Algebra

Problem 28501

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
8) $\log_6 \left( \frac{x^3}{y^6} \right)$

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Problem 28502

Evaluate the expression without using a calculator. 9) $\log_{2}{\frac{1}{8}}$

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Problem 28503

Use the square root property to solve the equation. $(3 x-3)^{2}=39$

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Problem 28504

Use the given conditions to write an equation for the line in slope-intercept form. 10) Passing through $(-1, 5)$ and $(6, 4)$

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Problem 28505

Use the given conditions to write an equation for the line in point-slope form. 12) Passing through $(8, 8)$ and $(6, 5)$

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Problem 28506

Classify this polynomial. $-7 v^{3}+7 u$ linear quadratic cubic none of these

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Problem 28507

Solve the polynomial inequality and graph the solution notation.
13) $x^2 - 3x - 10 \le 0$

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Problem 28508

For the following equation, find three ordered pair solutions by completing the table. Then use the order pairs to graph the equation. $y=2 x$
Find three ordered pair solutions of the given equation \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 0 & 0 \\ \hline-2 & $\square$ \\ \hline \end{tabular}

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Problem 28509

on 7 Question 2, 7.7.3 Part 3 of 4
For the following equation, find three ordered pair solutions by completing the table. Then use the orde pairs to graph the equation. $y=2 x$
Find three ordered pair solutions of the giver equatio \begin{tabular}{|c|c|} \hline $\mathbf{x}$ & $\mathbf{y}$ \\ \hline 0 & 0 \\ \hline-2 & $-4^{2}$ \\ \hline 1 & $\square$ \\ \hline \end{tabular}

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Problem 28510

Question 5 The partial fraction decomposition of $\frac{x^{2}+12}{(x-3)\left(x^{2}+4\right)}$ can be written in the form of $\frac{f(x)}{x-3}+\frac{g(x)}{x^{2}+4}$ . The possible anwsers for $f(x)$ and $g(x)$ are (a) $A$ , a constant, or (b) $A x+B$ , a linear function. $f(x)$ is in the form of (input a or b) $\square$ and $g(x)$ is in the form of (input a or b ) $\square$

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Problem 28511

Adult tickets to Century Cinema cost \ $9.50. Children's tickets cost$ \ $5.75$ . The Neighborhood Movie Club purchased 34 tickets for a total cost of $\$ 240.50$ . Which system of equations can be used to determine $x$ , the number of adult tickets purchased, and $y$ , the number of children's tickets purchased? $\begin{array}{l} 5.75 x+9.5 y=34 \\ x+y=240.5 \end{array}$ (B) $\begin{array}{l} 5.75 x+9.5 y=240.5 \\ x+y=34 \end{array}$ (C) $\begin{array}{l} 9.5 x+5.75 y=240.5 \\ x+y=34 \end{array}$ $\begin{array}{l} \text { (D) } 9.5 x+5.75 y=34 \\ x+y=240.5 \end{array}$

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Problem 28512

Solve the absolute value inequality. set on a number line. 17) $|x + 2| + 5 \le 9$

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Problem 28513

For the following equation, find three ordered pair solutions by completing the table. Then use the ordered pairs to graph the equation. $y=2 x$
To graph this linear equation, find three ordered pair solutions. Since this equation is solved for $y$ , choose three values for $x$ .
If $x=0, y=2 \cdot 0=$ $\square$

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Problem 28514

Solve the exponential equation. Use a calculator to obtain a decimal approximation, solution. 19) $e^{4x} = 8$ B) $32$ C) $0.52$

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Problem 28515

Use the given conditions to write an equation for the line in the indicated form. 20) Passing through $(3, -4)$ and parallel to the line whose equation is $y = -7x + 9$ ; slope-intercept form

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Problem 28516

This is the graph of a polynomial function. The absolute maximum is shown on the graph.
Find the domain and range.

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Problem 28517

5 times the sum of $x$ and 3.

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Problem 28518

(d) $\frac{x^2 - 3x + 2}{x^3 + 4x} \le 0$
When does the graph of $\frac{x^2 + 2x - 4}{x(x-2)^2}$ lie above the graph of $\frac{2}{x(x-2)}$ ?
3. Logarithmic Functions

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Problem 28519

Rewrite the following equation in slope-intercept form.
$13y = 2x - 2$
Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Problem 28520

Question 3 (1 point) Imagine you need $\$ 425$ to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $\$ 30$ fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?
Your Answer: $\square$ Answer

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Problem 28521

Write the quadratic equation whose roots are 5 and -3 , and whose leading coefficient is 3 . (Use the letter $x$ to represent the variable.) $\square$ $=0$

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Problem 28522

15. In a football game, all of the home team's points are from 7 -point touchdowns and 3-point field goals. The team scores six times. Write and solve a system of linear equations to find the numbers of touchdowns and field goals that the home team scores. (Section 5.1, Section 5.2, and Section 5.3)

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Problem 28523

7. Find $t$ given that these vectors are perpendicular: a. $\mathbf{p} = \begin{pmatrix} 3 \\ t \end{pmatrix}$ and $\mathbf{q} = \begin{pmatrix} -2 \\ 1 \end{pmatrix}$ b. $\mathbf{r} = \begin{pmatrix} t \\ t+2 \end{pmatrix}$ and $\mathbf{s} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}$ c. $\mathbf{a} = \begin{pmatrix} t \\ t+2 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2-3t \\ t \end{pmatrix}$ d. $\mathbf{a} = \begin{pmatrix} 3 \\ -1 \\ t \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2t \\ -3 \\ -4 \end{pmatrix}$
8. For question 7 find, where possible, the value(s) of $t$ for which the given vectors are

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Problem 28524

The graph of the relation $T$ is shown below.
Give the domain and range of $T$ . Write your answers using set notation. $\text { domain }=$ $\square$ range = $\square$

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Problem 28525

The cubic function $y = x^3$ is transformed into $y = -2x^3 - 7$ . What effect will this have on the graph of the function?
The graph will be reflected over the x-axis, shifted down 7 units and vertical stretch of 2. The graph will be reflected over the x-axis, shifted up 7 units and vertical stretch of 2. The graph will be reflected over the y-axis, shifted down 2 units and vertical shrink of 2. The graph will be reflected over the y-axis, shifted up 2 units and vertical shrink of 2.

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Problem 28526

Is $(-7, -10)$ a solution to this system of inequalities?
$y \le -4$
$20x - 16y \ge 20$
yes
no
Submit

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Problem 28527

10. True or False: Is every relation a function? For problems 15-26, check if each relation is a function and find the domain and range.
16. $\{(-2,5),(-1,3),(3,7),(4,12)\}$
20. $\{(0,-2),(1,3),(2,3),(3,7)\}$
24. $\{(-4,4),(-3,3),(-2,2),(-1,1),(-4,0)\}$

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Problem 28528

Simplify the expression: $\frac{\sqrt{5 x^{2} y^{4}}}{\sqrt{2 x^{3} y^{2}}}$

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Problem 28529

Find the value of $i^{120}$ .

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Problem 28530

Determine if the following equations define $y$ as a function of $x$ : 28. $y=x^{3}$ , 31. $y^{2}=4-x^{2}$ , $y=|x-3|$ .

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Problem 28531

Express the statement "One does not run fast" using the symbol $\neg p$ .

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Problem 28532

Symbolically express: I get an A and I do not study using $p$ and $q$ .

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Problem 28533

Write the symbolic form of: I do not work hard or I pass the course using $p$ and $q$ .

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Problem 28534

For functions 42 and 43, compute $f(0)$ , $f(1)$ , $f(-1)$ , $f(-x)$ , $-f(x)$ , $f(x+1)$ , $f(2x)$ , $f(x+h)$ .

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Problem 28535

Symbolically express: If not $p$ , then not $q$ .

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Problem 28536

Factor the quadratic equation $3r^{2}+21r-54=0$ .

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Problem 28537

Let $p$ be "The campus is closed" and $q$ be "It is Sunday." Express "Being Sunday is necessary and sufficient for the campus being closed" symbolically.

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Problem 28538

An investor deposits \$1200 yearly in an annuity at 7% interest. Find the total value after 1, 2, and 3 years.

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Problem 28539

Symbolically express: "It is time to sleep and it is Tuesday, or it is snowing outside" using $p$ , $q$ , and $r$ .

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Problem 28540

Keiko deposits \ $950 annually in a 6% annuity. Find values at the end of years 1, 2, and 3: (a)$ V_1 $, (b)$ V_2 $, (c)$ V_3$.

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Problem 28541

Ravi deposits \$625 yearly in an annuity at 8% interest. Find its value at the end of years 1, 2, and 3.

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Problem 28542

Simplify the expression: $3z - 2 + 7z - 8z =$

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Problem 28543

Solve the equation: $0.5y + 1.3 = -5.2$ . What is the solution set?

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Problem 28544

Solve the equation: $3y + 1 = -14$ . What is the solution set?

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Problem 28545

Solve the equation -2.2 + 3.5z = -5.7 and find the solution set.

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Problem 28546

Find the slope of the line given by $f(x)=-2x+4$ at the point $(5,-6)$ .

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Problem 28547

Simplify $-7 \sqrt{20}$ .

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Problem 28548

Find an ordered pair $(x, y)$ that solves the equation $x - 4y = 8$ . Is $(0, 0)$ a solution?

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Problem 28549

7. Of 107 athletes, some play basketball. If 48 play baseball and 33 do not, find those who do not play basketball.
8. Last year, 216,000 cars were sold, which was 39,000 more than three times the number of trucks $t$ . Find $t$ .

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Problem 28550

Find the domain of each function: 48. $f(x)=x^{2}+2$ , 52. $h(x)=\frac{2x}{x^{2}-4}$ , 54. $G(x)=\frac{x+4}{x^{3}-4x}$ , 56. $G(x)=\sqrt{1-x}$ , 58. $f(x)=\frac{x}{\sqrt{x-4}}$ .

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Problem 28551

Southern Land Company needs to raise \$300,000 in 3 years with quarterly payments at 8\% interest. Find the quarterly payment.

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Problem 28552

Solve the equation: $\frac{2}{9} m + 3 = \frac{2}{9} m - 5$ . What is the solution set?

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Problem 28553

A lady has 4 gold chains with 3 links each. Can she join them for less than 4\$? How many cuts for 5 chains?

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Problem 28554

Sara has $\$ 320$ and saves $\$ 180$ monthly. How many months until she reaches $\$ 5,000$ for college?

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Problem 28555

Find the inverse function of $f(x)=\left(\frac{\sqrt[3]{x}}{4}\right)^{7}$ .

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Problem 28556

Solve the system of equations: $2x^{2} + y = 3$ and $y = x^{2}$ .

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Problem 28557

Write the expression for: subtracting $f$ from 5 and then doubling the result. Do not simplify.

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Problem 28558

Write the expression: $u^2 + 10$ .

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Problem 28559

Write the expression for 5 + \frac{6}{t}.

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Problem 28560

Determine the slope of the line represented by the equation $3x + 2y = 6$ .

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Problem 28561

Write an expression: double $k$ , then multiply the result by 10.

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Problem 28562

Create an expression: double $g$ , then raise the result to the 6th power. Do not simplify.

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Problem 28563

Solve the system of equations: $2y = -x^2$ and $y^2 = -2x$ .

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Problem 28564

Solve the system: $ab + c = 2020$ and $a + bc = 2021$ .

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Problem 28565

Find the slope of the line given by $x + 5y = -15$ .

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Problem 28566

Determine the slope of the line given by the equation $x + 5 + y = 0$ .

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Problem 28567

A cyclist rides uphill at $x \mathrm{mph}$ and downhill at $x + 5 \mathrm{mph}$ . Which inequality models average speed $\geq 12 \mathrm{mph}$ ? Options:
1. $\frac{1}{x}+\frac{1}{x+5} \leq \frac{2}{12}$
2. $\frac{1}{x}+\frac{1}{5 x} \geq \frac{2}{12}$
3. $\frac{1}{x}+\frac{1}{x+5} \geq \frac{2}{12}$
4. $\frac{1}{x-5}+\frac{1}{x+5} \geq \frac{2}{12}$

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Problem 28568

Find integers $a$ , $b$ , and $c$ such that $ab + c = 2020$ and $a + bc = 2021$ .

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Problem 28569

Simplify and express as a single term with exponents: $186^{1} \cdot 186^{2} \cdot 186^{1}$ .

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Problem 28570

Simplify the expression: $825^{95} \cdot 825^{46} \cdot 825^{6}$ as a single term using exponents.

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Problem 28571

Solve the equation $c(x+2)-5=b(x-3)$ .

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Problem 28572

Find the slope of the line given by the equation $3x + 20 = -4y$ .

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Problem 28573

Solve for $w$ in the equation $-6=-3|w|$ . Provide your answer as an integer or a fraction.

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Problem 28574

Solve for $r$ in the equation $1=|r-8|$ . Provide your answer as an integer or fraction.

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Problem 28575

Find the range of a graph with valleys, passing through (9,6), and having a lowest point between -10 and y-axis.

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Problem 28576

Solve for $b$ : $9|b|=9$ . Provide answers as integers or simplified fractions. $b=$

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Problem 28577

Solve for $b$ in the equation $|-8 b|=0$ . Provide your answer as an integer or fraction in simplest form.

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Problem 28578

Write an expression for $u < t - v$ without simplifying it.

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Problem 28579

Find a quadratic function $y=a x^{2}$ that goes through the point $(-2,12)$ . What is the equation?

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Problem 28580

Find the integer value of $j$ that satisfies the equation $|j-4|=0$ . What is $j$ ?

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Problem 28581

Determine the number of solutions for the equation $|3w|=12$ : no solution, one solution, or two solutions?

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Problem 28582

Solve the equation $4|n|-4=-4$ . How many solutions does it have: none, one, or two?

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Problem 28583

Determine the number of solutions for the equation: $-20 = -|s|$ (no solution, one solution, or two solutions).

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Problem 28584

Solve for $t$ : $-2|t|=-2$ . Provide answers as integers or simplified fractions. $t=$

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Problem 28585

Find the number of solutions for the equation $3=|-u|$ : no solution, one solution, or two solutions?

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Problem 28586

Solve for $f$ :
$-16=-8|-f|$
Provide your answer as an integer or fraction in simplest form.
$f=$

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Problem 28587

Solve for $u$ : $|2u| + 8 = 28$ . Provide your answer as an integer or fraction in simplest form.

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Problem 28588

Solve the equation $|\frac{t}{2}|=6$ .

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Problem 28589

Solve the equation $|f|-3=-50$ . How many solutions does it have: none, one, or two?

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Problem 28590

In a basketball game, Maria scored 3 times Holly's points. In the next game, Maria scored 7 fewer and Holly 9 more. They tied in the second game. Find their scores in the first game.

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Problem 28591

Find the integer or fraction solutions for $t$ in the equation $5=|t-5|$ .

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Problem 28592

Find the function $g$ if $f(x)=\frac{1}{x}$ and $\left(\frac{f}{g}\right)(x)=\frac{x+1}{x^{2}-x}$ .

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Problem 28593

Solve the equation $|m+3|=7$ .

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Problem 28594

Find the values of $q$ that satisfy the equation $|q-8|=14$ .

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Problem 28595

Solve the equation $|x-1|+5=2$ .

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Problem 28596

The Eiffel Tower is 497 ft taller than the Washington Monument. If both were 58 ft shorter, the Eiffel Tower would be twice the height of the Washington Monument. Find their heights.

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Problem 28597

The Eiffel Tower is 497 ft taller than the Washington Monument. If both were 58 ft shorter, find their heights.

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Problem 28598

Determine the domain of the function $f(x)=\frac{x-8}{x+8}$ in interval notation.

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Problem 28599

Determine the domain of the function $F(x)=7 x^{5}-4 x^{4}+4$ in interval notation.

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Problem 28600

Simplify $f(x-3)$ for the function $f(x)=x^{2}-2$ . What is $f(x-3)=?$

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1 ...283 284 285 286 287 288 289 ...313

Algebra

Problem 28501

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.8) log⁡6(x3y6)\log_6 \left( \frac{x^3}{y^6} \right)log6​(y6x3​)

Problem 28502

Evaluate the expression without using a calculator. 9) log⁡218\log_{2}{\frac{1}{8}}log2​81​

Problem 28503

Use the square root property to solve the equation. (3x−3)2=39(3 x-3)^{2}=39(3x−3)2=39

Problem 28504

Use the given conditions to write an equation for the line in slope-intercept form. 10) Passing through (−1,5)(-1, 5)(−1,5) and (6,4)(6, 4)(6,4)

Problem 28505

Use the given conditions to write an equation for the line in point-slope form. 12) Passing through (8,8)(8, 8)(8,8) and (6,5)(6, 5)(6,5)

Problem 28506

Classify this polynomial. −7v3+7u-7 v^{3}+7 u−7v3+7u linear quadratic cubic none of these

Problem 28507

Solve the polynomial inequality and graph the solution notation.13) x2−3x−10≤0x^2 - 3x - 10 \le 0x2−3x−10≤0

Problem 28508

Problem 28509

Problem 28510

Problem 28511

Problem 28512

Solve the absolute value inequality. set on a number line. 17) ∣x+2∣+5≤9|x + 2| + 5 \le 9∣x+2∣+5≤9

Problem 28513

Problem 28514

Solve the exponential equation. Use a calculator to obtain a decimal approximation, solution. 19) e4x=8e^{4x} = 8e4x=8 B) 323232 C) 0.520.520.52

Problem 28515

Use the given conditions to write an equation for the line in the indicated form. 20) Passing through (3,−4) (3, -4) (3,−4) and parallel to the line whose equation is y=−7x+9 y = -7x + 9 y=−7x+9; slope-intercept form

Problem 28516

This is the graph of a polynomial function. The absolute maximum is shown on the graph.Find the domain and range.

Problem 28517

5 times the sum of xxx and 3.

Problem 28518

(d) x2−3x+2x3+4x≤0\frac{x^2 - 3x + 2}{x^3 + 4x} \le 0x3+4xx2−3x+2​≤0When does the graph of x2+2x−4x(x−2)2\frac{x^2 + 2x - 4}{x(x-2)^2}x(x−2)2x2+2x−4​ lie above the graph of 2x(x−2)\frac{2}{x(x-2)}x(x−2)2​?3. Logarithmic Functions

Problem 28519

Rewrite the following equation in slope-intercept form.13y=2x−213y = 2x - 213y=2x−2Write your answer using integers, proper fractions, and improper fractions in simplest form.

Problem 28520

Question 3 (1 point) Imagine you need $425\$ 425$425 to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $30\$ 30$30 fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?Your Answer: □\square□ Answer

Problem 28521

Write the quadratic equation whose roots are 5 and -3 , and whose leading coefficient is 3 . (Use the letter xxx to represent the variable.) □\square□ =0=0=0

Problem 28522

Problem 28523

Problem 28524

The graph of the relation TTT is shown below.Give the domain and range of TTT. Write your answers using set notation. domain =\text { domain }= domain = □\square□ range = □\square□

Problem 28525

Problem 28526

Is (−7,−10)(-7, -10)(−7,−10) a solution to this system of inequalities?y≤−4y \le -4y≤−420x−16y≥2020x - 16y \ge 2020x−16y≥20yesnoSubmit

Problem 28527

Problem 28528

Simplify the expression: 5x2y42x3y2\frac{\sqrt{5 x^{2} y^{4}}}{\sqrt{2 x^{3} y^{2}}}2x3y2​5x2y4​​

Problem 28529

Find the value of i120i^{120}i120.

Problem 28530

Determine if the following equations define yyy as a function of xxx: 28. y=x3y=x^{3}y=x3, 31. y2=4−x2y^{2}=4-x^{2}y2=4−x2, y=∣x−3∣y=|x-3|y=∣x−3∣.

Problem 28531

Express the statement "One does not run fast" using the symbol ¬p\neg p¬p.

Problem 28532

Symbolically express: I get an A and I do not study using ppp and qqq.

Problem 28533

Write the symbolic form of: I do not work hard or I pass the course using ppp and qqq.

Problem 28534

For functions 42 and 43, compute f(0)f(0)f(0), f(1)f(1)f(1), f(−1)f(-1)f(−1), f(−x)f(-x)f(−x), −f(x)-f(x)−f(x), f(x+1)f(x+1)f(x+1), f(2x)f(2x)f(2x), f(x+h)f(x+h)f(x+h).

Problem 28535

Symbolically express: If not ppp, then not qqq.

Problem 28536

Factor the quadratic equation 3r2+21r−54=03r^{2}+21r-54=03r2+21r−54=0.

Problem 28537

Let ppp be "The campus is closed" and qqq be "It is Sunday." Express "Being Sunday is necessary and sufficient for the campus being closed" symbolically.

Problem 28538

An investor deposits \$1200 yearly in an annuity at 7% interest. Find the total value after 1, 2, and 3 years.

Problem 28539

Symbolically express: "It is time to sleep and it is Tuesday, or it is snowing outside" using ppp, qqq, and rrr.

Problem 28540

Keiko deposits \950annuallyina6950 annually in a 6% annuity. Find values at the end of years 1, 2, and 3: (a) 950annuallyina6V_1,(b), (b) ,(b)V_2,(c), (c) ,(c)V_3$.

Problem 28541

Ravi deposits \$625 yearly in an annuity at 8% interest. Find its value at the end of years 1, 2, and 3.

Problem 28542

Simplify the expression: 3z−2+7z−8z=3z - 2 + 7z - 8z = 3z−2+7z−8z=

Problem 28543

Solve the equation: 0.5y+1.3=−5.20.5y + 1.3 = -5.20.5y+1.3=−5.2. What is the solution set?

Problem 28544

Solve the equation: 3y+1=−143y + 1 = -143y+1=−14. What is the solution set?

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
8) $\log_6 \left( \frac{x^3}{y^6} \right)$

Evaluate the expression without using a calculator. 9) $\log_{2}{\frac{1}{8}}$

Use the square root property to solve the equation. $(3 x-3)^{2}=39$

Use the given conditions to write an equation for the line in slope-intercept form. 10) Passing through $(-1, 5)$ and $(6, 4)$

Use the given conditions to write an equation for the line in point-slope form. 12) Passing through $(8, 8)$ and $(6, 5)$

Classify this polynomial. $-7 v^{3}+7 u$ linear quadratic cubic none of these

Solve the polynomial inequality and graph the solution notation.
13) $x^2 - 3x - 10 \le 0$

Solve the absolute value inequality. set on a number line. 17) $|x + 2| + 5 \le 9$

Solve the exponential equation. Use a calculator to obtain a decimal approximation, solution. 19) $e^{4x} = 8$ B) $32$ C) $0.52$

Use the given conditions to write an equation for the line in the indicated form. 20) Passing through $(3, -4)$ and parallel to the line whose equation is $y = -7x + 9$ ; slope-intercept form

This is the graph of a polynomial function. The absolute maximum is shown on the graph.
Find the domain and range.

5 times the sum of $x$ and 3.

(d) $\frac{x^2 - 3x + 2}{x^3 + 4x} \le 0$
When does the graph of $\frac{x^2 + 2x - 4}{x(x-2)^2}$ lie above the graph of $\frac{2}{x(x-2)}$ ?
3. Logarithmic Functions

Rewrite the following equation in slope-intercept form.
$13y = 2x - 2$
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Question 3 (1 point) Imagine you need $\$ 425$ to cover unexpected car repairs. You decide to get a payday loan. The payday lender charges a $\$ 30$ fee for a two-week loan. If this loan was to be rolled over for an entire year then how much would be owed?
Your Answer: $\square$ Answer

Write the quadratic equation whose roots are 5 and -3 , and whose leading coefficient is 3 . (Use the letter $x$ to represent the variable.) $\square$ $=0$

The graph of the relation $T$ is shown below.
Give the domain and range of $T$ . Write your answers using set notation. $\text { domain }=$ $\square$ range = $\square$

Is $(-7, -10)$ a solution to this system of inequalities?
$y \le -4$
$20x - 16y \ge 20$
yes
no
Submit

Simplify the expression: $\frac{\sqrt{5 x^{2} y^{4}}}{\sqrt{2 x^{3} y^{2}}}$

Find the value of $i^{120}$ .

Determine if the following equations define $y$ as a function of $x$ : 28. $y=x^{3}$ , 31. $y^{2}=4-x^{2}$ , $y=|x-3|$ .

Express the statement "One does not run fast" using the symbol $\neg p$ .

Symbolically express: I get an A and I do not study using $p$ and $q$ .

Write the symbolic form of: I do not work hard or I pass the course using $p$ and $q$ .

For functions 42 and 43, compute $f(0)$ , $f(1)$ , $f(-1)$ , $f(-x)$ , $-f(x)$ , $f(x+1)$ , $f(2x)$ , $f(x+h)$ .

Symbolically express: If not $p$ , then not $q$ .

Factor the quadratic equation $3r^{2}+21r-54=0$ .

Let $p$ be "The campus is closed" and $q$ be "It is Sunday." Express "Being Sunday is necessary and sufficient for the campus being closed" symbolically.

Symbolically express: "It is time to sleep and it is Tuesday, or it is snowing outside" using $p$ , $q$ , and $r$ .

Keiko deposits \ $950 annually in a 6% annuity. Find values at the end of years 1, 2, and 3: (a)$ V_1 $, (b)$ V_2 $, (c)$ V_3$.

Simplify the expression: $3z - 2 + 7z - 8z =$

Solve the equation: $0.5y + 1.3 = -5.2$ . What is the solution set?

Solve the equation: $3y + 1 = -14$ . What is the solution set?

Find the slope of the line given by $f(x)=-2x+4$ at the point $(5,-6)$ .

Simplify $-7 \sqrt{20}$ .

Find an ordered pair $(x, y)$ that solves the equation $x - 4y = 8$ . Is $(0, 0)$ a solution?

7. Of 107 athletes, some play basketball. If 48 play baseball and 33 do not, find those who do not play basketball.
8. Last year, 216,000 cars were sold, which was 39,000 more than three times the number of trucks $t$ . Find $t$ .

Find the domain of each function: 48. $f(x)=x^{2}+2$ , 52. $h(x)=\frac{2x}{x^{2}-4}$ , 54. $G(x)=\frac{x+4}{x^{3}-4x}$ , 56. $G(x)=\sqrt{1-x}$ , 58. $f(x)=\frac{x}{\sqrt{x-4}}$ .

Solve the equation: $\frac{2}{9} m + 3 = \frac{2}{9} m - 5$ . What is the solution set?

Sara has $\$ 320$ and saves $\$ 180$ monthly. How many months until she reaches $\$ 5,000$ for college?

Find the inverse function of $f(x)=\left(\frac{\sqrt[3]{x}}{4}\right)^{7}$ .

Solve the system of equations: $2x^{2} + y = 3$ and $y = x^{2}$ .

Write the expression for: subtracting $f$ from 5 and then doubling the result. Do not simplify.

Write the expression: $u^2 + 10$ .

Determine the slope of the line represented by the equation $3x + 2y = 6$ .

Write an expression: double $k$ , then multiply the result by 10.

Create an expression: double $g$ , then raise the result to the 6th power. Do not simplify.

Solve the system of equations: $2y = -x^2$ and $y^2 = -2x$ .

Solve the system: $ab + c = 2020$ and $a + bc = 2021$ .

Find the slope of the line given by $x + 5y = -15$ .

Determine the slope of the line given by the equation $x + 5 + y = 0$ .

Find integers $a$ , $b$ , and $c$ such that $ab + c = 2020$ and $a + bc = 2021$ .

Simplify and express as a single term with exponents: $186^{1} \cdot 186^{2} \cdot 186^{1}$ .

Simplify the expression: $825^{95} \cdot 825^{46} \cdot 825^{6}$ as a single term using exponents.

Solve the equation $c(x+2)-5=b(x-3)$ .

Find the slope of the line given by the equation $3x + 20 = -4y$ .

Solve for $w$ in the equation $-6=-3|w|$ . Provide your answer as an integer or a fraction.

Solve for $r$ in the equation $1=|r-8|$ . Provide your answer as an integer or fraction.