At Bobbi's Baby Bargains, they make and sell baby blocks in sets of 24 blocks. Bobbi has asked you to design a box to package these blocks that will require the least amount of cardboard. What is your recommendation? Provide a justification as to why your design is the most efficient..

In Exercise verify thattrigonometric equation is an identity.

$$\tan ^2 \alpha \sin ^2 \alpha=\tan ^2 \alpha+\cos ^2 \alpha-1$$

Use the quadratic formula to solve the equation.

x^2-4x+3=0

In this exercise, the graph of y=A sin (2x+h)+k is the graph of y=A sin (2x)+k shifted to the left by h units.

Factor completely. If the polynomial is prime, say so.

$$2 h ^ { 2 } + 7 h k - 15 k ^ { 2 }$$

The first four terms of a sequence are given. Determine whether they can be the terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic or geometric, find the fifth term.
5,5.5,6,6.5, .........

Given the discriminant of a quadratic equation, determine the number of real solutions. 0

Let $h(x)=4 x^2-5 x+1, k(x)=x$, and $m(x)=7$ for all $x$. Compute the following.

$k[h(x)]$

a. Find a, h, and k:

$$y = 6 ( x - 5 ) ^ { 2 } - 9$$

b. Find a, h, and k:

$$x = - 3 ( y + 2 ) ^ { 2 } + 1$$

Graph $y=f(x)$ and its tangent line at $x=c$.

$$c=4, f(x)= \begin{cases}-\sqrt{3-x}, & x<3 \\ \sqrt{x-3}, & x \geq 3\end{cases}$$

In this exercise, you will need to verify that the equation is an identity.

$$\frac{2 \cos 2 \alpha}{\sin 2 \alpha}=\cot \alpha-\tan \alpha$$

In this exercise, you will need to find the value of x so that $\overline{G J} \| \overline{F K}$.

$$G H=x+3.5, H J=x-8.5, F H=21, H K=7$$

Simplify each expression.

If $\csc \alpha=\sqrt{3}$ and $2 \pi<\alpha<5 \pi / 2$, compute $\cos \alpha$ and $sin\alpha$

Complete parts for the piecewise-defined function.

At what points $c$ does only the right-hand limit exist?

$$f(x)= \begin{cases}\cos x, & -\pi \leq x<0 \\ \sec x, & 0 \leq x \leq \pi\end{cases}$$