Expressions, Equations, and Functions

Find the solution set for each equation if the replacement sets are $\mathit{y}\mathbf{=}\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{5}\mathbf{,}\mathbf{7}\mathbf{,}\mathbf{9}\mathbf{\}}$ and $\mathit{z}\mathbf{=}\mathbf{\{}\mathbf{10}\mathbf{,}\mathbf{12}\mathbf{,}\mathbf{14}\mathbf{,}\mathbf{16}\mathbf{,}\mathbf{18}\mathbf{\}}$

$\mathit{z}\mathbf{+}\mathbf{10}\mathbf{=}\mathbf{22}$

Find the solution set for each equation if the replacement sets are $y=\{1,3,5,7,9\}$ and $z=\{10,12,14,16,18\}$

$111=z^2+11$

Solve each equation

$\mathit{a}\mathbf{=}\mathbf{32}\mathbf{-}\mathbf{9}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$

Solve each equation

$\mathit{w}\mathbf{=}\mathbf{56}\mathbf{÷}\mathbf{(}{\mathbf{2}}^{\mathbf{2}}\mathbf{+}\mathbf{3}\mathbf{)}$

Solve each equation.

$\frac{\mathbf{27}\mathbf{+}\mathbf{5}}{\mathbf{16}}\mathbf{=}\mathit{g}$

Solve each equation.

$\frac{\mathbf{12}\mathbf{·}\mathbf{5}}{\mathbf{15}\mathbf{-}\mathbf{3}}\mathbf{=}\mathit{y}$

Solve each equation.

$\mathit{r}\mathbf{=}\frac{\mathbf{9}\mathbf{\left(}\mathbf{6}\mathbf{\right)}}{\mathbf{(}\mathbf{8}\mathbf{+}\mathbf{1}\mathbf{)}\mathbf{3}}$

Solve each equation.

$\mathit{a}\mathbf{=}\frac{\mathbf{4}\mathbf{(}\mathbf{14}\mathbf{-}\mathbf{1}\mathbf{)}}{\mathbf{3}\mathbf{\left(}\mathbf{6}\mathbf{\right)}\mathbf{-}\mathbf{5}}\mathbf{+}\mathbf{7}$

Solve each equation.

$7+x-(3+32÷8)=3$

Solve each equation.

$3^2-2·3+u=(3^3-3·8)\left(2\right)+u$

Solve each equation.

$(3·6÷2)v+10=3^{2}v+9$

Solve each equation.

$\mathbf{6}\mathit{k}\mathbf{+}\mathbf{(}\mathbf{3}\mathbf{·}\mathbf{10}\mathbf{-}\mathbf{8}\mathbf{)}\mathbf{=}\mathbf{(}\mathbf{2}\mathbf{·}\mathbf{3}\mathbf{)}\mathit{k}\mathbf{+}\mathbf{22}$

Solve each equation.

$\mathbf{(}\mathbf{3}\mathbf{·}\mathbf{5}\mathbf{)}\mathit{t}\mathbf{+}\mathbf{(}\mathbf{21}\mathbf{-}\mathbf{12}\mathbf{)}\mathbf{=}\mathbf{15}\mathit{t}\mathbf{+}{\mathbf{3}}^{\mathbf{2}}$

SCHOOL A conference room can seat a maximum of 85 people. The principal and two counselors need to meet with the school's juniors to discuss college admissions. If each student must bring a parent with them, how many students can attend each meeting? Assume that each student has a unique set of parents.

The perimeter of a regular octagon is 128 inches. Find the length of each side.

An electric generator can power 3550 watts of electricity. Write and solve an equation to find how many 75 -watt light bulbs a generator could power.

Determine whether the given number is a solution to the equation.

$\mathit{x}\mathbf{+}\mathbf{6}\mathbf{=}\mathbf{15}\mathbf{;}\mathbf{9}$

PORTS A 200-pound athlete who trains for four hours per day requires 2836 Calories for basic energy requirements. During training, the same athlete requires 3091 Calories for extra energy requirements. Write an equation to find C, the total daily Calorie requirement for this athlete. Then solve the equation.

Determine whether the given number is a solution to the equation.

$\mathbf{12}\mathbf{+}\mathit{y}\mathbf{=}\mathbf{26}\mathbf{;}\mathbf{14}$

Determine whether the given number is a solution to the equation.

$\mathbf{2}\mathit{t}\mathbf{-}\mathbf{10}\mathbf{=}\mathbf{4}\mathbf{;}\mathbf{3}$

Determine whether the given number is a solution to the equation.

$\mathbf{3}\mathit{r}\mathbf{+}\mathbf{7}\mathbf{=}\mathbf{-}\mathbf{5}\mathbf{;}\mathbf{2}$

Determine whether the given number is a solution to the equation.

$\mathbf{6}\mathbf{+}\mathbf{4}\mathit{m}\mathbf{=}\mathbf{18}\mathbf{;}\mathbf{3}$

Determine whether the given number is a solution to the equation.

Determine whether the given number is a solution to the equation.

$\frac{\mathbf{q}}{\mathbf{2}}\mathbf{=}\mathbf{20}\mathbf{;}\mathbf{10}$

Determine whether the given number is a solution to the equation.

$\frac{\mathbf{w}\mathbf{-}\mathbf{4}}{\mathbf{5}}\mathbf{=}\mathbf{-}\mathbf{3}\mathbf{;}\mathbf{-}\mathbf{11}$

Determine whether the given number is a solution to the equation.

$\frac{\mathbf{g}}{\mathbf{3}}\mathbf{-}\mathbf{4}\mathbf{=}\mathbf{12}\mathbf{;}\mathbf{48}$

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (quarter)

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (dime)

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (quarter or nickel)

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (value greater than $0.10)

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (value less than $1)

One coin is randomly selected from a jar containing 70 nickels, 100 dimes, 80 quarters, and 50 one-dollar coins. Find each probability.

P (value at most $1)

One of the polygons below is chosen at random. Find each probability.

P (Triangle)

One of the polygons below is chosen at random. Find each probability.

P (pentagon)

One of the polygons below is chosen at random. Find each probability.

P (not a quadrilateral)

One of the polygons below is chosen at random. Find each probability.

P (more than 2 right angles)

Use a tree diagram to find the sample space for each event. State the number of possible outcomes.

The spinner at the right is spun and two coins are tossed.

Use a tree diagram to find the sample space for each event. State the number of possible outcomes.

At a restaurant, you have several choices of sides to have with breakfast. You can choose white or whole-wheat toast. You can choose sausage links, sausage patties, or bacon.

Use a tree diagram to find the sample space for each event. State the number of possible outcomes.

How many different 3 -character codes are there using A, B, or C for the first character, 8 or 9 for the second character, and 0 or 1 for the third character?

A bag is full of different colored marbles. The probability of randomly selecting a red marble from the bag is $\frac{1}{8}$. The probability of selecting a blue marble is $\frac{13}{24}$. Find each probability.

P (not red)

A bag is full of different colored marbles. The probability of randomly selecting a red marble from the bag is $\frac{1}{8}$. The probability of selecting a blue marble is $\frac{13}{24}$. Find each probability.

P (not blue)

Find the odds of each outcome if a computer randomly picks a letter in the name THE UNITED STATES OF AMERICA.

The letter A.

Find the odds of each outcome if a computer randomly picks a letter in the name THE UNITED STATES OF AMERICA.

The letter T

Find the odds of each outcome if a computer randomly picks a letter in the name THE UNITED STATES OF AMERICA.

P(a vowel)

Find the odds of each outcome if a computer randomly picks a letter in the name THE UNITED STATES OF AMERICA.

A consonant

Margaret wants to order a sub at the local deli.

Find the number of possible orders of a sub with one topping and one dressing option.

Margaret wants to order a sub at the local deli.

Find the number of possible ham subs with mayonnaise, any combination of toppings or no toppings at all.

Margaret wants to order a sub at the local deli.

Find the number of possible orders of a sub with any combination of dressing and/or toppings.

Compare and contrast an expression and an equation.

OPEN-ENDED Write an equation that is an identity.