Browse Algebra problems Studdy Solved!

Problem 2501

8. $\frac{(x-5)}{3}+4 x=7$

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Problem 2502

Graph the quadratic equation in desmos, then determine if the vertex is a maximum or minimum. * 1 point 5) Maximum or Minimum? $y=-x^{2}+3 x-4$ A) Maximum B) Minimum $A$ $B$

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Problem 2503

2. $x^{3}+3 x^{2}-4 x-12=0$

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Problem 2504

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width, what is the largest possible length? Write an equation and solve. $(2 w+3) 4=60 ; 15$

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Problem 2505

1. $x^{3}-3 x^{2}-13 x+15=0$

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Problem 2506

$\frac{3+x}{-7}=0$

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Problem 2507

$x^{4}+2 x^{3}-8 x^{2}-18 x-9=0$

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Problem 2508

$2 x^{3}-3 x^{2}-5 x+6=0$

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Problem 2509

$3 x^{3}-4 x^{2}-17 x+6=0$

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Problem 2510

$P(x)=x^{3}+6 x^{2}+11 x+6 \quad, x_{1}=-3$

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Problem 2511

$P(x)=3 x^{4}-16 x^{3}+21 x^{2}+4 x-12 \quad, x_{1}=-2 / 3$

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Problem 2512

$P(x)=2 x^{3}-15 x^{2}+27 x-10 \quad x_{1}=5$

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Problem 2513

Select the appropriate description of how the graph of each function is derived from the graph of $y=x^{2}$ . Place the number next to the correct answer. a) $\quad y=\left[\frac{1}{3}(x)\right]^{2}$ $\qquad$ (1) horizontal translation 3 units left (2) vertical translation 3 units up (3) vertical translation 3 units down b) $y=(3 x)^{2}$ $\qquad$ c) $y=x^{2}-3$ $\qquad$ (4) horizontal translation 3 units right and vertical translation 3 units up (5) reflection in $x$ -axis and vertical translation 3 units up (6) vertical compression by a factor of $\frac{1}{3}$ (7) vertical stretching by a factor of 3 d) $y=(x-3)^{2}$ $\qquad$ (8) horizontal translation 3 units right (9) reflection in $x$ -axis and horizontal translation 3 units left (10) horizontal stretching by a factor of 3. e) $\quad y=-(x+3)^{2}$ $\qquad$ (11) horizontal compression by a factor of $\frac{1}{3}$ f) $y=-x^{2}+3$ $\qquad$

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Problem 2514

me: $\qquad$ plication Date: $\qquad$
1. Determine the inverse of following relation and state the domain and range of $f(x)$ as well as its inverse. Show all work. Is the inverse a function? $f(x)=(x-4)^{2}+6$

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Problem 2515

Determine the inverse of the function given in the graph. The points are $(-3, 4)$ , $(1, -1)$ , $(2, 3)$ , $(4, 3)$ .

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Problem 2516

Solve the following equation $(y-2)(y+1)=-2 y$

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Problem 2517

nomework1.4: Prodiem 4 (1 point)
Write equations for each of the following three lines. a. The line given by the table of values \begin{tabular}{|l|l|l|} \hline $x=$ & 1 & 1 \\ \hline $y=$ & 2 & 4 \\ \hline \end{tabular} ? $\square$ b. The line given by the graph ? $\square$ c. The line for which the $y$ coordinate of every point is -3 . ? $\square$
Note: In order to get credit for this problem all answers must be correct.

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Problem 2518

Using Thevenin's theorem, calculate the current flowing through a $10 \Omega$ resistor in the figure below.

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Problem 2519

2. Richard Petty has a utility function $u(x, y, z)=x y(1+z)$ where $x$ is food, $y$ is clothing, and $z$ is automobiles. The price of a unit of food is $\$ 1$ , a unit of clothes is $\$ 2$ , and a 1 unit of cars is $\$ 2000$ . Cars must be bought in discrete units. Richard has an income of $\$ 9000$ . Calculate the bundle of goods that maximizes Richard's utility.

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Problem 2520

$(4 y+5)(5 y-1)=0$

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Problem 2521

[6] 2. Given the equation $\quad f(x)=-3|2(x-1)|+4$ a) State the parent function: $\qquad$ c) Graph the function, showing the original an graph. Label all point final clearly b) Show transformation of 5 points of your choice:

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Problem 2522

$+\infty)^{+\infty}$ therefore, the solution set is PRACTCE: Find the solution set of the following inequalitio (1) $x^{2}+9 x+14>0$ (2) $x^{2}+6 x \geq-5$

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Problem 2523

Thinking/Inquiry
1. Simplify each of the following. State all restrictions on variables. [6] a) $\frac{x-8}{x+7} \times \frac{x+15}{x^{2}+12 x-45}$ b) $\frac{x^{2}+12 x+20}{x+5} \div \frac{x^{2}+7 x-30}{x+10}$ d) $\frac{-10 x}{x^{2}+18 x+32}+\frac{12 x}{x^{2}+6 x-160}$ c) $\frac{3}{x^{2}+7 x+10}-\frac{5 x}{x^{2}-4}$ 4

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Problem 2524

Factor as the product of two binomials. $9-6 x+x^{2}=$

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Problem 2525

fact $\frac{(3 x+2)^{1 / 2}-(x+3)(3 x+2)^{-1 / 2}}{3 x+2}$ $\square$ Submit Answer

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Problem 2526

If the sum of three consecutive even integers is 90, what is the smallest of the three integers?

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Problem 2527

$\left[\begin{array}{cc}3 & -2 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right]$

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Problem 2528

$2|x-9|+10<6$

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Problem 2529

Solve for $p$ . $3.5-p=18$ $-14.5$ $-21.5$ 21.5 14.5

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Problem 2530

[3] 3. Given $f(x)=3 k-2 x$ , find the value of $k$ if $f^{-1}(5)=-2$ .

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Problem 2531

Explaining Linear Functions
Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

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Problem 2532

Factor out the greatest common factor.
1. $12 x^{7}+15 x^{5}-6 x^{2}$ $3 x^{2}\left(4 x^{5}+3 x^{3}-2\right)$
2. $2 x^{6}-4 x^{2}$ $2 x^{2}\left(x^{4}-2\right)$
3. $32 x^{6}-24 x^{3}+60 x^{2}$

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Problem 2533

4 Use the drawing tools to form the correct answer on the provided number line. Daniel is buying gas for his car. Gas costs $\$ 2.50$ per gallon. Daniel typically spends around $\$ 30$ to fill his gas tank, with a variance of up to $\$ 3$ . Write an inequality to model this [situation. Then use the inequality to display the range of possible gallons of gas that Daniel will buy.

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Problem 2534

What value of $y$ is a solution to ais a $61=7 y-16$ $y=11$ $y=12$

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Problem 2535

What is the equation of the line that passes through the point $(5,3)$ and has a slope of $\frac{3}{5}$ ?

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Problem 2536

$\qquad$
4. Find the constant $a$ that makes $f(x)$ a continuous functions. A. 0 B. 3 $f(x)=\left\{\begin{array}{cc} x^{2}-2 x+3, & x \leq 1 \\ a x^{2}+4 x-2, & x>1 \end{array}\right.$ C. 2 D. -2

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Problem 2537

The table represents a linear function. The rate of change between the points $(-5,10)$ and $(-4,5)$ is -5 . What is the rate of change between the points $(-3,0)$ and $(-2,-5)$ ? \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-5 & 10 \\ \hline-4 & 5 \\ \hline-3 & 0 \\ \hline-2 & -5 \\ \hline \hline \end{tabular} $-5$ $-\frac{1}{5}$ $\frac{1}{5}$ 5 Mark this and return Save and Exit Next Submit

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Problem 2538

Part A
Latoya puts soil in 7 flowerpots. How much potting soil remains? $\square$ pounds
Part B Part B
Latoya realizes that she actually has two 25-pound bags of potting soil. Write a new expression to represent the number of pounds of potting soil remaining after Latoya puts 3 pounds in each of $f$ flowerpots. $+-\times \div\left|\frac{\square}{\square} \quad \square \quad \sqrt{\square} \quad \sqrt{\square}\right|=\neq \leq \geq \mid \text { () } \mid \pi$ $\square$

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Problem 2539

Use the formula for ${ }_{n} C_{T}$ to evaluate the given expression. ${ }_{10} C_{7}$ ${ }_{10} C_{7}=$ $\square$ (Type an integer or a simplified fraction.)

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Problem 2540

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 2541

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -3 \\ \hline 2 & -2 \\ \hline 3 & -1 \\ \hline 4 & 0 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 2542

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & -5 \\ \hline 1 & -3 \\ \hline 3 & -1 \\ \hline 5 & 1 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

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Problem 2543

Directions: Solve each system of equations by graphing. Clearly identify your solution.
1. $y=\frac{1}{4} x+1$ $y=-x-9$
3. $3 x+7 y=-63$ $x-y=-1$
5. $-6 y=36-x$ $4 x-3 y=-3$
4. $3 x-2 y=10$ $x=2$
6. $-12 x=30 y+60$ $2 x+5 y=20$

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Problem 2544

Use the square root property to solve the equation. $x^{2}-5=0$

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Problem 2545

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & 17 \\ \hline 1 & -3 \\ \hline 5 & -23 \\ \hline 9 & -43 \\ \hline \end{tabular}
Answer $\square$ Submit Answer Forixey Policyl Permes of Sentice

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Problem 2546

Solve the following problem and select your answer from the choices given.
Question Under ideal conditions, the population of a certain species doubles every nine years. If the population starts with 100 individuals, which of the following expressions would give the population of the species $t$ years after the start, assuming that the population is living under ideal conditions? $2 \times 100^{9 t}$ $2 \times 100^{\frac{t}{9}}$ $100 \times 2^{9 t}$ $100 \times 2^{\frac{t}{9}}$

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Problem 2547

The graph of $y=f(x)$ is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 $y=-f(x)-2$ $y=-f(x+2)$ Submit Answer $y=-f(x-2)$ $y=-f(x)+2$

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Problem 2548

The graph of $y=f(x)$ is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 $y=-f(x+4)$ $y=-f(x)+4$ $y=-f(x)-4$ $y=-f(x-4)$

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Problem 2549

Suppose you win a small lottery that pays you $\$ 250$ every month for the next 6 months.
Further suppose that your personal beliefs are such that you believe the discount rate of future sums of money is $10 \%$ .
At month \#6, what will that final payment of $\$ 250$ be worth to you under your current financial perspective on the time value of money?

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Problem 2550

1) Find the slope of the line that passes through the following two points: $(-1,3) \quad 3(5,5)$

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Problem 2551

Numeric For the following exercises, evaluate the base $b$ logarithmic expression without using a calculator.
42. $\log _{3}\left(\frac{1}{27}\right)$
43. $\log _{6}(\sqrt{6})$
44. $\log _{2}\left(\frac{1}{8}\right)+4$
45. $6 \log _{8}(4)$

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Problem 2552

(2) 2. 2

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Problem 2553

Simplify the following expression. Assume that each variable is positive. $\frac{3-6 \sqrt{192 y^{3}}}{6}$

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Problem 2554

Find the unit vector that has the same direction as the vector $\mathbf{v}$ . $\mathbf{v}=-24 \mathbf{i}+7 \mathbf{j}$
The unit vector that has the same direction as the vector $\mathbf{v}$ is $\left(\frac{-24}{25}, \frac{7}{25}\right)$ . (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressio

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Problem 2555

PROBLEM I Solving a System of Equations by Graphing
What is the solution of the system? Use a graph. $y=x+2$ $y=3 x-2$
1. Graph both equations on Desmos.
2. How many solutions does this system have? (Choose one) a. One solution b. Infinitely many solutions c. No solution
3. If a solution exists, draw an arrow to the solution on your graph.
Draw graphs here: $c f b$

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Problem 2556

1. $x(x+3)(x-4)$
2. $\left(y^{2}+3 x-4\right)(2 y-3)$
3. $\left(3 x^{2}-4 x+2\right)(4 x-5)$
4. $\left(\frac{1}{2} x^{2}+4 x+8\right)(2 x-6)$
5. $\left(2 x^{2}+3 x+1\right)(5 x-4)$

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Problem 2557

Question Watch Video Show Examples
Moussa is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee is $\$ 25$ and the one-time joining fee is $\$ 100$ . Write an equation for $C$ , in terms of $t$ , representing the total cost of the gym membership over $t$ months.
Answer Attempt 1 out of 2 $C=$ $\square$ Submit Answer

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Problem 2558

$(2 \sqrt{3})^{-5}$

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Problem 2559

Solve the system using elimination. $\begin{aligned} 4 x+14 y & =32 \\ x-14 y & =-27 \end{aligned}$

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Problem 2560

ind the product. Simplify your answer. $7\left(-2 w^{2}-2 w-3\right)$

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Problem 2561

Your school's talent show will feature 12 solo acts and 2 ensemble acts. The show will last 92 minutes. The 6 solo performers judged best will give a repeat performance at a second 56 minute show, which will also feature the 2 ensemble acts. Each solo act lasts $x$ minutes, and each ensemble act lasts y minutes. Use this information to answer parts (a) and (b). b) Solve the system from part (a).

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Problem 2562

0.6 Multiply a polynomar
Find the product. simplify your answer. $-4\left(m^{2}-4 m+3\right)$

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Problem 2563

1. Identify the slope and $y$ -intercept in the linear equation $y=3 x-13$ $Y=M x+b \quad M=3 \quad b=-13$

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Problem 2564

Find the product. Simplify your answ $2 r\left(r^{2}-2 r-2\right)$

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Problem 2565

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\log _{7}(13-5)$

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Problem 2566

1) $b^{2}+8 \mathrm{~b}+12$ $3 \quad x^{2}+x-6$ $4 \quad a^{2}-6 a+8$ $5 \quad x^{4}-2 x^{2}-3$ $6 \quad y^{2}-5 y-6$ $7 \quad b^{2}-4 b-21$ $8 \quad x^{2}+x-2$ $9 \quad b^{2}+6 b-16$
11 $a^{2}+9 a+20$ $11 \quad b^{2}+7 b+12$ $12 \quad a^{4}-9 a^{2}+18$ $13 \quad b^{2}+2 b-24$ $14 a^{2}+6 a-16$ $(b+6)(b+2)$ $2 y^{2}-8 y-20$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $15 \quad a^{2}+7 a-30$ $16 \quad x^{2}-x-30$ $17 \quad b^{2}+10 b+9$ $18 a^{2}-9 a+14$ $19 \quad b^{2}-2 b+-15$ $20 \quad a^{2}-8 a+16$ $21 \quad y^{2}+2 y-35$ $22 \quad x^{2}-4 x-5$ $23 \quad y^{2}+12 y+36$ $24 \quad a^{2}-14 a+24$ $25 x^{2}-x-12$ $26 \quad b^{2}+b-2$ $27 \quad y^{2}-13 y+42$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$ $\qquad$
Name: Date $\qquad$ Clant $\qquad$
Factor each expression. Write the factors on the lines, then hiplight the trexes in the grid containing each factor. When you ars finished, writa the latters that ars formet by the highlighted boxes in order te ereatz a wort.

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Problem 2567

Line 1: $y=\frac{x}{2} x$
Line 2: $-3 x+2 y=0$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=x$
Line 2: $y=-\frac{1}{2} x-3$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=1$
Line 2: $y=-4$
This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution

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Problem 2568

Find the product Simplify your answer. $2 j^{j}(-4 j-4 j+3)$

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Problem 2569

$V(t o)=30 \mathrm{mi} / \mathrm{hr}$
A motorist enters a freeway at $30 \mathrm{mi} / \mathrm{h}$ and accelerates uniformly to $60 \mathrm{mi} / \mathrm{h}$ . From the odometer in the car, the motorist knows that she traveled 550 ft while accelerating. Determine ( $a$ ) the acceleration of the car, (b) the time required to reach $60 \mathrm{mi} / \mathrm{h}$ . a) Below, draw a figure showing the coordinate system used and labelling all of the Givens, as we did in class. Then, below the figure, list the Finds in variable form (as they are written in the equations below). है $\begin{array}{l} \frac{5280 \mathrm{Ft}}{36005} \\ 1 \mathrm{mi} / \mathrm{hr}=\frac{5280 \mathrm{ft}}{360} \\ \begin{array}{l} v\left(t_{0}\right)=30 \times \frac{5280}{3600} \mathrm{ft} / \mathrm{s} \\ 2(\mathrm{~A})=60 \times \frac{5280}{3} \mathrm{ft} / \mathrm{s} \end{array} \\ z(t)=60 \times \frac{5280}{3600} \mathrm{Ft} / \mathrm{s} \end{array}$ $\begin{array}{l} t^{t o 0 d s} \\ \text { 1. } v(t)^{2}=v\left(t_{0}\right)^{2}+2 a_{c}\left[x(t)-x\left(t_{0}\right)\right] \\ \text { 2. } v(t)=v\left(t_{0}\right)+a_{c}\left[t-t_{0}\right] \end{array}$ b) Based on the given info from part a above, develop a gameplan for your solution: On the equations below, write why you are using those equations and then write check marks above the variables that you know/are given, and draw a box around all the variables you have to Find. Write a circled " 1 " next to which equation you would solve first and a circled " 2 " next to the equation you would solve next, like I did in the class example. DO NOT SOLVE! CASE 2: $a(t)=$ constant $=a c$ $\qquad$ $v(t)^{2}=v\left(t_{o}\right)^{2}+2 a_{c}\left[x(t)-x\left(t_{o}\right)\right]$
CASE 3: $\mathrm{v}(\mathrm{t})=\mathrm{constant}=\mathrm{vc}$ $x(t)=x\left(t_{0}\right)+v_{C}\left[t-t_{0}\right] \quad a(t)=\frac{d v(t)}{d t}=\frac{d v_{C}}{d t}=0$

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Problem 2570

Find the equation of the axis of symmetry of the following parabola algebraically. $y=2 x^{2}+20 x+68$

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Problem 2571

Find the roots of the function $g(x) = -x^3 + 4x^2 - 2x - 2$ .

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Problem 2572

Задача 1. Коллинеарны ли векторы $\vec{c}$ и $\vec{d}$ , построенные по векторам $\vec{a}$ и $\vec{b}$ ? \begin{tabular}{|c|c|c|c|c|} \hline № & $\vec{a}$ & $\vec{b}$ & $\vec{c}$ & $\vec{d}$ \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline 9 & $(2,4,-6)$ & $(3,6,-2)$ & $2 \vec{a}-3 \vec{b}$ & $6 b-5 \vec{a}$ \\ \hline \end{tabular}

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Problem 2573

Line 1: $y=-3 x+4$
Line 2: $3 x+y=4$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=3 x-3$
Line 2: $y=3 x+2$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ $\square$ infinitely many solutions no solution
Line 1: $y=-2 x+1$ Line 2: $y=-\frac{1}{2} x+1$
This system of equations is: consistent independent consistent dependent inconsistent This means the system has: a unique solution Solution: $\square$ ( $\square$ $\square$ infinitely many solutions no solution

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Problem 2574

X-6X --6x+8 X-3X-10 X-X-12 NAME (X-2)-(X-4X Facto Ploce th are the boxes b X2-7X+12 X2-X-6 X²+2X-8 v258 th x²+3X-10 (X

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Problem 2575

$-8+\sqrt[3]{-4-x}=-6$

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Problem 2576

Find the unit vector that has the same direction as the vector $\mathbf{v}$ . $\mathbf{v}=8 \mathrm{j}$
The unit vector that has the same direction as the vector $\mathbf{v}$ is $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form ai + bj.)

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Problem 2577

Rewrite using a positive exponent. $c^{-9}$

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Problem 2578

4. The flight of an aircraft from Toronto to Montréal can be modelled by the relation $h=-2.5 t^{2}+200 t$ , where $t$ is the time, in minutes, and $h$ is the height, in metres. a) Graph the relation. b) How long does it take to fly from Toronto to Montréal? c) What is the maximum height of the aircraft? At what time does the aircraft reach this height? 4.3 Investigate Transformations of Quadratics, pages 174-179, and 4.4 Graph $y=a(x-h)^{2}+k$ , pages $180-188$
5 sketch the graph of each parabola. Describe

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Problem 2579

omplete the square to re-write the quadratic function in vertex form: $y=x^{2}+8 x-4$

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Problem 2580

Let $C=\left[\begin{array}{cc}7 & 7 \\ 4 & 4 \\ 3 & -1\end{array}\right]$ and $D=\left[\begin{array}{ccc}7 & -4 & 4 \\ 6 & 7 & -4 \\ 2 & 3 & 0\end{array}\right]$ . Find $C D$ if it is defined. Otherwise, click on "Undefined". $C D=$ $\square$

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Problem 2581

Find the remainder when the polynomial $P(x)=-4 x^{4}+2 x^{3}+5 x^{2}-2 x-1$ is divided by $x-1$ The remainder is

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Problem 2582

Question Wat
What is the product of $2 \sqrt{8}$ and $6 \sqrt{12}$ in simplest radical form?
Answer Attempt 1 out of 2 $\square$ Submit $\sqrt{ }$

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Problem 2583

Consider the following matrix. $A=\left[\begin{array}{ll} 3 & -2 \\ 9 & -6 \end{array}\right]$
Choose the correct description of $A$ . Find $A^{-1}$ if it exists. $A$ is nonsingular. That is, it has an inverse. $A^{-1}=$ $\square$ $A$ is singular. That is, its inverse doesn't exist.

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Problem 2584

Question Watch Vid
What is the product of 3 and $10 \sqrt{40}$ in simplest radical form?

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Problem 2585

Question Watch Video
Express as a fraction in simplest form with a rational denominator: $\frac{-3}{9-\sqrt{5}}$
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 2586

Simplify the complex fraction. Leave your answer in factored form when appropriate. $\frac{\frac{5 x+3}{x}}{\frac{x-9}{x}}$

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Problem 2587

Evaluate or simplify the expression without using a calculator. $\begin{array}{c} e^{\ln 4 x^{5}} \\ e^{\ln 4 x^{5}}= \end{array}$ $\square$

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Problem 2588

20) Choose the correct property of inequality.
For all expressions $a, b$ , and $c$ , If $a+b=c$ and $b>0$ , then $c>a$ . transitive addition comparison subtraction

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Problem 2589

Question Watch Video
Express as a fraction in simplest form with a rational denominator: $\frac{-9}{7+\sqrt{14}}$
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 2590

Question Watch Video
Express as a fraction in simplest form with a rational denominator: $\frac{-7}{-7-\sqrt{15}}$
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 2591

Question Solve for x : $\sqrt{7 x+113}+3=11$
Answer Attempt 1 out of 2 $x=$ $\square$ Sub

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Problem 2592

100\%
After the community clean-up, the ecology club collected all the empty drink containers. There were 40 more $5 申$ deposit containers than 10 \& deposit containers. If the club received $\$ 24.80$ from the recycling center, how many $5 \notin$ deposit containers did they have? A. 112 B. 125 C. 152 D. 165

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Problem 2593

Question
Solve for all possible values of x . $\sqrt{5 x+26}=x+6$
Answer Altempt 1 out of 2

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Problem 2594

4. Let's say you invest an amount now and leave it in the bank for 50 years.
WOULD YOU RATHER... - OPTION A - Invest $\$ 2000$ now, interest rate of $4 \%$ compounded annually - OPTION B - Invest $\$ 4000$ now, interest rate of $2 \%$ compounded annually

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Problem 2595

Question
Solve for all possible values of x . $\sqrt{3 x+18}=x+6$
Answer Attempt 1 out of 2 (†) Additional Solution No Solution

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Problem 2596

Function Operations and Inverses Graphing an absolute value equation in the plane: Advan
Graph the equation. $y=3|x+4|-5$

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Problem 2597

Question Watch
Solve for all possible values of x . $\sqrt{5 x+36}=x+8$
Answer Attempt 1 out of 2 () Additional Solution $\Theta$ No Solution $x=$ $\square$ Submit Ans

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Problem 2598

Question
Solve for x : $\sqrt{2 x+11}-11=-8$
Answer Attempt 1 out of 2 $x=$

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Problem 2599

Question
Solve for x : $\sqrt{6 x-41}+15=16$
Answer Attempt 1 out of 2 $x=$ $\square$

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Problem 2600

Question
Solve for x : $\sqrt{3 x+39}+6=12$

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Algebra

Problem 2501

8. (x−5)3+4x=7\frac{(x-5)}{3}+4 x=73(x−5)​+4x=7

Problem 2502

Graph the quadratic equation in desmos, then determine if the vertex is a maximum or minimum. * 1 point 5) Maximum or Minimum? y=−x2+3x−4y=-x^{2}+3 x-4y=−x2+3x−4 A) Maximum B) Minimum AAA BBB

Problem 2503

2. x3+3x2−4x−12=0x^{3}+3 x^{2}-4 x-12=0x3+3x2−4x−12=0

Problem 2504

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width, what is the largest possible length? Write an equation and solve. (2w+3)4=60;15(2 w+3) 4=60 ; 15(2w+3)4=60;15

Problem 2505

1. x3−3x2−13x+15=0x^{3}-3 x^{2}-13 x+15=0x3−3x2−13x+15=0

Problem 2506

3+x−7=0\frac{3+x}{-7}=0−73+x​=0

Problem 2507

x4+2x3−8x2−18x−9=0x^{4}+2 x^{3}-8 x^{2}-18 x-9=0x4+2x3−8x2−18x−9=0

Problem 2508

2x3−3x2−5x+6=02 x^{3}-3 x^{2}-5 x+6=02x3−3x2−5x+6=0

Problem 2509

3x3−4x2−17x+6=03 x^{3}-4 x^{2}-17 x+6=03x3−4x2−17x+6=0

Problem 2510

P(x)=x3+6x2+11x+6,x1=−3P(x)=x^{3}+6 x^{2}+11 x+6 \quad, x_{1}=-3P(x)=x3+6x2+11x+6,x1​=−3

Problem 2511

P(x)=3x4−16x3+21x2+4x−12,x1=−2/3P(x)=3 x^{4}-16 x^{3}+21 x^{2}+4 x-12 \quad, x_{1}=-2 / 3P(x)=3x4−16x3+21x2+4x−12,x1​=−2/3

Problem 2512

P(x)=2x3−15x2+27x−10x1=5P(x)=2 x^{3}-15 x^{2}+27 x-10 \quad x_{1}=5P(x)=2x3−15x2+27x−10x1​=5

Problem 2513

Problem 2514

me: \qquad plication Date: \qquad1. Determine the inverse of following relation and state the domain and range of f(x)f(x)f(x) as well as its inverse. Show all work. Is the inverse a function? f(x)=(x−4)2+6f(x)=(x-4)^{2}+6f(x)=(x−4)2+6

Problem 2515

Determine the inverse of the function given in the graph. The points are (−3,4)(-3, 4)(−3,4), (1,−1)(1, -1)(1,−1), (2,3)(2, 3)(2,3), (4,3)(4, 3)(4,3).

Problem 2516

Solve the following equation (y−2)(y+1)=−2y(y-2)(y+1)=-2 y(y−2)(y+1)=−2y

Problem 2517

Problem 2518

Using Thevenin's theorem, calculate the current flowing through a 10Ω10 \Omega10Ω resistor in the figure below.

Problem 2519

Problem 2520

(4y+5)(5y−1)=0(4 y+5)(5 y-1)=0(4y+5)(5y−1)=0

Problem 2521

[6] 2. Given the equation f(x)=−3∣2(x−1)∣+4\quad f(x)=-3|2(x-1)|+4f(x)=−3∣2(x−1)∣+4 a) State the parent function: \qquad c) Graph the function, showing the original an graph. Label all point final clearly b) Show transformation of 5 points of your choice:

Problem 2522

+∞)+∞+\infty)^{+\infty}+∞)+∞ therefore, the solution set is PRACTCE: Find the solution set of the following inequalitio (1) x2+9x+14>0x^{2}+9 x+14>0x2+9x+14>0 (2) x2+6x≥−5x^{2}+6 x \geq-5x2+6x≥−5

Problem 2523

Problem 2524

Factor as the product of two binomials. 9−6x+x2=9-6 x+x^{2}=9−6x+x2=

Problem 2525

fact (3x+2)1/2−(x+3)(3x+2)−1/23x+2\frac{(3 x+2)^{1 / 2}-(x+3)(3 x+2)^{-1 / 2}}{3 x+2}3x+2(3x+2)1/2−(x+3)(3x+2)−1/2​ □\square□ Submit Answer

Problem 2526

If the sum of three consecutive even integers is 90, what is the smallest of the three integers?

Problem 2527

[3−201][1−111]\left[\begin{array}{cc}3 & -2 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right][30​−21​][11​−11​]

Problem 2528

2∣x−9∣+10<62|x-9|+10<62∣x−9∣+10<6

Problem 2529

Solve for ppp. 3.5−p=183.5-p=183.5−p=18 −14.5-14.5−14.5 −21.5-21.5−21.5 21.5 14.5

Problem 2530

[3] 3. Given f(x)=3k−2xf(x)=3 k-2 xf(x)=3k−2x, find the value of kkk if f−1(5)=−2f^{-1}(5)=-2f−1(5)=−2.

Problem 2531

Explaining Linear FunctionsGiven a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

Problem 2532

Problem 2533

Problem 2534

What value of yyy is a solution to ais a 61=7y−1661=7 y-1661=7y−16 y=11y=11y=11 y=12y=12y=12

Problem 2535

What is the equation of the line that passes through the point (5,3)(5,3)(5,3) and has a slope of 35\frac{3}{5}53​ ?

Problem 2536

\qquad4. Find the constant aaa that makes f(x)f(x)f(x) a continuous functions. A. 0 B. 3 f(x)={x2−2x+3,x≤1ax2+4x−2,x>1f(x)=\left\{\begin{array}{cc} x^{2}-2 x+3, & x \leq 1 \\ a x^{2}+4 x-2, & x>1 \end{array}\right.f(x)={x2−2x+3,ax2+4x−2,​x≤1x>1​ C. 2 D. -2

Problem 2537

Problem 2538

Problem 2539

Use the formula for nCT{ }_{n} C_{T}n​CT​ to evaluate the given expression. 10C7{ }_{10} C_{7}10​C7​ 10C7={ }_{10} C_{7}=10​C7​= □\square□ (Type an integer or a simplified fraction.)

Problem 2540

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}Answer □\square□ Submit Answer

Problem 2541

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline 1 & -3 \\ \hline 2 & -2 \\ \hline 3 & -1 \\ \hline 4 & 0 \\ \hline \end{tabular}Answer □\square□ Submit Answer

Problem 2542

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline-1 & -5 \\ \hline 1 & -3 \\ \hline 3 & -1 \\ \hline 5 & 1 \\ \hline \end{tabular}Answer □\square□ Submit Answer

Problem 2543

Problem 2544

Use the square root property to solve the equation. x2−5=0x^{2}-5=0x2−5=0

8. $\frac{(x-5)}{3}+4 x=7$

Graph the quadratic equation in desmos, then determine if the vertex is a maximum or minimum. * 1 point 5) Maximum or Minimum? $y=-x^{2}+3 x-4$ A) Maximum B) Minimum $A$ $B$

2. $x^{3}+3 x^{2}-4 x-12=0$

Katie wants to create a rectangular frame for a picture. She has 60 inches of material. If she wants the length to be 3 more than 2 times the width, what is the largest possible length? Write an equation and solve. $(2 w+3) 4=60 ; 15$

1. $x^{3}-3 x^{2}-13 x+15=0$

$\frac{3+x}{-7}=0$

$x^{4}+2 x^{3}-8 x^{2}-18 x-9=0$

$2 x^{3}-3 x^{2}-5 x+6=0$

$3 x^{3}-4 x^{2}-17 x+6=0$

$P(x)=x^{3}+6 x^{2}+11 x+6 \quad, x_{1}=-3$

$P(x)=3 x^{4}-16 x^{3}+21 x^{2}+4 x-12 \quad, x_{1}=-2 / 3$

$P(x)=2 x^{3}-15 x^{2}+27 x-10 \quad x_{1}=5$

me: $\qquad$ plication Date: $\qquad$
1. Determine the inverse of following relation and state the domain and range of $f(x)$ as well as its inverse. Show all work. Is the inverse a function? $f(x)=(x-4)^{2}+6$

Determine the inverse of the function given in the graph. The points are $(-3, 4)$ , $(1, -1)$ , $(2, 3)$ , $(4, 3)$ .

Solve the following equation $(y-2)(y+1)=-2 y$

Using Thevenin's theorem, calculate the current flowing through a $10 \Omega$ resistor in the figure below.

$(4 y+5)(5 y-1)=0$

[6] 2. Given the equation $\quad f(x)=-3|2(x-1)|+4$ a) State the parent function: $\qquad$ c) Graph the function, showing the original an graph. Label all point final clearly b) Show transformation of 5 points of your choice:

$+\infty)^{+\infty}$ therefore, the solution set is PRACTCE: Find the solution set of the following inequalitio (1) $x^{2}+9 x+14>0$ (2) $x^{2}+6 x \geq-5$

Factor as the product of two binomials. $9-6 x+x^{2}=$

fact $\frac{(3 x+2)^{1 / 2}-(x+3)(3 x+2)^{-1 / 2}}{3 x+2}$ $\square$ Submit Answer

$\left[\begin{array}{cc}3 & -2 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right]$

$2|x-9|+10<6$

Solve for $p$ . $3.5-p=18$ $-14.5$ $-21.5$ 21.5 14.5

[3] 3. Given $f(x)=3 k-2 x$ , find the value of $k$ if $f^{-1}(5)=-2$ .

Explaining Linear Functions
Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

What value of $y$ is a solution to ais a $61=7 y-16$ $y=11$ $y=12$

What is the equation of the line that passes through the point $(5,3)$ and has a slope of $\frac{3}{5}$ ?

$\qquad$
4. Find the constant $a$ that makes $f(x)$ a continuous functions. A. 0 B. 3 $f(x)=\left\{\begin{array}{cc} x^{2}-2 x+3, & x \leq 1 \\ a x^{2}+4 x-2, & x>1 \end{array}\right.$ C. 2 D. -2

Use the formula for ${ }_{n} C_{T}$ to evaluate the given expression. ${ }_{10} C_{7}$ ${ }_{10} C_{7}=$ $\square$ (Type an integer or a simplified fraction.)

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -9 \\ \hline 2 & -13 \\ \hline 3 & -17 \\ \hline 4 & -21 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & -3 \\ \hline 2 & -2 \\ \hline 3 & -1 \\ \hline 4 & 0 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-1 & -5 \\ \hline 1 & -3 \\ \hline 3 & -1 \\ \hline 5 & 1 \\ \hline \end{tabular}
Answer $\square$ Submit Answer

Use the square root property to solve the equation. $x^{2}-5=0$

Find the equation of the linear function represented by the table below in slope-intercept form. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & 17 \\ \hline 1 & -3 \\ \hline 5 & -23 \\ \hline 9 & -43 \\ \hline \end{tabular}
Answer $\square$ Submit Answer Forixey Policyl Permes of Sentice

The graph of $y=f(x)$ is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 $y=-f(x)-2$ $y=-f(x+2)$ Submit Answer $y=-f(x-2)$ $y=-f(x)+2$

The graph of $y=f(x)$ is the solid black graph below. Which function represents the dotted graph?
Answer Attempt 1 out of 3 $y=-f(x+4)$ $y=-f(x)+4$ $y=-f(x)-4$ $y=-f(x-4)$

1) Find the slope of the line that passes through the following two points: $(-1,3) \quad 3(5,5)$

Simplify the following expression. Assume that each variable is positive. $\frac{3-6 \sqrt{192 y^{3}}}{6}$

$(2 \sqrt{3})^{-5}$

Solve the system using elimination. $\begin{aligned} 4 x+14 y & =32 \\ x-14 y & =-27 \end{aligned}$

ind the product. Simplify your answer. $7\left(-2 w^{2}-2 w-3\right)$

0.6 Multiply a polynomar
Find the product. simplify your answer. $-4\left(m^{2}-4 m+3\right)$

1. Identify the slope and $y$ -intercept in the linear equation $y=3 x-13$ $Y=M x+b \quad M=3 \quad b=-13$

Find the product. Simplify your answ $2 r\left(r^{2}-2 r-2\right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. $\log _{7}(13-5)$

Find the product Simplify your answer. $2 j^{j}(-4 j-4 j+3)$

Find the equation of the axis of symmetry of the following parabola algebraically. $y=2 x^{2}+20 x+68$

Find the roots of the function $g(x) = -x^3 + 4x^2 - 2x - 2$ .