Solve for y given the set of constraints.

Given $\triangle P Q R \cong \triangle D E F, P Q=15, Q R=10, R P=8$, and $E F=6 y+4$.

Bob gave four-fifths of his pencils to Barbara, then he gave two-thirds of the remaining pencils to Bonnie. If he ended up with ten pencils for himself, with how many did he start?

Perform the indicated operation. Simplify the answer when possible.

$$\frac { \sqrt { 75 } } { \sqrt { 3 } }$$

Objective function:
C = 4x + 3y
Constraints:
x $\geq$ 0
2x + 3y $\geq$ 6
3x - 2y $\leq$ 9
x + 5y $\leq$ 20

The problem involves two constraints.
Find the extreme values of the function $f(x, y, z)=x y+z^2$ on the circle in which the plane $y-x=0$ intersects the sphere $x^2+y^2+z^2=4$.

Determine whether the following statement is sometimes, always, or never true. Justify your argument.

The sum of three consecutive odd integers equals an even integer.

Fill in the blank spot in the following sentence.

If citizens believe their city is ruled by gods, they might call their government a $\underline{\phantom{\text{justekst}}}$.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. a. Use the formulas shown in the voice balloons to write the company's profit function, $P$, from producing and selling $x$ radios. b. Find the company's profit if 20,000 radios are produced and sold.

Which of the following is not a type of prejudice? a. homophobia b. racism c. sexism d. individualism

A room is $8$ meters long, $5$ meters wide, and $3$ meters high. Find the following lengths.

Diagonal from one corner of the floor to the opposite corner of the ceiling

Considering again the argument from Question 4. Which of the following conclusions is true? a. Paul is a knight. b. Paul is not a knight. c. Paul may or may not be a knight.

Write the letter for the word that best completes given sentence.
____________ The police officer's ________ statements about the confidential details of the case ended up causing _________ damage to his reputation.
a. aversive....diversionary
b. inadvertent...irreversible
c. inverse....diversified

Develop a class BankAccount that supports these methods:

init(): Initializes the bank account balance to the value of the input argument, or to 0 if no input argument is given

withdraw(): Takes an amount as input and withdraws it from the balance

deposit(): Takes an amount as input and adds it to the balance

balance(): Returns the balance on the account

>>> x = BankAccount(700)
>>> x.balance()
700.00
>>> x.withdraw(70)
>>> x.balance()
630.00
>>> x.deposit(7)
>>> x.balance()
637.00

Using the discussion earlier, answer the questions below:

(a) How does Lee define secession?

(b) In your own words, explain Lee's argument against secession.