In Exercise given below, an equation of the form |f(x)|=|g(x)| is given.

(a) Solve the equation analytically and support the solution graphically.

(b) Solve |f(x)|>|g(x)| graphically.

(c) Solve |f(x)|<|g(x)| graphically.

$$|3 x+1|=|2 x-7|$$

Explain why you can always solve a right triangle if you know the lengths of two sides.

A Ferrari with a mass of $1400 \mathrm{~kg}$ approaches a freeway underpass that is $12 \mathrm{~m}$ across. At what speed must the car be moving, in order for it to have a wavelength such that it might somehow "diffract" after passing through this "single slit"? How do these conditions compare to normal freeway speeds of $30 \mathrm{~m} / \mathrm{s}$ ?

Graph the function. Compare the graph to the graph of $f ( x ) = x ^ { 2 }$. $g ( x ) = x ^ { 2 } + 5$

Alicia says the expression 2(m+4)+5 is equivalent to the expression 2m +13. Identify two properties that can be used to support Alicia's claim and justify your answer.

Graph the quadratic function defined by $f(x)=-x^2-2 x+1$, and identify the vertex. Give the domain and range.

Find the indefinite integral.

$$\int \sin 8 x \cos 7 x d x$$

Evaluate the indefinite integral.

$$\int \frac{\csc ^2 x}{\cot ^3 x} d x$$

Find the indefinite integral. $\int \frac{2}{3 \sqrt[3]{x}} d x$

Write $C$ if the italicized word is used correctly. Write $I$ if the word is used incorrectly. The airline lost Vera's suitcase, but she had thrown away her baggage check, so she could not substantiate her claim.

Evaluate the indefinite integral as an infinite series.
$\displaystyle\int e^{x^3} d x$

Find the 10th term of the sequence defined by the given rule.

f(1) = 2,f(n) = f(n - 1) + 7

Simplify.

4f * g raised to -5 divided by 5 * h raised to -3

In given of the following sentence, underline the pronoun or pair of pronouns in parentheses that agrees with the antecedent.
No one enjoys having (their, his or her) car doors frozen shut.