Find the vertex, the $y$-intercept, and symmetric point, and use these to sketch the graph.
$y=8 x^2+40 x+37$

Find the slant height of the right cone of radius 5.6 cm and height 9.2 cm.

$\odot Q$ and $\odot R$ both have a radius of $3 \mathrm{cm} .$ Therefore the circles are ____________. (concentric or congruent)

Why was Alexander the Great buried in Egypt?

Define budgetary slack. Why might managers try to build slack into their budgets?

The horny scales that cover the skin of reptiles prevent them from

a. using their skin as an organ of gas exchange.

b. sustaining high levels of metabolic activity.

c. laying their eggs in water.

d. flying.

e. crawling into small spaces.

Circles T and S intersect at points A and B. What is the relationship between

$$\overline{AB}\ and\ {\overleftrightarrow{TS}}?$$

Explain.

Phytochrome responds faster to red light than to far-red light. If the seeds had been placed in white light instead of the dark after their red and far-red light treatments, would the results have been different? Explain.

When an alternating current of frequency f and peak current

$$I_0$$

passes through a resistance R, then the power delivered to the resistance at time t seconds is

$$P = I _ { 0 } ^ { 2 } R \sin ^ { 2 } 2 \pi f t$$

Write an expression for the power in terms of

$$\csc ^ { 2 } 2 \pi \mathrm { ft }$$

Find the second Taylor polynomial of $x(x+1)^{3 / 2}$ at x=0.

Let f be a linear transformation. Show that f*f is symmetric. We will use this fact in the proof of the singular value decomposition .

If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled? F. The x-intercept becomes four times as great. G. The x-intercept becomes twice as great. H. The x-intercept becomes one-fourth as great. J. The x-intercept remains the same.

Suppose that a merchant buys a patio set from the wholesaler for $180. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant a 40% profit on his$180 investment.

If q is a quadratic form on $\mathbb{R}^{n}$ with symmetric matrix A and if $L(\vec{x})=R \vec{x}$ is a linear transformation from $\mathbb{R}^{m}$ to $\mathbb{R}^{n},$ show that the composite function $p(\vec{x})=q(L(\vec{x}))$ is a quadratic form on $\mathbb{R}^{m}.$ Express the symmetric matrix of p in terms of R and A.