equation, and find the opposite of it.

5x = 33 + 7

Step 2:

Add "33" and "+7" to get "40."

5x = 40

Step 3:

Divide both side by "5."

5x/5 = 40/5

x = 8

Thus, Kathy's daughter is 8 years old.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)