TheXSquaredFactor

This might be a nice visual aide:
 

In order to figure out the surface area of this rectangular prism, we just need to find the area of the faces. That's all! All you have to do is double the visible faces shown in the above diagram.

\(A_1=4*4=16ft^2\\ A_2=8*4=32ft^2\\ A_3=8*4=32ft^2\\ SA=2(A_1+A_2+A_3)\\ SA=2(16ft^2+32ft^2+32ft^2)\\ SA=2*80ft^2\\ SA=160ft^2\)

Try and see if you can do the next one!

Be careful! I know that this is a lot of information to take in at once.

\(x_1=2\text{ and }x_2=?\\ y_1=17\text{ and }y_2=?\\ A=P\\ C=M\\ Q=B=(x_2,y_2)\\ \)

We know that \(\frac{x_1+x_2}{2}=-4\text{ and }\frac{y_1+y_2}{2}=5\). We just have to solve for the missing variables. That's all.

If you know the area of the base of the triangular prism and you know the height of the prism, then the only step left to do is to multiply these two values together.

\(36\text{ft}^2*2.5\text{ft}=90\text{ft}^3\)

Hello, Mr.Owl. I hope you are doing well.

Generally, when we face problems that involve the midpoint, we are generally tasked with identifying the midpoint. This is not the case here. I have provided a nice visual of the midpoint formula in action. 

Coordinate A with coordinates \((x_1,y_1)\) on the above diagram has \((2,17)\). Therefore, \(x_1=2\text{ and }y_1=17\). The midpoint, coordinate C, represented as \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\) on the visual, has coordinates \((-4,5)\). This means that \(\frac{x_1+x_2}{2}=-4\text{ and }\frac{y_1+y_2}{2}=5\). Does this give you an idea on how to proceed?

That's ok! We got your back in this community.

Rick, it appears as if tertre's slight typo has caused an askew answer. 

The original function was defined as \(Q(t)=9t^3+8t^2-4t-9\). Unfortunately, terte evaluated the function as \(Q(t)=9t^{\textcolor{red}{2}}+8t^2-4t-9\). What a tragic error!

Continue evaluating the function at \(Q(-1)\text{ and }Q(-b)\), and you will be done quite soon. 

**OOPS, I know you have told me to call you Rick in future posts.**

Order of operations is a strict set of rules that dictate how to evaluate any expression. I have laid the order of operations out for you:
 

1. Simplify within grouping symbols such as parentheses or brackets from left to right.

2. Simplify exponents from left to right.

3. Perform multiplication or division, whichever operation comes first from left to right.

4. Perform addition or subtraction, whichever operation comes first from left to right.

If something is higher on the list, then it has greater priority. Let's apply this knowledge to this particular problem:

I encourage you to utilize the reference problems that you have been given already to tackle this problem. Below is the link to those reference problems:

Substitute in the given value for x and y into the given expression and evaluate.

\(-3x+6y; x=-3, y=6\\ -3*-3+6*6\\ 9+36\\ 45\)

This is quite simple to simplify.

\(-4 < x-2 < \hspace{1mm} 3 \\ +2 \hspace{8mm} + 2 \hspace{1mm} +2 \\ \overline{\quad\quad\quad\quad\quad\quad\quad}\\ -2 < x < \hspace{8mm} 5\)

When this inequality is represented via a number line graph, it looks like this: