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Problem 28401

Question 12 ot 25 16 Final Exam
Find the following product, and write the product in rectangular form. $\left(\sqrt{2} \text { cis } 30^{\circ}\right)\left(\sqrt{2} \text { cis } 60^{\circ}\right)$ $\left(\sqrt{2}\right.$ 6ie $\left.30^{\circ}\right)\left(\sqrt{2}+60^{\circ}\right)=$ $\square$

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Problem 28402

Solve the system by the method of substitution. $\begin{array}{l} 2 x+y=2 \\ x^{3}-2+y=0 \end{array}$

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Problem 28403

$3^{x-4} = 7^{2x+5}$

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Problem 28404

Finding the $x$ and $y$ -intercepts of the polynomial functions
$y = 2x^4 + 8x^3 + 4x^2 - 8x - 6$
$+1$ $+6$ $-1$ $-6$ $+2$ $+3$ $-2$ $-3$ $+3$ $+2$ $-3$ $-2$
Constant = $+1, -1, +2, -2, +3, -3, +6, -6$ leading coop = $+1, -1$ $(+2)$ $y = 2x^4 + 8x^3 + 4x^2 - 8x - 6$

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Problem 28405

Given $y = \frac{x}{x-1}$ and $x > 1$ , which of the following is a possible value of $y$ ?
A. $-1.9$ B. $-0.9$ C. $0.0$ D. $0.9$ E. $1.9$

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Problem 28406

The vector $i$ represents 1 mile per hour east, and the vector $j$ represents 1 mile per hour north. Maria is jogging south at 12 miles per hour. One of the following vectors represents Maria's velocity, in miles per hour. Which one?
A. $-12i$ B. $-12j$ C. $12i$ D. $12j$ E. $12i + 12j$

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Problem 28407

$2x + y \geq 4$ $2x + y < 4$ $2x + y > 4$ $y > 6$ $y \leq 6$ $x \leq 6$ $(-1, 6)$ Look At the graph: Select two linear inequalities whose solution is shown in the graph.

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Problem 28408

$8 = \frac{1}{2}(3x + 10)$

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Problem 28409

$c^{3x-7} \cdot c^{-2x} = 4e$

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Problem 28410

Für beliebige $x, y \in \mathbb{R}$ definieren wir $x \heartsuit y = x + y^2$ , also zum Beispiel $5 \heartsuit 4 = 21$ .
(a) Berechnen Sie $6 \heartsuit 2$ .
(b) Gilt $a \heartsuit 1 \ge 1 \heartsuit a$ für alle $a \in \mathbb{R}$ ? Gilt $a \heartsuit 1 < 1 \heartsuit a$ für alle $a \in \mathbb{R}$ ?
(c) Wie viele Paare $(x, y)$ mit $x \heartsuit y = 10$ und $x, y \in \mathbb{N}_0$ gibt es? Bemerkung: $\mathbb{N}_0 = \{0, 1, 2, 3, 4, \dots\}$ .

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Problem 28411

Use the arithmetic sequence formula to find the 38th number in the sequence: $3,6,9 \ldots$

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Problem 28412

Objects 1 and 2 attract each other with a gravitational force of 18.0 units. If the mass of Object 2 is tripled, then the new gravitational force will be units. Tap in the field to enter the answer OR tap on the icon to use our built-in Number Pad. New Grav. Force = units

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Problem 28413

A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes this proportion: $\frac{4}{6}=\frac{24}{16}$
Explain the error in the student's work

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Problem 28414

What is the slope of the line that passes through the points $(-9, 0)$ and $(-17, 4)$ ? Write your answer in simplest form. Answer Attempt 1 out of 2

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Problem 28415

$144y^2 - x^2 = 1$
Graph the hyperbola. Choose the correct graph below.
The foci is/are at the point(s) $\square$ . (Type an ordered pair. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
The equation of the asymptote with the positive slope is $\square$ . The equation of the asymptote with the negative slope is $\square$ . (Simplify your answers. Use integers or fractions for any numbers in the equation.)

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Problem 28416

5. Which is the domain of the line represented by the graph?
Domain $=\{x|x=0\}$ ; Range $=\{y|y=0\}$ Domain $=\{x|-4 \le x \le 4\}$ ; Range $=\{y|-3 \le y \le 3\}$ Domain $=\{x|-\infty \le x \le \infty\}$ ; Range $=\{y|-\infty \le y \le \infty\}$ Domain $=\{x|0 \le x \le 4\}$ ; Range $=\{y|0 \le y \le 3\}$

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Problem 28417

Exit Ticket: $f(x)=(x-3)^{2}(x+2)$

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Problem 28418

Write the form of the partial fraction decomposition of the rational expression given below. Do not solve for the constants. $\frac{x-5}{x^2 + 9x + 18}$

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Problem 28419

$\left(\frac{s\sqrt{2}}{4}\right)^2 + \left(\frac{s\sqrt{2}}{4}\right)^2 =$

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Problem 28420

5. A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a $1.0$ cm $^2$ area is 50 m from the speaker.
a. What is the sound intensity at the position of the microphone? ( $1.115 \times 10^{-3} W/m^2$ )
b. How much sound energy impinges on the microphone each second? ( $1.1 \times 10^{-7} J$ )
$P = 35$

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Problem 28421

Identify the greatest common factor of 25 c and 50 acw .
Answer Attempt 1 out of 2 $\square$

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Problem 28422

Identify the greatest common factor of $24 a z$ and $24 a w z$ .
Answer Attempt I ont of 2 $\qquad$

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Problem 28423

2 2) $j+5=18$

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Problem 28424

Question
Combine like terms. $-7 y-6 y^{3}+2 y+4 y^{3}-5-1-2 y^{3}$ $\square$ Sulbmit Answer

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Problem 28425

Answer the following questions for the graph of $y=5 \log x$ . A. What is the x -intercept? Write in point form. Write DNE if the point does not exist. $\square$ B. What is the $y$ -intercept? Write in point form. Write DNE if the point does not exist. $\square$ C. Draw the graph. There is a large margin for error for the graph. You just need the general shape of the graph.

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Problem 28426

Evaluate: $g(f(-1))$ $y = f(x)$ $y = g(x)$

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Problem 28427

The magnitude of a vector $\mathbf{t}$ is 5 and its direction angle $\theta$ is $180^{\circ}$ . Write the component form for $t$ .
Write each component in exact simplified form.
Save answer

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Problem 28428

If $f(x) = 3^x$ , then the solution set in $\mathbb{R}$ for $f(2x) - 28f(x) + f(3) = 0$ is ......... (a) $\{1, 27\}$ (b) $\{27\}$ (c) $\{0, 3\}$ (d) $\{3\}$

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Problem 28429

Use the given conditions to write an equation for the line in slope-intercept form. 13) Passing through $(2, 3)$ and $(5, 2)$ A) $y - 3 = -\frac{1}{3}(x - 2)$ B) $y = mx + \frac{11}{3}$ C) $y = -\frac{1}{3}x + \frac{11}{3}$ D) $y = \frac{1}{3}x + \frac{11}{3}$

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Problem 28430

4.57 Ein Wachstumsprozess verläuft nach dem folgenden Wachstumsgesetz. Gib das Wachstumsgesetz mit Hilfe der Zahl $e$ an! Wie groß ist die Wachstumskonstante? a) $N(t) = 800 \cdot 1{,}25^t$ b) $N(t) = 450 \cdot 1{,}36^t$ c) $N(t) = 180 \cdot 1{,}05^t$
4.58 Ein Abnahmeprozess verläuft nach dem folgenden Abnahmegesetz. Gib das Abnahmegesetz mit Hilfe der Zahl $e$ an! Wie groß ist die Abnahmekonstante? a) $N(t) = 480 \cdot 0{,}8^t$ b) $N(t) = 540 \cdot 0{,}36^t$ c) $N(t) = 910 \cdot 0{,}03^t$

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Problem 28431

A quadratic function has the complex roots $3 \pm 2i$ . What is the equation of the function in standard form? The value of $a$ is given as 1 for this quadratic. $f(x) = x^2 + bx + c$ $b =$ $c =$ Note: Your answers should be integers.

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Problem 28432

ro7.core.learn.edgenuity.com/player/ thematics
Using a Rate Table to Solve a Proportion \begin{tabular}{|c|c|} \hline Pages & Hours \\ \hline $4 / 3$ & $1 / 4$ \\ \hline $8 / 3$ & $1 / 2$ \\ \hline 4 & $3 / 4$ \\ \hline $16 / 3$ & 1 \\ \hline $20 / 3$ & $5 / 4$ \\ \hline 8 & $3 / 2$ \\ \hline $28 / 3$ & \\ \hline $32 / 3$ & \\ \hline \end{tabular}
Lee can type $11 / 3$ pages every 15 minutes. How many hours does it take him to type $102 / 3$ pages? Complete the rate table to solve the proportion. $\frac{\text { pages }}{\text { hours }} \rightarrow \frac{\frac{4}{3}}{\frac{1}{4}}=\frac{\frac{32}{3}}{x}$
Lee can type $102 / 3$ pages in Intro Done

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Problem 28433

Proportions Instruction Active Using a Rate Table to Solve a Proportion \begin{tabular}{|c|c|} \hline Pages & Hours \\ \hline $4 / 3$ & $1 / 4$ \\ \hline $8 / 3$ & $1 / 2$ \\ \hline 4 & $3 / 4$ \\ \hline $16 / 3$ & 1 \\ \hline $20 / 3$ & $5 / 4$ \\ \hline 8 & $3 / 2$ \\ \hline $28 / 3$ & \\ \hline $32 / 3$ & \\ \hline \end{tabular}
Lee can type $11 / 3$ pages every 15 minutes. How many hours does it take him to type $102 / 3$ pages? Complete the rate table to solve the proportion. $\frac{\text { pages } \rightarrow \frac{4}{3}}{\text { hours } \rightarrow \frac{1}{4}}=\frac{\frac{32}{3}}{x}$
Lee can type $102 / 3$ pages in $\square$ hours. $13 / 4$ 2 $21 / 4$ $21 / 2$

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Problem 28434

d. $3 x^{2}-2 x-7=0$

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Problem 28435

Question 4 A closed bin is made by cutting squares out of a rectangular piece of cardboard to build storage bins with the greatest possible volume. Each rectangular sheet is 36 feet by 28 ft. The sketch shows the squares removed from each sheet. The dashed lines indicate where to fold the cardboard sheets to form the prism-shaped storage bins with tops.
a). Write a function $V(x)$ to represent the volume of bin in terms of the side length, $x$ , of the removed squares. Explain your reasoning.
b). Calculate the volume for each value of $x$ .
$x$ | $V(x)$ ---|--- 0 | 2.25 | 3.75 | 4.295 | 5.3 | 12 | 13.1 | 14 | 18 |
c). Determine the domain and range of the function as they relate to this problem situation.
d). Determine the $x$ - and $y$ - intercepts of the graph of $V(x)$ . What do they represent in this problem situation?
c). From the table determine the maximum volume of a bin. What are the dimensions of a bin with the maximum volume?

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Problem 28436

1 An expression is given. $(3x^2 + 3) + (-2x^2 + 7)$ Create an equivalent expression using the fewest terms possible.

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Problem 28437

Timed Problem Score: 0/3 Current Time: 9.5 Which equation is equivalent to the given equation? $3x = -3x^2 + 60$ Answer $3x^2 + 3x - 60 = 0$ $3x^2 - 3x + 60 = 0$ $3x^2 - 3x - 60 = 0$ $3x^2 + 3x + 60 = 0$ Keyboard shortcuts Watch Video Stop

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Problem 28438

Which equation is equivalent to the given equation?
$2x - 24 = -x^2$
Answer $x^2 + 2x - 24 = 0$ $x^2 + 2x + 24 = 0$ $x^2 - 2x + 24 = 0$ $x^2 - 2x - 24 = 0$ Keyboard shortcuts

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Problem 28439

$\log _{2}(x+14)+2 \log _{2}(x+2)=6$

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Problem 28440

1. Calculez le potentiel du couple $Ag^{+} | Ag$ on donne $[Cl^{-}] = 10^{-2} M$ , $Ks \; AgCl = 1.6 \cdot 10^{-10} M$ et $E^{0}_{Ag^{+} | Ag} = 0.80 V$

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Problem 28441

1. Drag and drop the correct domain and range for each of the graphs below: A. B. C. D. Domain: 1 Range: 2 Domain: 3 Range: 4 Domain: 5 Range: 6 Domain: 7 Range: 8

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Problem 28442

art 2. Solve the following equations using algebra and write your answer as an ordered pair. Show all work and box your final answer.
7. $x+7 y=25 ; 2 x+5 y=14$
8. $4 x-5 z=28 ; x+3 z=7$
Part 3. Complete the following operations without a calculator. Show all work and box your final answer.
9. $\frac{5}{3}-\frac{3}{9}=$ ?
10. $4312 \div 5=$ ?
Part 4. Factor the following completely. Show all work and box your final answer.
11. $\mu^{3}+2 \mu^{2}+\mu$
12. $6 \mu^{2}+\mu-15$

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Problem 28443

Find the equation of the line shown.

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Problem 28444

A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of be and 6 potatoes. Which proportion represents the situation? 2 O ㅇ-ㅎ 1 6

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Problem 28445

Writing a Proportion
The recipe for beef stew calls for $1 / 4$ teaspoon of pepper for every 3 potatoes. If 9 potatoes are used pepper is needed?
Which proportion represents this problem? $\frac{1 / 4}{3}-\frac{9}{p}$ $\frac{1 / 4}{3}-\frac{p}{9}$ $\frac{1 / 4}{9}-\frac{3}{p}$ $\frac{114}{p}=\frac{9}{3}$

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Problem 28446

The recipe for beef stew calls for $1 / 4$ teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?
Solve the proportion $\frac{1 / 4}{3}=\frac{p}{9}$ to answer the question. Explain your steps

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Problem 28447

A function is shown below. $f(x) = \begin{cases} -x^2 + 2x & \text{for } x \le -3 \\ 2\left(\frac{1}{3}\right)^{2x} & \text{for } -3 < x < 4 \\ \frac{2x - 5}{x - 7} & \text{for } x \ge 4 \end{cases}$ Find $-3f(0) + 5(6)$

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Problem 28448

Solve the following: a) $4 x-3=2 x+7$
Optional working
Answer

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Problem 28449

a. $(-3)^{-4}$

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Problem 28450

b. $\frac{4}{x^{0}+7}$

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Problem 28451

A floor plan of a living room is labeled with dimensions below.
$(x+8)$ $(7x+10)$ Living Room
Which expressions can be used to determine the area of the living room?
A $7x^2 + 10x + 56x + 80$ B $7x^2 + 2x + 4$ C $7x^2 + 66x + 80$ D $8x + 2 + 14x^2$ E $16x + 36$

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Problem 28452

16. (10 points) The temperature, $f(t)$ of a cup of coffee, in degrees Celsius, after $t$ minutes can be determined by the equation $f(t) = 65(0.75)^t + 5$ . A graph of the function $f(t)$ is shown below. Estimate the temperature after 5 minutes.

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Problem 28453

What is the value of $x$ in $\log_2(x) - 3 = 1$ ?

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Problem 28454

12. A parabola has a vertex at $(3, 4)$ and passes through the point $(5, -4)$ . What is the standard form equation for the parabola?
$y = -2(x - 3)^2 + 4$
$y = -2x^2 + 12x - 14$
$y = 2(x - 5)^2 - 4$
$y = 2x^2 - 20x + 46$

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Problem 28455

7) $y = -2(x - 4)^2 - 6$
8) $y = (x - 4)^2 + 4$

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Problem 28456

2) Determine how much of the total loan payment applies toward principal and how much applies toward interest for a student loan of \$38,156 at a fixed APR of 8\% for 11 years. A) \$38,156 pays off the principal and \$19,321.94 represents interest payments. B) \$38,156 pays off the principal and \$19,398.46 represents interest payments. C) \$38,156 pays off the principal and \$19,362.76 represents interest payments. D) \$38,156 pays off the principal and \$19,338.95 represents interest payments.

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Problem 28457

Question: 15 Look
Tracy works at a hot dog stand. - She sells 3 hot dogs and 2 pretzels for $\$ 15.00$ . - She sells 5 hot dogs and 1 pretzel for $\$ 21.50$ .
This situation can be modeled by the system of equations shown below. $\left\{\begin{array}{l} 3 h+2 p=15 \\ 5 h+p=21.5 \end{array}\right.$
Then Tracy sells 2 hot dogs and 4 pretzels. What is the total cost of this order? A. $\$ 14.00$ B. $\$ 19.00$ C. $\$ 21.42$ D. $\$ 26.26$

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Problem 28458

15. $x^2 + 3x - 70 = 0$

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Problem 28459

Find the vertical asymptotes. $g(r)=\frac{r-7}{r^{2}-2 r-8}$
Enter your answers in increasing order. $\begin{array}{l} r= \\ r= \end{array}$

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Problem 28460

4) A 0.425 kg water balloon is dropped from the top of a $\left\{v^{2}=\sqrt{\frac{E k(2)}{m}}\right.$ school gymnasium onto some unsuspecting physics students (those were the days...). If the gym is 8.50 m high how much kinetic energy does it have just before it hits the ground? Law of Conservation of Enerov.

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Problem 28461

If the Macaulay Duration of the Bond is 7.7 semi-annual years and semi-annual yield is $5 \%$ (i.e., YTM $=10 \%$ , remember YTM is always an APR and is quoted on an annual basis). What is the \% change in the bond price $\left(\frac{\Delta P}{P}\right)$ for a 10 bps decrease in semi-annual yield (i.e. 20bps decrease in annual yield)? ( $1 \mathrm{bps}=0.01 \%$ ) Use the linear approximation formula that ignores convexity (1 mark) $\frac{\Delta P}{P}=-D^{\text {Modifled }}(\Delta Y)$ A. 75 bps or $0.75 \%$ B. 73.33 bps or $0.7333 \%$ C. 71 bps or 0.71\% D. 72 bps or 0.72\%

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Problem 28462

$f(x) = x^2(x+9)$ $x = -9$ $x = 0$ 2

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Problem 28463

7. Solve the system: $\left\{\begin{array}{l}7 x-3 y=-14 \\ -3 x+y=6\end{array}\right.$

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Problem 28464

Factor completely.
$6j^5 + 3j^4 - 8j^3 - 4j^2$

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Problem 28465

1. $\text { 1. } \sqrt{-25} \cdot \sqrt{-15}$

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Problem 28466

Consider a U.S. economy consisting of 4 sectors: (1) Textiles, (2) Apparel, (3) Farms, and (4) Wholesale Trade. The following $(I-A)^{-1}$ matrix was computed from an input-output table for this economy: $(I-A)^{-1}=\left[\begin{array}{cccc} 1.2197 & 0.1723 & 0.0006 & 0.0038 \\ 0.0134 & 1.070 & 0 & 0.0011 \\ 0.0875 & 0.0123 & 1.2047 & 0.0022 \\ 0.0050 & 0.0007 & -0.0034 & 1.0413 \end{array}\right]$
What is the interpretation of the 3,2 -entry of $(I-A)^{-1}$ ? a. It takes $\$ 0.0123$ worth of goods from the Farms sector to produce $\$ 1$ worth of Apparel sector goods. b. The Farms sector must increase production by $\$ 0.0123$ in order to meet a $\$ 1$ increase in demand in the Apparel sector. c. The Apparel sector must increase production by $\$ 0$ in order to meet a $\$ 1$ increase in demand in the Farms sector. d. It takes $\$ 0$ worth of goods from the Apparel sector to produce $\$ 1$ worth of the Farms sector goods.

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Problem 28467

$(-4.3v + 3.4t) - (2.8v - 4.1t)$

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Problem 28468

Type the missing number in this sequer 1, 3, 9, 27, 81,

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Problem 28469

Solve the following equation for $A$ . You may assume all variables are positive so do not use $\pm$ or absolute values. $5 h^{3}=b A^{2}-G$

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Problem 28470

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
$\log_9(81x^2)$
Answer 2 Points

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Problem 28471

$f(x) = c - x$
What do all members of the family of linear functions $f(x) = c - x$ have in common?
All members of the family of linear functions $f(x) = c - x$ have graphs that are lines with slope \_\_\_\_\_\_\_\_\_\_\_\_ and y-intercept \_\_\_\_\_\_\_\_\_\_\_\_.
Sketch several members of the family.
$c = 2$ $c = 1$ $c = 0$ $c = -1$ $c = -2$
$c = 2$ $c = 1$ $c = 0$ $c = -1$ $c = -2$
$c = 2$ $c = 1$ $c = 0$ $c = -1$ $c = -2$
$c = -2$ $c = -1$ $c = 0$ $c = 1$ $c = 2$

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Problem 28472

What is the least possible degree of the polynomial graphed above?

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Problem 28473

لاينا المعطيات التالية لعقد تأمين مختلط لعلاوات سنوية: بلغ رأس المال المؤمن: الماريار 25000 دينار، n=10، x=35 كما توفر لدينا البيانات التالية حول: مصاريف التحصىل: \% = عمولة الاكتساب: افترض/ي أن المؤمن له رفض تسديد العلاوة الثامنة، مما اضطر المؤمن إلى اقتراح لخفض رأس ماله المؤمن. المطلوب: حساب رأس المال المؤمن الجديد (المخض) باستخدام التبديلات

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Problem 28474

Solve the following radical equation. $\sqrt{4z+17} + 2 = z + 1$ Answer 2 Points Write your answer(s) beginning with the first answer box. If applicable, the second answer box may be left blank. $z =$

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Problem 28475

Сколько атомов азота в $3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$ ? 3 12 24 9 6

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Problem 28476

$\log_7(x-1) + \log_7(x+3) = \log_7(x+2)$

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Problem 28477

Consider the following function. $f(x) = \frac{x^2}{4} - 3$
Step 1 of 2: Graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.

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Problem 28478

Use the long division method to find the result when $2x^3 + 19x^2 + 5x - 27$ is divided by $x + 9$ . If there is a remainder, express the result in the form $q(x) + \frac{r(x)}{b(x)}$ .

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Problem 28479

Consider the following rational function. $f(x) = \frac{-2}{x-5}$ Step 1 of 3: Find equations for the vertical asymptotes, if any, for the function. Answer (opens in new window) 2 Points Separate multiple equations with a comma. Selecting a button will replace the entered answer value. The value of the button is used instead of the value in the none

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Problem 28480

Use Cramer's rule to solve the system $\begin{cases} 12x - 14y = 62 \\ 4x + 13y = 3 \end{cases}$ . If there is a solution, write your answer in the format $(x, y)$ . Answer 2 Points Selecting an option will display any text boxes needed to complete your answer. No Solution One Solution Infinitely Many Solutions

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Problem 28481

SELECT ALL of the expressions that are a factor of the quadratic? $x^{2}+2 x-15$ $(x+5)$ $(x+3)$ $(x+15)$ $(x-5)$ $(x-15)$

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Problem 28482

Step 4 (b) $g(t) = \sin(e^t - 3)$ To find the domain of $g(t) = \sin(e^t - 3)$ , we examine the domains of the exponential and sine functions. Remembering that $e^x$ exists for all values of $x$ , the domain $s = e^t - 3$ is what? (Enter your answer using interval notation.) $(-\infty, \infty)$ Step 5 Next, we examine the sine. Since $\sin(x)$ exists for all values of $x$ , then the domain of $y = \sin(s)$ is what? (Enter your answer using interval notation.)

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Problem 28483

70 / 212 Marks
Work out the equation of the line which has a gradient of 2 and passes through the point (1,4). Optional working

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Problem 28484

$V(x) = x^3 + 3x^2 - 11x - 33$ Step 1 of 2: Use the Rational Zero Theorem to list all of the potential rational zeros. Answer 2 Points Enter only the positive values. Separate multiple answers with commas. $\pm\{$ \}

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Problem 28485

The function $f(x)=5 x^{3}-7 x+2$ has at least one rational root. Use the rational root theorem to find that root, then proceed to find all complex roots. (Note: roots may be integ rational, irrational, and/or complex.)
Answer

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Problem 28486

Radicals Introduction to simplifying a radical expressior
Simplify. $\sqrt{x^{25}}$
Assume that the variable represents a positive

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Problem 28487

16 of 18
Solve the following equation algebraically: $\sqrt{x+4} = 3x - 12$
Separate your answers with commas. Do not use spaces. Write leftmost (most negative) answers first. If there is no solution write "DNE" in the answer box. Write your answers as fractions if possible, not decimals.
Write the value for x below:

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Problem 28488

Which values are NOT in the domain of the rational function? $f(x) = \frac{(x - 1)(x + 2)}{x^2 - 9}$

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Problem 28489

Identify the vertical asymptote(s) of the rational function. $f(x) = \frac{x(x+6)(x-10)}{(x-5)(x+6)}$

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Problem 28490

Question 2 (10 marks)
A certain sand quarry in the outskirt of Dar es Salaam uses a horizontal belt conveyor. The conveyor is used for transporting sand from the quarry entrance to the loading point that is 275 m away with a total weight of 2000 kg on belt length. The conveyor employs a plane belt with width and thickness of 700 mm and 20 mm respectively securely wrapped at $200^{\circ}$ wrap angle around east iron drive drum. The pulley has internal and external diameter of 275 and 300 mm respectively. Support and drive shaft of mild steel material 70 mm dia $\times$ 800 mm length is used for drive drum. Steel end plates of 275 mm dia $\times 10 \mathrm{~mm}$ thick is use to secure drum and drive shaft. Belt weight per unit volume is $600 \mathrm{~kg} / \mathrm{m}^{3}$ , with a anide (anido) reinforcement materials and conveying speed of $1.9 \mathrm{~m} / \mathrm{s}$ . The friction coefficient between belt and drum is 0.33 while the coefficient of friction between belt and flatbed support is 0.15 .
Determine $\begin{array}{rrr} \rho_{\text {stcol }} & =7850 \mathrm{~kg} / \mathrm{m}^{3} & \quad \rho_{\text {cast inon }}=730 \\ c_{1} & =1.5 & c_{3}=25 \quad(3 \text { mark }) \\ & & (1 \text { mark }) \end{array}$ 2.1 Effective belt force 2.2 Maximum belt force
Page 2 of 5
23 Power required at the motor drive (2 marks) 2.4 Power of the drive motor taking efficiency of the drive unit to be 8904 (1 marlea) 2.5 Considering friction between belt and support, recalculate 2.1 to 2.4 above and comments on the difference (3 marks)

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Problem 28491

$7t - 14 - 16r + 9c + (-14c)$ $8 - 8c - 8c - 4b - 12b$ $10n - 15 - 5n + 6 + 2c$ $3x + (-17) + 21f + 3x - (-21f)$ $-19m + 5 - (-m) + c - 7c$ $y - 14 + 30c - 2y + 16c$ $10 + (-4g) + 10 - 13x - 2g + 5x$ $20j + 20j - 16m - 16m + 16$ $-25d + 2s - 7 + 15s - 20d$ $9m - 14 - 6m + 4r + 12r$ $m + 15c + (-3m) - 4$ simplifies to $8mc$ $30x + 9 + 9m + 14x - 3m$ simplifies to $34x + 9 + 6m$ $6 + 4m - 17g + 6m + 3g$ simplifies to $6 + 10m - 14g$ $17 + 6y - 10 + m + 7m$ simplifies to $27 + 6y + 8m$ $-j + 10s - j + 12 - 8s$ simplifies to $-2j + 2s + 12$

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Problem 28492

Find the steady-state vector for the transition matrix. $\begin{bmatrix} \frac{6}{7} & \frac{2}{7} \\ \frac{1}{7} & \frac{5}{7} \end{bmatrix}$ x = $\begin{bmatrix} \rule{0.5cm}{0.15mm} \\ \rule{0.5cm}{0.15mm} \end{bmatrix}$

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Problem 28493

Step 8 To estimate the time for the population to reach 20,000, we graph $y = 600(4^t)$ and $y = 20,000$ and estimate the value of $t$ at the intersection point.
Rounding to one decimal place, we see that the two curves intersect at the following value of $t$ . $t =$
This allows us to estimate the time (in hours) for the population to reach 20,000. (Round your answer to one decimal place.) hr

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Problem 28494

Halla el valor de la variable desconocida. $\begin{array}{l} \mathbf{A}=\mathbf{P}+\text { Prt; Dado } \mathbf{A}=1600, P=100, r=3 \\ \mathbf{t 1}=\square \text { Hecho } \end{array}$

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Problem 28495

Use the vertex and intercepts to sketch the graph of the quadratic function. 1) $f(x) = (x - 3)^2 - 1$

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Problem 28496

Determina le equazioni delle rette passanti per $P(0,1)$ la cui distanza dal punto $Q(1,0)$ è $\frac{\sqrt{5}}{5}$ . $\left[y=-2 x+1, y=-\frac{1}{2} x\right]$

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Problem 28497

(a) [2 pt] Let $\vec{u} = 4\vec{i} + 2\vec{j}$ and let $\vec{v} = -6\vec{i} + \vec{j}$ . Compute the following sum. $\vec{u} + \vec{v} =$ $-2\vec{i} + 3\vec{j}$ (b) [2 pt] Let $\vec{u} = (3, -9)$ . Compute the following scalar product. $-5\vec{u} =$ (c) [2 pt] Let $\vec{u} = (8, 7, 10, 5)$ and $\vec{v} = (8, 6, 9, 7)$ . Compute the following vector. $\frac{\vec{u} + \vec{v}}{2} =$ (d) Let $\vec{u} = (2, -2, 1)$ , and let $\vec{v} = (-2, 6, 2)$ . i. [1 pt] Compute the magnitude of $\vec{u}$ . $||\vec{u}|| =$ ii. [1 pt] Compute the magnitude of $\vec{v}$ . $||\vec{v}|| =$ iii. [2 pt] Compute the magnitude of $\vec{u} + \vec{v}$ . $||\vec{u} + \vec{v}|| =$

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Problem 28498

4) $\log_{5}{x} + \log_{5}{(x - 24)} = 2$

See Solution

Problem 28499

Solve the compound inequality. on a number line. 5) $-4 \le -4x - 12 < 4$

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Problem 28500

Solve the equation by expressing 6) $3(3x - 6) = 27$

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Algebra

Problem 28401

Problem 28402

Solve the system by the method of substitution. 2x+y=2x3−2+y=0\begin{array}{l} 2 x+y=2 \\ x^{3}-2+y=0 \end{array}2x+y=2x3−2+y=0​

Problem 28403

3x−4=72x+53^{x-4} = 7^{2x+5}3x−4=72x+5

Problem 28404

Problem 28405

Given y=xx−1y = \frac{x}{x-1}y=x−1x​ and x>1x > 1x>1, which of the following is a possible value of yyy?A. −1.9-1.9−1.9 B. −0.9-0.9−0.9 C. 0.00.00.0 D. 0.90.90.9 E. 1.91.91.9

Problem 28406

Problem 28407

2x+y≥42x + y \geq 42x+y≥4 2x+y<42x + y < 42x+y<4 2x+y>42x + y > 42x+y>4 y>6y > 6y>6 y≤6y \leq 6y≤6 x≤6x \leq 6x≤6 (−1,6)(-1, 6)(−1,6) Look At the graph: Select two linear inequalities whose solution is shown in the graph.

Problem 28408

8=12(3x+10)8 = \frac{1}{2}(3x + 10)8=21​(3x+10)

Problem 28409

c3x−7⋅c−2x=4ec^{3x-7} \cdot c^{-2x} = 4ec3x−7⋅c−2x=4e

Problem 28410

Problem 28411

Use the arithmetic sequence formula to find the 38th number in the sequence: 3,6,9…3,6,9 \ldots3,6,9…

Problem 28412

Objects 1 and 2 attract each other with a gravitational force of 18.0 units. If the mass of Object 2 is tripled, then the new gravitational force will be ______ units. Tap in the field to enter the answer OR tap on the icon to use our built-in Number Pad. New Grav. Force = ______ units

Problem 28413

A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes this proportion: 46=2416\frac{4}{6}=\frac{24}{16}64​=1624​Explain the error in the student's work

Problem 28414

What is the slope of the line that passes through the points (−9,0)(-9, 0)(−9,0) and (−17,4)(-17, 4)(−17,4)? Write your answer in simplest form. Answer Attempt 1 out of 2

Problem 28415

Problem 28416

Problem 28417

Exit Ticket: f(x)=(x−3)2(x+2)f(x)=(x-3)^{2}(x+2)f(x)=(x−3)2(x+2)

Problem 28418

Write the form of the partial fraction decomposition of the rational expression given below. Do not solve for the constants. x−5x2+9x+18\frac{x-5}{x^2 + 9x + 18}x2+9x+18x−5​

Problem 28419

(s24)2+(s24)2=\left(\frac{s\sqrt{2}}{4}\right)^2 + \left(\frac{s\sqrt{2}}{4}\right)^2 =(4s2​​)2+(4s2​​)2=

Problem 28420

Problem 28421

Identify the greatest common factor of 25 c and 50 acw .Answer Attempt 1 out of 2 □\square□

Problem 28422

Identify the greatest common factor of 24az24 a z24az and 24awz24 a w z24awz.Answer Attempt I ont of 2 \qquad

Problem 28423

2 2) j+5=18j+5=18j+5=18

Problem 28424

QuestionCombine like terms. −7y−6y3+2y+4y3−5−1−2y3-7 y-6 y^{3}+2 y+4 y^{3}-5-1-2 y^{3}−7y−6y3+2y+4y3−5−1−2y3 □\square□ Sulbmit Answer

Problem 28425

Problem 28426

Evaluate: g(f(−1))g(f(-1))g(f(−1)) y=f(x)y = f(x)y=f(x) y=g(x)y = g(x)y=g(x)

Problem 28427

The magnitude of a vector t\mathbf{t}t is 5 and its direction angle θ\thetaθ is 180∘180^{\circ}180∘. Write the component form for ttt.Write each component in exact simplified form.Save answer

Problem 28428

If f(x)=3xf(x) = 3^xf(x)=3x, then the solution set in R\mathbb{R}R for f(2x)−28f(x)+f(3)=0f(2x) - 28f(x) + f(3) = 0f(2x)−28f(x)+f(3)=0 is ......... (a) {1,27}\{1, 27\}{1,27} (b) {27}\{27\}{27} (c) {0,3}\{0, 3\}{0,3} (d) {3}\{3\}{3}

Problem 28429

Problem 28430

Problem 28431

A quadratic function has the complex roots 3±2i3 \pm 2i3±2i. What is the equation of the function in standard form? The value of aaa is given as 1 for this quadratic. f(x)=x2+bx+cf(x) = x^2 + bx + cf(x)=x2+bx+c b=b = b= c=c = c= Note: Your answers should be integers.

Problem 28432

Problem 28433

Problem 28434

d. 3x2−2x−7=03 x^{2}-2 x-7=03x2−2x−7=0

Problem 28435

Problem 28436

1 An expression is given. (3x2+3)+(−2x2+7)(3x^2 + 3) + (-2x^2 + 7)(3x2+3)+(−2x2+7) Create an equivalent expression using the fewest terms possible.

Problem 28437

Problem 28438

Which equation is equivalent to the given equation?2x−24=−x22x - 24 = -x^22x−24=−x2Answer x2+2x−24=0x^2 + 2x - 24 = 0x2+2x−24=0 x2+2x+24=0x^2 + 2x + 24 = 0x2+2x+24=0 x2−2x+24=0x^2 - 2x + 24 = 0x2−2x+24=0 x2−2x−24=0x^2 - 2x - 24 = 0x2−2x−24=0 Keyboard shortcuts

Problem 28439

log⁡2(x+14)+2log⁡2(x+2)=6\log _{2}(x+14)+2 \log _{2}(x+2)=6log2​(x+14)+2log2​(x+2)=6

Problem 28440

1. Calculez le potentiel du couple Ag+∣AgAg^{+} | AgAg+∣Ag on donne [Cl−]=10−2M[Cl^{-}] = 10^{-2} M[Cl−]=10−2M, Ks AgCl=1.6⋅10−10MKs \; AgCl = 1.6 \cdot 10^{-10} MKsAgCl=1.6⋅10−10M et EAg+∣Ag0=0.80VE^{0}_{Ag^{+} | Ag} = 0.80 VEAg+∣Ag0​=0.80V

Problem 28441

1. Drag and drop the correct domain and range for each of the graphs below: A. B. C. D. Domain: 1 Range: 2 Domain: 3 Range: 4 Domain: 5 Range: 6 Domain: 7 Range: 8

Problem 28442

Problem 28443

Find the equation of the line shown.

Problem 28444

A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of be and 6 potatoes. Which proportion represents the situation? 2 O ㅇ-ㅎ 1 6

Problem 28445

Problem 28446

The recipe for beef stew calls for 1/41 / 41/4 teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?Solve the proportion 1/43=p9\frac{1 / 4}{3}=\frac{p}{9}31/4​=9p​ to answer the question. Explain your steps

Problem 28447

Problem 28448

Solve the following: a) 4x−3=2x+74 x-3=2 x+74x−3=2x+7Optional workingAnswer

Solve the system by the method of substitution. $\begin{array}{l} 2 x+y=2 \\ x^{3}-2+y=0 \end{array}$

$3^{x-4} = 7^{2x+5}$

Given $y = \frac{x}{x-1}$ and $x > 1$ , which of the following is a possible value of $y$ ?
A. $-1.9$ B. $-0.9$ C. $0.0$ D. $0.9$ E. $1.9$

$2x + y \geq 4$ $2x + y < 4$ $2x + y > 4$ $y > 6$ $y \leq 6$ $x \leq 6$ $(-1, 6)$ Look At the graph: Select two linear inequalities whose solution is shown in the graph.

$8 = \frac{1}{2}(3x + 10)$

$c^{3x-7} \cdot c^{-2x} = 4e$

Use the arithmetic sequence formula to find the 38th number in the sequence: $3,6,9 \ldots$

Objects 1 and 2 attract each other with a gravitational force of 18.0 units. If the mass of Object 2 is tripled, then the new gravitational force will be units. Tap in the field to enter the answer OR tap on the icon to use our built-in Number Pad. New Grav. Force = units

A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes this proportion: $\frac{4}{6}=\frac{24}{16}$
Explain the error in the student's work

What is the slope of the line that passes through the points $(-9, 0)$ and $(-17, 4)$ ? Write your answer in simplest form. Answer Attempt 1 out of 2

Exit Ticket: $f(x)=(x-3)^{2}(x+2)$

Write the form of the partial fraction decomposition of the rational expression given below. Do not solve for the constants. $\frac{x-5}{x^2 + 9x + 18}$

$\left(\frac{s\sqrt{2}}{4}\right)^2 + \left(\frac{s\sqrt{2}}{4}\right)^2 =$

Identify the greatest common factor of 25 c and 50 acw .
Answer Attempt 1 out of 2 $\square$

Identify the greatest common factor of $24 a z$ and $24 a w z$ .
Answer Attempt I ont of 2 $\qquad$

2 2) $j+5=18$

Question
Combine like terms. $-7 y-6 y^{3}+2 y+4 y^{3}-5-1-2 y^{3}$ $\square$ Sulbmit Answer

Evaluate: $g(f(-1))$ $y = f(x)$ $y = g(x)$

The magnitude of a vector $\mathbf{t}$ is 5 and its direction angle $\theta$ is $180^{\circ}$ . Write the component form for $t$ .
Write each component in exact simplified form.
Save answer

If $f(x) = 3^x$ , then the solution set in $\mathbb{R}$ for $f(2x) - 28f(x) + f(3) = 0$ is ......... (a) $\{1, 27\}$ (b) $\{27\}$ (c) $\{0, 3\}$ (d) $\{3\}$

A quadratic function has the complex roots $3 \pm 2i$ . What is the equation of the function in standard form? The value of $a$ is given as 1 for this quadratic. $f(x) = x^2 + bx + c$ $b =$ $c =$ Note: Your answers should be integers.

d. $3 x^{2}-2 x-7=0$

1 An expression is given. $(3x^2 + 3) + (-2x^2 + 7)$ Create an equivalent expression using the fewest terms possible.

Which equation is equivalent to the given equation?
$2x - 24 = -x^2$
Answer $x^2 + 2x - 24 = 0$ $x^2 + 2x + 24 = 0$ $x^2 - 2x + 24 = 0$ $x^2 - 2x - 24 = 0$ Keyboard shortcuts

$\log _{2}(x+14)+2 \log _{2}(x+2)=6$

1. Calculez le potentiel du couple $Ag^{+} | Ag$ on donne $[Cl^{-}] = 10^{-2} M$ , $Ks \; AgCl = 1.6 \cdot 10^{-10} M$ et $E^{0}_{Ag^{+} | Ag} = 0.80 V$

The recipe for beef stew calls for $1 / 4$ teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed?
Solve the proportion $\frac{1 / 4}{3}=\frac{p}{9}$ to answer the question. Explain your steps

Solve the following: a) $4 x-3=2 x+7$
Optional working
Answer

a. $(-3)^{-4}$

b. $\frac{4}{x^{0}+7}$

16. (10 points) The temperature, $f(t)$ of a cup of coffee, in degrees Celsius, after $t$ minutes can be determined by the equation $f(t) = 65(0.75)^t + 5$ . A graph of the function $f(t)$ is shown below. Estimate the temperature after 5 minutes.

What is the value of $x$ in $\log_2(x) - 3 = 1$ ?

7) $y = -2(x - 4)^2 - 6$
8) $y = (x - 4)^2 + 4$

15. $x^2 + 3x - 70 = 0$

Find the vertical asymptotes. $g(r)=\frac{r-7}{r^{2}-2 r-8}$
Enter your answers in increasing order. $\begin{array}{l} r= \\ r= \end{array}$

$f(x) = x^2(x+9)$ $x = -9$ $x = 0$ 2

7. Solve the system: $\left\{\begin{array}{l}7 x-3 y=-14 \\ -3 x+y=6\end{array}\right.$

Factor completely.
$6j^5 + 3j^4 - 8j^3 - 4j^2$

1. $\text { 1. } \sqrt{-25} \cdot \sqrt{-15}$

$(-4.3v + 3.4t) - (2.8v - 4.1t)$

Solve the following equation for $A$ . You may assume all variables are positive so do not use $\pm$ or absolute values. $5 h^{3}=b A^{2}-G$

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
$\log_9(81x^2)$
Answer 2 Points

Solve the following radical equation. $\sqrt{4z+17} + 2 = z + 1$ Answer 2 Points Write your answer(s) beginning with the first answer box. If applicable, the second answer box may be left blank. $z =$