Question

Math help pls, thank u

Answer 1

Answer:

11x+1

Step-by-step explanation:

First, lets ignore all the functions it is giving us. Ignore everything not important at this second; sometimes it can cloud some people's ability to process problems.

We need to look. It asks us for area. Area is length times width. We have the area, we have the width, but we need the length. So we need to divide!

$\frac{66x^{2} + 17x + 1}{6x+1}$ Is going to be our equation! Now, we just need to simplify!

First, lets factor the top function!

66 times 1 is 66, so we need two numbers that add to 17 and multiply to 66.

Off the top of my head, 6 and 11 seem like a perfect match! They add to 17, and multiply to 66!

So now lets sub these in for 17x!

$66x^{2} + 11x + 6x + 1$

Now lets factor!

$(66x^{2} + 11x) ==> 11x(6x + 1)\\(6x + 1) ==> 1(6x+1)\\(11x + 1)(6x+1)$

Now lets get back to the original equation!

$\frac{(11x+1)(6x+1)}{6x+1}$

We can simply cross out the (6x+1), since there is one on each side, leaving us with 11x+1!

So the length of the top surface, h(x) = 11x+1!

Hope this helps!

Answer 2

Answer:

11x + 1

Step-by-step explanation:

f(x) = 66x² + 17x + 1

Factoring:

f(x) = (6x + 1) (11x + 1)

Area of a rectangle is width times length.  So if g(x) = 6x + 1, then h(x) = 11x + 1.