Algebra

Problem 27501

Study this table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & -2 \\ \hline-2 & 0 \\ \hline 0 & 4 \\ \hline 4 & 12 \\ \hline \hline \end{tabular}
Which best describes the function represented by the data in the table? linear with a common ratio of 2 linear with a common first difference of 2 quadratic with a common ratio of 2 quadratic with a common first difference of 2

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Problem 27502

Find the value of $(f \circ g)(2)$ $f(x) = 5x + 2$ and $g(x) = 3x - 4$

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Problem 27503

$(cd)^{-\frac{1}{3}}$ Simplify. Assume all variables Write your answer in the that have no variables in

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Problem 27504

```latex \textbf{Aufgabe 1}
\begin{enumerate} \item[a)] Stelle eine Exponentialfunktion auf, welche die Summe der weltweiten Exporte seit 1948 beschreibt. \item[b)] Wie hoch waren die US-Exporte im Jahr 1983? \item[c)] Begründe, warum die Grafik mit „Explosives Wachstum" überschrieben ist. \item[d)] \textit{In welchem Jahr erreichten die US-Exporte erstmals die Höhe von 10.000 Mrd. US-\$?} \end{enumerate}
\textbf{Explosives Wachstum}
Summe der weltweiten Exporte in Mrd. US-\$
\textbf{Zusätzliche Informationen:}
Es steht, dass es im Jahr 1948 59 waren und im Jahr 2010 14851.

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Problem 27505

14. For each quadratic relation, i) write the equation in factored form ii) determine the coordinates of the vertex iii) write the equation in vertex form iv) sketch the graph
a) $y = x^2 - 8x + 15$ b) $y = 2x^2 - 8x - 64$ c) $y = -4x^2 - 12x + 7$

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Problem 27506

Solve $(w+1)^{2}-75=0$ , where $w$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with cor If there is no solution, click "No solution." $w=$

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Problem 27507

8. $y = -\frac{3}{2}x - 4$

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Problem 27508

Divide. $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}$ $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=$ $\square$ (Simplify your answer.)

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Problem 27509

$3\sqrt[4]{6y^4} \cdot 9\sqrt[4]{35x^4y^4}$

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Problem 27510

Find the solution of the exponential equation. (Enter your answers as a comn $\begin{array}{l} 6^{4 x-5}=6^{4+7 x} \\ x=\frac{9}{11} \end{array}$ Need Help? Watch It

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Problem 27511

Solve the equation. Show all work $5(x+1)=9 x+3-3 x$

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Problem 27512

*E12.11 (LO 4), AP K. Kolmer, C. Eidman, and C. Ryno share income on a 5:3:2 basis. They have capital balances of $\$ 34,000, \$ 26,000$ , and $\$ 21,000$ , respectively, when Do Jernigan is admitted to the partnership. Instructions Prepare the journal entry to record the admission of Don Jernigan under each of the following assumptions. a. Don Jernigan purchases $50 \%$ of Kolmer's equity for \ $19,000. b. Don Jernigan purchases$ 50 \% $of Eidman's equity for \$12,000. c. Don Jernigan purchases$ 33 \%$ of Ryno's equity for \$9,000.
Journalize admission of a new partner by investment.

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Problem 27513

2. $3(x+1)^{2}-3=0$ . .xis of symmetry: Vertex: Solution(s):

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Problem 27514

$3 x-4=12$

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Problem 27515

Evaluate the expression $(-6+7 i)+(-8-1 i)$ and write the result in the form $a+b i$ . The real number $a$ equals $\square$ The real number $b$ equals $\square$

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Problem 27516

To calculate the enthalpy change ( $\Delta \mathrm{H}$ ) for the reaction:
$\mathrm{CO} + 2 \mathrm{H}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{OH}$
using the bond energies provided from Tables 7.2 and 7.3, we need to determine the bonds broken and formed during the reaction.
Bonds Broken: - 1 C≡O bond in CO (bond energy = 1080 kJ/mol) - 2 H-H bonds in 2 H₂ (bond energy = 436 kJ/mol each)
Bonds Formed: - 1 C-O bond in CH₃OH (bond energy = 350 kJ/mol) - 3 C-H bonds in CH₃OH (bond energy = 415 kJ/mol each) - 1 O-H bond in CH₃OH (bond energy = 464 kJ/mol)
Calculate the enthalpy change ( $\Delta \mathrm{H}$ ) for the reaction using the bond energies:
$\Delta \mathrm{H} = \text{(Sum of bond energies of bonds broken)} - \text{(Sum of bond energies of bonds formed)}$
$\Delta \mathrm{H} = \left(1080 + 2 \times 436\right) - \left(350 + 3 \times 415 + 464\right)$
Calculate the value of $\Delta \mathrm{H}$ in kJ/mol.
$\square$ kJ/mol

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Problem 27517

For numbers 3-6, simplify.
3. $\sqrt{-32}$ $32 / i$

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Problem 27518

Solve the compound or inequality. $2 x+7<3 \text { or } 7+x>9$
The solution set of the compound inequality is $\square$ (Type your answer in interval notation.)

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Problem 27519

The population of Adamsville grew from 10,000 to 17,000 in 5 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years? The expected population is 21,020.

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Problem 27520

Solve the compound and inequality. $2(x+2)-3>5 \text { and } 3(2 x+1)+2<11$
Select the correct choice below and, if necessary, fill in the answer box to complete $y$ A. The solution set is $\square$

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Problem 27521

iny solutions. Show your work $93+12 x=3(1-4 x)+96$

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Problem 27522

15. If $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a linear transformation such that $T\left[\begin{array}{l} 1 \\ 4 \end{array}\right]=\left[\begin{array}{r} -2 \\ 22 \end{array}\right] \quad \text { and } \quad T\left[\begin{array}{r} 2 \\ -3 \end{array}\right]=\left[\begin{array}{r} 18 \\ -11 \end{array}\right]$ find the matrix that induces this transformation.

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Problem 27523

Question 1 (Mandatory) (1 point) An amusement park usually charges $\$34$ per ticket, but wants to raise the price by $\$1$ per ticket. The revenue that could be generated is modelled by the function $R(x) = -125(x-12)^2 + 35\,000$ , where $x$ is the number of $\$1$ increases and the revenue, $R(x)$ , is in dollars. What should the ticket price be if the park wants to earn $\$15\,000$ ?

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Problem 27524

Write an equation to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $-1, 2, -4, \dots$ Write your answer using decimals and integers. $a_n = \boxed{\phantom{0}}\left(\boxed{\phantom{0}}\right)^{n-1}$

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Problem 27525

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function $P(x) = -22.5x^2 + 428x + 1100$ , where x is the number of years since 1990. According to the model, when will the population be the highest?

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Problem 27526

Find the x- and y-intercepts of the graph of $7x + 7y = 21$ . State each answer as an integer or an improper fraction in simplest form. x-intercept: y-intercept:

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Problem 27527

Question 4 (Mandatory) (1 point) Determine the values of $a$ , $h$ , and $k$ that make the equation. $-3x^2 + 9x - 6 = a(x - h)^2 + k$ .

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Problem 27528

Question 5 (Mandatory) (1 point)
Identify the values of $a$ , $b$ , and $c$ you would use to substitute into the quadratic formula to solve $14x + 20x^2 = 17x - 25$ .

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Problem 27529

Question 6 (Mandatory) (1 point) A rocket is launched into the sky and follows a path modelled by the function $h(t) = -5(t-6.32)^2 + 200$ , where time, $t$ , is in seconds and height, $h(t)$ , is in metres. Approximately how high will the rocket be after 9 seconds?

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Problem 27530

6. Friction does $-400 \text{ J}$ of net work on a moving car. How does this affect the kinetic energy of the car? a. The kinetic energy increases by $400 \text{ J}$ . b. The kinetic energy decreases by $400 \text{ J}$ . c. The kinetic energy decreases by $160 \text{ kJ}$ . d. The kinetic energy does not change.
7. Which of the following does not affect gravitational potential energy? a. an object's mass b. an object's height relative to a zero level c. the free-fall acceleration d. an object's speed
8. How does the elastic potential energy in a mass-spring system change if the displacement of the mass is doubled? a. The elastic potential energy decreases to half its original value. b. The elastic potential energy doubles. c. The elastic potential energy increases or decreases by a factor of 4. d. The elastic potential energy does not change.
9. Which has more kinetic energy, a $4.0 \text{ kg}$ bowling ball moving at $1.0 \text{ m/s}$ or a $1.0 \text{ kg}$ bocce ball moving at $4.0 \text{ m/s}$ ? Explain your answer.

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Problem 27531

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

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Problem 27532

Paragraph Styles
14. A 20.0 g piece of clay moves with a constant speed of $15.0 \mathrm{~m} / \mathrm{s}$ . The piece of clay collides and sticks to a massive ball of mass 0.900 kg suspended at the end of a string. a. Calculate the momentum of the piece of clay before the collision. b. Calculate the kinetic energy of the piece of clay before the collision. c. What is the momentum of the two objects after the collision? d. Calculate the velocity of the combination of the two objects after the collision. e. Calculate the kinetic energy of the combination of two objects after the collision. f. Calculate the change in kinetic energy during the collision. g. Calculate the maximum vertical height of the combination of the two objects after the collision.

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Problem 27533

Question 8 (Mandatory) (1 point) Use the quadratic formula to solve $-6x^2 + 5x + 8 = 0$ . Round your answer to two decimal places.

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Problem 27534

Question 9 (Mandatory) (1 point) What is the factored form of $x^2 + 2x + 1$

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Problem 27535

Question 10 (Mandatory) (1 point) Which equation represents $y = -2x^2 - 12x - 7$ in vertex form?

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Problem 27536

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of $f(x) = 4x^2 - 8x + 11$ without graphing the parabola.

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Problem 27537

Question 12 (Mandatory) (1 point)
What number must you add to $x^2 + 12x$ to create a perfect square?

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Problem 27538

Given the demand equation $Qdy = 200 - 2P_y + 3P_x$ , determine if goods $X$ and $Y$ are substitutes or complements.

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Problem 27539

Solve the equations: $2 \sqrt{x+8}=4$ , $\sqrt{3 x+6}-9=0$ , and $\frac{2 \sqrt{2 x-8}}{4}=\sqrt{2 x+6}=\sqrt{-2 x+15}$ .

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Problem 27540

Find $f(99)$ given the function $f(x)=5-\frac{x}{99}$ .

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Problem 27541

How many grams of calcium carbonate are required to produce 2.2 grams of carbon dioxide from the reaction?

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Problem 27542

Find the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

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Problem 27543

Find the wavelength of a photon with energy $6.89 \times 10^{-19} \mathrm{~J}$ .

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Problem 27544

Find the energy of a photon with a wavelength of $999 \mu \mathrm{m}$ .

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Problem 27545

How many photons are in a laser pulse with energy $7.53 \mathrm{~mJ}$ at a wavelength of $601 \mathrm{~nm}$ ? Use 3 sig figs.

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Problem 27546

How many photons are in a laser pulse with energy $5.56 \mathrm{~mJ}$ at a wavelength of $401 \mathrm{~nm}$ ? Use 3 sig figs.

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Problem 27547

Calculate the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Report your answer in scientific notation to 3 sig figs.

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Problem 27548

Find the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Round to 3 significant figures, use scientific notation if needed.

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Problem 27549

How much energy is in 2.50 mol of UV light at $235 \mathrm{~nm}$ ?

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Problem 27550

How much energy is in $2.50 \mathrm{~mol}$ of UV light at $235 \mathrm{~nm}$ ?

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Problem 27551

Calculate the number of photons in a laser pulse with energy $5.98 \mathrm{~mJ}$ and wavelength $675 \mathrm{~nm}$ .

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Problem 27552

Calculate $6(n-4)$ for $n=6$ .

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Problem 27553

Solve for $a$ in the equation $a+(a+4)+(2 a-3)=13$ .

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Problem 27554

Solve the equation $2(y-3)=12$ for $y$ .

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Problem 27555

Solve for $m$ in the equation $8(m-1)=8$ .

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Problem 27556

Solve for $x$ in the equation: $-2(4x - 3) = -14$ .

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Problem 27557

Solve for $x$ in the equation $5 = x + 2 \frac{1}{3}$ .

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Problem 27558

Simplify the expression: $\frac{1+\frac{1}{x+7}}{1-\frac{1}{x+7}}$ .

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Problem 27559

Solve the equations: A. $-5 t=30$ , B. $2 x=14$ , C. $\frac{x}{7}=-4$ , D. $\frac{3}{5} p=12$ .

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Problem 27560

Solve for $b$ in the equation: $b - 3.12 = 5.23$ .

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Problem 27561

Solve the equation for x: $2 x = 14$ .

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Problem 27562

Solve for $t$ in the equation $-5t = 30$ .

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Problem 27563

Solve for $p$ in the equation $\frac{3}{5} p=12$ .

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Problem 27564

Solve for $s$ in the equation $\frac{s}{5}=10$ .

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Problem 27565

Find the number such that $\frac{30}{x} = 6$ .

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Problem 27566

Find the number $c$ such that $9c = 27$ .

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Problem 27567

Solve for $j$ in the equation $\frac{j+2}{6}=1$ .

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Problem 27568

Solve for n in the equation: $\frac{2 n+8}{3}-8=32$ .

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Problem 27569

Solve the equation: $-4(r-2)+6r=36$ .

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Problem 27570

Solve the equation: $3p + 7 - 2p + 5 = -1$

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Problem 27571

Find three consecutive integers whose sum is 132. What are the integers?

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Problem 27572

Solve for $x$ in the equation $\frac{2}{3} x + 6 = 26$ .

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Problem 27573

Kelsey bought roses and tulips, with tulips being twice the number of roses. Roses cost \$5 each, tulips \$2 each, total \$36. Write an equation.

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Problem 27574

Find the GCF of the polynomial $4 x^{4}+12 x^{3}-36 x^{2}+24 x$ . Options: $2 x$ , $6 x$ , 4, $4 x$ .

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Problem 27575

Find another factor of $x^{3}-5 x^{2}+6 x$ if one factor is linear. Options: $x+3$ , $x-2$ , $x+2$ , $x^{2}+5 x+6$ .

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Problem 27576

Find the complete set of solutions for $3 x^{3}+9 x^{2}-54 x=0$ : $0,3,-6$ , $0$ , no solutions, or $0,-3,6$ .

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Problem 27577

Which pattern helps factor $16 x^{8}-49 x^{2}$ ? Options: difference of squares, perfect squares, or neither.

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Problem 27578

Factor the polynomial $50 x^{5}-32 x=0$ and find the solutions for $x$ .

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Problem 27579

Graph the piecewise function $f(x)=\left\{\begin{aligned} x, & x<\frac{1}{2} \\ 3 x-1, & x \geq \frac{1}{2} .\end{aligned}\right.$ and find its domain and range.

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Problem 27580

Solve for $x$ : $(x+2)^{7/5} = 128$ . What is $x$ ?

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Problem 27581

Solve $\sqrt{t}+3=\sqrt{t+9}$ . Find $t$ as an integer or simplified fraction A/B.

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Problem 27582

Solve for $k$ in the equation: $k^{2}-16=6 k^{3}-96 k$ . Provide integer or simplified fraction solutions, separated by commas.

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Problem 27583

Solve for x in the equation: $-8-9|9x+6|=73$ .

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Problem 27584

Solve by factoring: $5 x^{3}-10 x^{2}-75 x=0$ . Find all real solutions: $x=$ .

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Problem 27585

Solve for $x$ : $3 - 5|7x - 6| = -7$ . If there are two solutions, list them as $a, b$ .

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Problem 27586

Solve for $k$ in the equation: $k^{2}-16=6 k^{3}-96 k$ . What are the real solutions?
$k=$

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Problem 27587

Solve $\log _{a}(5 x+14 a)+1=2 \log _{a} x-\log _{x} 1$ for $x$ in terms of $a$ .

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Problem 27588

Identify the linear function from these equations: $y=x^{2}$ , $y=2x+4$ , $y=4x^{3}+1$ , $y=2x^{2}-5$ .

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Problem 27589

Write the equation for the function where $y$ is 7 more than 9 times $x$ : $y = 9x + 7$ .

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Problem 27590

Identify the linear function among these equations: $y=2 x^{2}$ , $y=-4 x+5$ , $y=-3 x^{2}+2$ , $y=x^{3}$ .

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Problem 27591

Solve the inequality $(x-3)(x-4)(x-5) \leq 0$ and list intervals with their signs in interval notation.

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Problem 27592

Solve the inequality $(x-5)(x-6)(x-7) \geq 0$ and list intervals with signs in each interval using interval notation.

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Problem 27593

Solve the inequality $(x-6)(x-7)(x-8) \geq 0$ and list intervals with signs in interval notation.

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Problem 27594

Solve the inequality: $(x-4)(x-5)(x-6) \geq 0$ . Provide the solution in interval notation.

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Problem 27595

Solve the inequality $(x-1)(x-2)(x-3) \geq 0$ and list intervals with signs in each. Use interval notation.

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Problem 27596

Solve the inequality: $(x-4)(x-5)(x-7) \leq 0$ . Provide the solution in interval notation.

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Problem 27597

Solve the inequality: $(x-3)(x-4)(x-5) \geq 0$ . List intervals and signs in each interval using interval notation.

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Problem 27598

Solve the inequality $(x-6)(x-7)(x-8) \geq 0$ and list intervals with signs in interval notation.

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Problem 27599

Find the middle number of three consecutive integers with a sum of $3n$ . If none exists, write $\varnothing$ .

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Problem 27600

Brian spent \$5.50 on a CD player from \$12.80. Which inequality helps find the number of \$0.75 CDs he can buy?

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Algebra

Problem 27501

Problem 27502

Find the value of (f∘g)(2)(f \circ g)(2)(f∘g)(2) f(x)=5x+2f(x) = 5x + 2f(x)=5x+2 and g(x)=3x−4g(x) = 3x - 4g(x)=3x−4

Problem 27503

(cd)−13 (cd)^{-\frac{1}{3}} (cd)−31​ Simplify. Assume all variables Write your answer in the that have no variables in

Problem 27504

Problem 27505

Problem 27506

Solve (w+1)2−75=0(w+1)^{2}-75=0(w+1)2−75=0, where www is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with cor If there is no solution, click "No solution." w=w=w=

Problem 27507

8. y=−32x−4y = -\frac{3}{2}x - 4y=−23​x−4

Problem 27508

Divide. 37x2−q÷2121x2−3q\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}7x2−q3​÷21x2−3q21​ 37x2−q÷2121x2−3q=\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=7x2−q3​÷21x2−3q21​= □\square□ (Simplify your answer.)

Problem 27509

36y44⋅935x4y443\sqrt[4]{6y^4} \cdot 9\sqrt[4]{35x^4y^4}346y4​⋅9435x4y4​

Problem 27510

Find the solution of the exponential equation. (Enter your answers as a comn 64x−5=64+7xx=911\begin{array}{l} 6^{4 x-5}=6^{4+7 x} \\ x=\frac{9}{11} \end{array}64x−5=64+7xx=119​​ Need Help? Watch It

Problem 27511

Solve the equation. Show all work 5(x+1)=9x+3−3x5(x+1)=9 x+3-3 x5(x+1)=9x+3−3x

Problem 27512

Problem 27513

2. 3(x+1)2−3=03(x+1)^{2}-3=03(x+1)2−3=0 . .xis of symmetry: Vertex: Solution(s):

Problem 27514

3x−4=123 x-4=123x−4=12

Problem 27515

Evaluate the expression (−6+7i)+(−8−1i)(-6+7 i)+(-8-1 i)(−6+7i)+(−8−1i) and write the result in the form a+bia+b ia+bi. The real number aaa equals □\square□ The real number bbb equals □\square□

Problem 27516

Problem 27517

For numbers 3-6, simplify.3. −32\sqrt{-32}−32​ 32/i32 / i32/i

Problem 27518

Solve the compound or inequality. 2x+7<3 or 7+x>92 x+7<3 \text { or } 7+x>92x+7<3 or 7+x>9The solution set of the compound inequality is □\square□ (Type your answer in interval notation.)

Problem 27519

The population of Adamsville grew from 10,000 to 17,000 in 5 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years? The expected population is 21,020.

Problem 27520

Solve the compound and inequality. 2(x+2)−3>5 and 3(2x+1)+2<112(x+2)-3>5 \text { and } 3(2 x+1)+2<112(x+2)−3>5 and 3(2x+1)+2<11Select the correct choice below and, if necessary, fill in the answer box to complete yyy A. The solution set is □\square□

Problem 27521

iny solutions. Show your work 93+12x=3(1−4x)+9693+12 x=3(1-4 x)+9693+12x=3(1−4x)+96

Problem 27522

Problem 27523

Problem 27524

Problem 27525

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function P(x)=−22.5x2+428x+1100P(x) = -22.5x^2 + 428x + 1100P(x)=−22.5x2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?

Problem 27526

Find the x- and y-intercepts of the graph of 7x+7y=217x + 7y = 217x+7y=21. State each answer as an integer or an improper fraction in simplest form. x-intercept: y-intercept:

Problem 27527

Question 4 (Mandatory) (1 point) Determine the values of aaa, hhh, and kkk that make the equation. −3x2+9x−6=a(x−h)2+k-3x^2 + 9x - 6 = a(x - h)^2 + k−3x2+9x−6=a(x−h)2+k.

Problem 27528

Question 5 (Mandatory) (1 point)Identify the values of aaa, bbb, and ccc you would use to substitute into the quadratic formula to solve 14x+20x2=17x−2514x + 20x^2 = 17x - 2514x+20x2=17x−25.

Problem 27529

Problem 27530

Problem 27531

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, xxx, for a given value of the dependent variable, f(x)f(x)f(x), then substitute the number in for

Problem 27532

Problem 27533

Question 8 (Mandatory) (1 point) Use the quadratic formula to solve −6x2+5x+8=0-6x^2 + 5x + 8 = 0−6x2+5x+8=0. Round your answer to two decimal places.

Problem 27534

Question 9 (Mandatory) (1 point) What is the factored form of x2+2x+1x^2 + 2x + 1x2+2x+1

Problem 27535

Question 10 (Mandatory) (1 point) Which equation represents y=−2x2−12x−7y = -2x^2 - 12x - 7y=−2x2−12x−7 in vertex form?

Problem 27536

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of f(x)=4x2−8x+11f(x) = 4x^2 - 8x + 11f(x)=4x2−8x+11 without graphing the parabola.

Problem 27537

Question 12 (Mandatory) (1 point)What number must you add to x2+12xx^2 + 12xx2+12x to create a perfect square?

Problem 27538

Given the demand equation Qdy=200−2Py+3PxQdy = 200 - 2P_y + 3P_xQdy=200−2Py​+3Px​, determine if goods XXX and YYY are substitutes or complements.

Problem 27539

Solve the equations: 2x+8=42 \sqrt{x+8}=42x+8​=4, 3x+6−9=0\sqrt{3 x+6}-9=03x+6​−9=0, and 22x−84=2x+6=−2x+15\frac{2 \sqrt{2 x-8}}{4}=\sqrt{2 x+6}=\sqrt{-2 x+15}422x−8​​=2x+6​=−2x+15​.

Problem 27540

Find f(99)f(99)f(99) given the function f(x)=5−x99f(x)=5-\frac{x}{99}f(x)=5−99x​.

Problem 27541

How many grams of calcium carbonate are required to produce 2.2 grams of carbon dioxide from the reaction?

Problem 27542

Find the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

Problem 27543

Find the wavelength of a photon with energy 6.89×10−19 J6.89 \times 10^{-19} \mathrm{~J}6.89×10−19 J.

Problem 27544

Find the energy of a photon with a wavelength of 999μm999 \mu \mathrm{m}999μm.

Problem 27545

How many photons are in a laser pulse with energy 7.53 mJ7.53 \mathrm{~mJ}7.53 mJ at a wavelength of 601 nm601 \mathrm{~nm}601 nm? Use 3 sig figs.

Find the value of $(f \circ g)(2)$ $f(x) = 5x + 2$ and $g(x) = 3x - 4$

$(cd)^{-\frac{1}{3}}$ Simplify. Assume all variables Write your answer in the that have no variables in

Solve $(w+1)^{2}-75=0$ , where $w$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with cor If there is no solution, click "No solution." $w=$

8. $y = -\frac{3}{2}x - 4$

Divide. $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}$ $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=$ $\square$ (Simplify your answer.)

$3\sqrt[4]{6y^4} \cdot 9\sqrt[4]{35x^4y^4}$

Find the solution of the exponential equation. (Enter your answers as a comn $\begin{array}{l} 6^{4 x-5}=6^{4+7 x} \\ x=\frac{9}{11} \end{array}$ Need Help? Watch It

Solve the equation. Show all work $5(x+1)=9 x+3-3 x$

2. $3(x+1)^{2}-3=0$ . .xis of symmetry: Vertex: Solution(s):

$3 x-4=12$

Evaluate the expression $(-6+7 i)+(-8-1 i)$ and write the result in the form $a+b i$ . The real number $a$ equals $\square$ The real number $b$ equals $\square$

For numbers 3-6, simplify.
3. $\sqrt{-32}$ $32 / i$

Solve the compound or inequality. $2 x+7<3 \text { or } 7+x>9$
The solution set of the compound inequality is $\square$ (Type your answer in interval notation.)

Solve the compound and inequality. $2(x+2)-3>5 \text { and } 3(2 x+1)+2<11$
Select the correct choice below and, if necessary, fill in the answer box to complete $y$ A. The solution set is $\square$

iny solutions. Show your work $93+12 x=3(1-4 x)+96$

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function $P(x) = -22.5x^2 + 428x + 1100$ , where x is the number of years since 1990. According to the model, when will the population be the highest?

Find the x- and y-intercepts of the graph of $7x + 7y = 21$ . State each answer as an integer or an improper fraction in simplest form. x-intercept: y-intercept:

Question 4 (Mandatory) (1 point) Determine the values of $a$ , $h$ , and $k$ that make the equation. $-3x^2 + 9x - 6 = a(x - h)^2 + k$ .

Question 5 (Mandatory) (1 point)
Identify the values of $a$ , $b$ , and $c$ you would use to substitute into the quadratic formula to solve $14x + 20x^2 = 17x - 25$ .

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

Question 8 (Mandatory) (1 point) Use the quadratic formula to solve $-6x^2 + 5x + 8 = 0$ . Round your answer to two decimal places.

Question 9 (Mandatory) (1 point) What is the factored form of $x^2 + 2x + 1$

Question 10 (Mandatory) (1 point) Which equation represents $y = -2x^2 - 12x - 7$ in vertex form?

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of $f(x) = 4x^2 - 8x + 11$ without graphing the parabola.

Question 12 (Mandatory) (1 point)
What number must you add to $x^2 + 12x$ to create a perfect square?

Given the demand equation $Qdy = 200 - 2P_y + 3P_x$ , determine if goods $X$ and $Y$ are substitutes or complements.

Solve the equations: $2 \sqrt{x+8}=4$ , $\sqrt{3 x+6}-9=0$ , and $\frac{2 \sqrt{2 x-8}}{4}=\sqrt{2 x+6}=\sqrt{-2 x+15}$ .

Find $f(99)$ given the function $f(x)=5-\frac{x}{99}$ .

Find the wavelength of a photon with energy $6.89 \times 10^{-19} \mathrm{~J}$ .

Find the energy of a photon with a wavelength of $999 \mu \mathrm{m}$ .

How many photons are in a laser pulse with energy $7.53 \mathrm{~mJ}$ at a wavelength of $601 \mathrm{~nm}$ ? Use 3 sig figs.

How many photons are in a laser pulse with energy $5.56 \mathrm{~mJ}$ at a wavelength of $401 \mathrm{~nm}$ ? Use 3 sig figs.

Calculate the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Report your answer in scientific notation to 3 sig figs.

Find the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Round to 3 significant figures, use scientific notation if needed.

How much energy is in 2.50 mol of UV light at $235 \mathrm{~nm}$ ?

How much energy is in $2.50 \mathrm{~mol}$ of UV light at $235 \mathrm{~nm}$ ?

Calculate the number of photons in a laser pulse with energy $5.98 \mathrm{~mJ}$ and wavelength $675 \mathrm{~nm}$ .

Calculate $6(n-4)$ for $n=6$ .

Solve for $a$ in the equation $a+(a+4)+(2 a-3)=13$ .

Solve the equation $2(y-3)=12$ for $y$ .

Solve for $m$ in the equation $8(m-1)=8$ .

Solve for $x$ in the equation: $-2(4x - 3) = -14$ .

Solve for $x$ in the equation $5 = x + 2 \frac{1}{3}$ .

Simplify the expression: $\frac{1+\frac{1}{x+7}}{1-\frac{1}{x+7}}$ .

Solve the equations: A. $-5 t=30$ , B. $2 x=14$ , C. $\frac{x}{7}=-4$ , D. $\frac{3}{5} p=12$ .

Solve for $b$ in the equation: $b - 3.12 = 5.23$ .

Solve the equation for x: $2 x = 14$ .

Solve for $t$ in the equation $-5t = 30$ .

Solve for $p$ in the equation $\frac{3}{5} p=12$ .

Solve for $s$ in the equation $\frac{s}{5}=10$ .

Find the number such that $\frac{30}{x} = 6$ .

Find the number $c$ such that $9c = 27$ .

Solve for $j$ in the equation $\frac{j+2}{6}=1$ .

Solve for n in the equation: $\frac{2 n+8}{3}-8=32$ .

Solve the equation: $-4(r-2)+6r=36$ .

Solve the equation: $3p + 7 - 2p + 5 = -1$

Solve for $x$ in the equation $\frac{2}{3} x + 6 = 26$ .

Find the GCF of the polynomial $4 x^{4}+12 x^{3}-36 x^{2}+24 x$ . Options: $2 x$ , $6 x$ , 4, $4 x$ .