Use your results above to complete these statements: The quotient of two integers with the same sign is ______. The quotient of two integers with different signs is ______.

Solve this absolute value equation and explain what algebraic properties make it possible to do so. 3|x - 2| = 5|x - 2| - 7

Solve the initial value problem. $y^{\prime \prime}-3 y^{\prime}+2 y=0, y(0)=0, y^{\prime}(0)=1$

Factor each expression. -x^2 + 3x + 40

Identify the W's, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured ( or note that they were not provided). Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them either the herbal compound or a sugar solution known to have no effect on colds. Several days later they assessed each patient's condition, using a cold severity scale ranging from 0 to 5. They found no evidence of benefits of the compound.

The absolute value of the sum of two different integers with the same sign is 8. Pat says there are three pairs of integers that match this description. Do you agree? Explain.

Mendel's _____ states that genes for different traits are inherited independently of each other.

On Monday, Jan made withdrawals of $25,$45, and $75 from her savings account. On the same day, her twin sister Julie made withdrawals of$35, $55, and$65 from her savings account. a. Write a sum of negative integers to show Jan's withdrawals on Monday. Find the total amount Jan withdrew. b. Write a sum of negative integers to show Julie's withdrawals on Monday. Find the total amount Julie withdrew. c. Julie and Jan's brother also withdrew money from his savings account on Monday. He made three withdrawals and withdrew $10 more than Julie did. What are three possible amounts he could have withdrawn?

Liz works at Food For Thought magazine. Her employer offers her a pension. Liz's employer uses a formula to calculate the pension. Retiring employees receive 2.1% of their average salary over the last 4 years of employment for every year worked. Liz is planning on retiring at the end of this year after, 20 years of employment. Her salaries for the last 4 years are $66,000;$66,000; $73,000; and$75,000. Calculate Liz's annual pension.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $\sqrt{\sqrt{16}}=2$

Determine the equilibrium solutions. The demand equation is given first and the supply equation second.

$$\begin{array}{l}{p=-3 x+15} \\ {p=2 x-5}\end{array}$$

Communicate Mathematical Ideas Is it possible for a system of two linear inequalities to have every point in the plane as a solution? Why or why not?

Find the number of permutations.

$$_ { 21 } P _ { 3 }$$

Graph each of the following polar functions on the same set of axes. a. $r=5 \csc (\theta)$ b. $r=5 \csc (\theta-\pi)$