Alright, so we are given that we have a rug that has a side of 7x+4 feet. With this information, we are able to determine the area of the square rug. Considering that it is a square rug, all the sides are equal to each other because a square has four equal sides and angles.

To solve this, you can do it in two ways.

One, write it as (7x+4)2. That 2 is supposed to represent squared.

If you know the rule, this is a perfect square trinomial.

The formula is a squared plus 2ab plus b squared. 7 and 4 are your a and b values. 7x squared is 49x squared and 4 squared is 16.

2ab, multiply 2 times 7x times 4. That is 56x.

Therefore, the area is 49xsquared plus 56x+16.

Another way is to write it like this (7x+4) (7x+4).

Since it is an exponent, we are multiplying the same thing two times. Apply the Distributive Property.

E.G. 2(x+5)= 2x+10.

With this, you are distributing two numbers into another two numbers. 7x times 7x is 49x squared and 7x times 4 is 28x. Then, go to 4. 4 times 7x is also 28 x and 4 times 4 is 16. Now, combine the like terms. 49x squared plus 28x plus 28x or 56x plus 16.

This represents your area.

I hope this helps, and I hope you have a good day!

5 0

3 years ago

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the poin

yarga [219]

$~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill$

$\begin{cases} h=3\\ k=-7 \end{cases}\implies y=a(x-3)^2-7\qquad \textit{we also know that} \begin{cases} x=1\\ y=-10 \end{cases} \\\\\\ -10=a(1-3)^2-7\implies -3=a(-2)^2\implies -3=4a\implies -\cfrac{3}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{3}{4}(x-3)^2-7~\hfill$

5 0

1 year ago