Browse Math Statement problems Studdy Solved!

Problem 23801

5. Find the longest interval in which the initial value problem $(x-3)y'' + xy' + (\ln{x})e^y = 0$ , $y(1) = 3$ and $y'(1) = 0$

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Problem 23802

In Exercises 15-20, write a rule for $g$ and then graph each function. Describe the graph of $g$ as a transformation of the graph of $\boldsymbol{f}$ . Example 3
15. $f(x)=x^{4}+1, g(x)=f(x+2)$
16. $f(x)=x^{6}-3 x^{3}+2, g(x)=f(x)-3$

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Problem 23803

13. (a) Expand $(2 a+3 b)^{2}$ . (b) Hence or otherwise, expand $(2 a+3 b-4 c)^{2}$ .

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Problem 23804

Subtract. $(9 u+6)-(u+1)$

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Problem 23805

$2(4 y-5)=70$
Simplify your answer as much as possible. $y=$

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Problem 23806

ch expression to an equivalent expression by using ra b. $\sqrt[4]{6} x^{3}$

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Problem 23807

Solve the following quadratic function by utilizing the square root method. Simplify your answer completely. $\begin{array}{c} f(x)=49 x^{2}-144 \\ x= \pm \frac{[?]}{\square} \end{array}$

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Problem 23808

27. $x^2 - 4x - 13 = 0$
30. $x^2 - 8x - 65 = 0$

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Problem 23809

The graphs of $y = x + 1$ intersects the graph of $y = 5\cos\left(x - \frac{\pi}{3}\right)$ at the point $A$ in the first quadrant. By using Newton-Raphson method, find the coordinates of $A$ correct to four decimal places.

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Problem 23810

Find the intersection of the line and the circle given below. $\begin{aligned} y & =-x-3 \\ x^{2}+y^{2} & =17 \end{aligned}$
Provide your answer below: $\square$ $\square$ $\square$ $\square$ )

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Problem 23811

Exercice 1(6pts)
1. Soit $f$ l'application de l'ensemble $\{1,2,3,4\}$ dans lui-même définie par: $\left\{\begin{array}{l} f(1)=3 \\ f(2)=0 \\ f(3)=1 \\ f(4)=4 \end{array}\right.$ a) Déterminer $f^{-1}(A)$ lorsque $A=\{2\}, A=\{1,4\}, A=\{3\}$ . b) $f$ est-elle injective ?surjective?bijective?
2. Soit $f$ l'application de $\mathbb{R}$ dans $\mathbb{R}$ définie par $f(x)=x^{2}$ a) Déterminer $f(A)$ lorsque $A=\{2\}, A=\{-2\}$ . Que peut-on conclur? b) Déterminer $f^{-1}(A)$ lorsque $A=\{4\}, A=[1,4]$ .

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Problem 23812

The polynomial $p(x)=x^{3}+7 x^{2}-36$ has a known factor of $(x+3)$ . Rewrite $p(x)$ as a product of linear factors. $p(x)=$ $\square$

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Problem 23813

1 Find the slant asymptote of the function $f(x)=\frac{x^{2}+4 x-8}{x+3}$ ?

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Problem 23814

4. $y = (x^2 + 1)$ arccot $x$ 9

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Problem 23815

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 23816

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 23817

$f(x) = \begin{cases} -2x+3 & \text{si } x < 2 \\ \frac{1}{2}x - 2 & \text{si } x \ge 2 \end{cases}$
1. $f$ est-elle continue sur $\mathbb{R}$ ?
2. $f$ est dérivable sur $\mathbb{R}$ ?
Exercice 2 (8 pts) :
Partie A : Étude d'une fonction auxiliaire Soit $g$ la fonction définie sur $\mathbb{R}$ par $g(x) = (x+2)e^{x-4} - 2$
1. Déterminer la limite de $g$ en $+\infty$ .
2. Démontrer que la limite de $g$ en $-\infty$ vaut $-2$ .
3. On admet que la fonction $g$ est dérivable sur $\mathbb{R}$ et on note $g'$ sa dérivée. Calculer $g'(x)$ pour tout réel $x$ puis dresser le tableau de variations de $g$ .
4. Démontrer que l'équation $g(x) = 0$ admet une unique solution $\alpha$ sur $\mathbb{R}$ .
5. En déduire le signe de la fonction $g$ sur $\mathbb{R}$ .
6. À l'aide de la calculatrice, donner un encadrement d'amplitude $10^{-3}$ de $\alpha$ .
Partie B : Étude de la fonction Soit $f$ la fonction définie sur $\mathbb{R}$ par $f(x) = x^2 - x^2e^{x-4}$
1. Résoudre l'équation $f(x) = 0$ sur $\mathbb{R}$ .
2. On admet que la fonction $f$ est dérivable sur $\mathbb{R}$ et on note $f'$ sa fonction dérivée. Montrer que, pour tout réel $x$ , $f'(x) = -xg(x)$ où la fonction $g$ est celle définie à la partie A.
3. Étudier les variations de la fonction $f$ sur $\mathbb{R}$ .
4. Démontrer que le maximum de la fonction $f$ sur $[0 ; +\infty[$ est égal à $\frac{\alpha^3}{\alpha+2}$ .

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Problem 23818

Find the distance from point $A(-9,-3)$ to the line $y=x-6$ . Round your answer to the nearest tenth.
The distance is about $\square$ units.

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Problem 23819

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

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Problem 23820

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 23821

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 23822

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

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Problem 23823

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

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Problem 23824

What is the diameter of the circle $(x + 3)^2 + y^2 = 100$ ? Write your answer in simplified, rationalized form.

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Problem 23825

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 23826

Determining Concavity In Exercises 5-16, determine the open intervals on which the graph of the function is concave upward or concave downward.
5. $f(x)=x^{2}-4 x+8$
6. $g(x)=3 x^{2}-x^{3}$
7. $f(x)=x^{4}-3 x^{3}$
8. $h(x)=x^{5}-5 x+2$
9. $f(x)=\frac{24}{x^{2}+12}$
10. $f(x)=\frac{2 x^{2}}{3 x^{2}+1}$

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Problem 23827

$144y^2 - x^2 = 1$
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 23828

2. $\frac{d}{dx} x^2 \sin(x)$ .

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Problem 23829

1. Show that the proposition $(p \implies q) \implies \neg(p \wedge \neg q)$ is a tautology.
2. If $\neg[\neg r \implies \neg(p \wedge q)]$ is true, then find the truth value of $[(p \implies r) \vee q] \iff (\neg p \wedge r)$
3. Use mathematical induction prove that a) For all $n \ge 1$ , $1 + 4 + 7 + \dots + (3n - 2) = \frac{n(3n-1)}{2}$ b) For any positive integer $n$ , $n^3 + 2n$ is divisible by 3
4. If 6 is even then 2 does not divide 7. Either 5 is not prime or 2 divide 7. But 5 is prime. Therefore 6 is not even. Investigate the validity by formal proof.
5. Discuss all the necessary steps and sketch the graph of $\frac{x^3 - 9x}{x^2 - 3x - 4}$
6. Find all the square roots of $-2 + 2\sqrt{3}i$
7. Find the number a and k so that $(x-1)$ is a factor of the polynomial $f(x) = x^4 - 2ax^3 + ax^2 - x + k$ and $f(-1) = 10$ , then find all zeros of $f(x)$

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Problem 23830

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

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Problem 23831

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 23832

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

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Problem 23833

3. $\frac{d}{dx} \frac{x+2}{\cos(x)} \cdot$ 4 pts.

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Problem 23834

Question 3, 11.2.37 21 points 0 Points: 0 of 1 Save
Use a calculator to estimate the given limit. $\lim _{x \rightarrow-\infty} \frac{x^{2 / 3}-x^{5 / 3}}{x^{3}}$
What is the limit? Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. $\lim _{x \rightarrow-\infty} \frac{x^{2 / 3}-x^{5 / 3}}{x^{3}}=$ $\square$ B. The limit does not exist and is not $\infty$ or $-\infty$ .

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Problem 23835

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 23836

Identify the greatest common factor of $36 z$ and 12 .
Answer Attempt 1 out of 2

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Problem 23837

2 2) $j+5=18$

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Problem 23838

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 23839

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 23840

4. Suppose $f$ is differentiable on $\mathbb{R}$ and $f(0)=0, f(1)=1$ , and $f(2)=1$ . (a) Show that $f^{\prime}(x)=\frac{1}{2}$ for some $x \in(0,2)$ . (b) Show that $f^{\prime}(x)=\frac{1}{7}$ for some $x \in(0,2)$ .

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Problem 23841

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 23842

Evaluate. $\frac{7}{9} + \frac{1}{6} \div \frac{3}{7}$ Write your answer in simplest form.

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Problem 23843

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 23844

c. $\lim_{x \to 2^{-}} \frac{x+2}{x-2}$ $= \frac{2}{0^{-}}$ 2 marks $= -\infty$ 1 mark

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Problem 23845

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

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Problem 23846

Which of the following statements is FALSE? Area under the curve $y=f(x)$ can be equal to 0 . $\int_{a}^{b} f(x) d x$ could be positive or negative if $f(x)>0$ between $x=a$ and $x=b$ . $\int_{0}^{10} f(x) d x$ could be positive, negative, or zero depending on what the function is. The area between the $x$ -axis and a function is always non-negative.

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Problem 23847

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 23848

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 23849

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 23850

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

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Problem 23851

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 23852

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 23853

$\int_{0}^{\pi / 2} \cos (3 x) \sin (3 x) d x$

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Problem 23854

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 23855

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

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Problem 23856

$16I^3 - \frac{d}{dI}(4I^4 - 3C^2I^2) = \frac{d}{dI}(2IC^4 + 4I + 2020)$
( apply the product rule as required and find the derivative with respect to $I$ of the other terms )
NOTE: Enter $dC/dI$ for $\frac{dC}{dI}$ or for $C'$
Step 2: Identify what the problem is asking Step 3: Find the appropriate formula Step 4: Draw a conclusion

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Problem 23857

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

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Problem 23858

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

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Problem 23859

16 / Final (April 25, 2024) - [9 points] The Taylor series centered at $x=1$ for a function $T(x)$ is given by: $T(x)=\sum_{n=0}^{\infty} \frac{(n!)^{2}}{(-5)^{n} \cdot(2 n)!}(x-1)^{4 n+3}$ a. [6 points] Find the radius of convergence of the Taylor series above. Show your work. Do not attempt to find the interval of convergence. page 1 x - 9 points] The Taylor series ces $T(x)=\sum_{n=0}^{\infty} \frac{(n!)^{2}}{(-5)^{n} \cdot(2 n)!}(x-1)^{4 n+3} \text { is given by: }$ - $\begin{array}{l} \frac{\left((n+1) \frac{\sqrt{k}}{\varepsilon}\right)^{2}}{(-5)^{\frac{2+2}{2}}} \frac{(2 n+2))}{(-5)} \\ 1^{(x} \\ \text { - } 1)^{4 n+7} \\ \frac{(25)^{2} \cdot(2 n)^{1}}{\left(x^{2}\right)^{\alpha}(x-1)^{4 n+3}} \\ \frac{(2 n+2)(2 n+1)(2 n)}{-5(2 n+1)(n+1)} \\ 2 n! \\ (n+2 n+2 \\ \left.(n+1)^{\prime}\right)^{2(n+1)} \end{array}$ $\begin{array}{c} 2 \\ 6+2=8 \\ 2+2=4 \\ 2+2+6 \end{array}$ $-60_{4} \cdot$ 1 b. [3 points] Compute $T^{(123)}(1)$ . Show your work. You do not need to simplify your answer. Answer: $\quad T^{(123)}(1)=$ $\qquad$

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Problem 23860

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

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Problem 23861

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

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Problem 23862

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

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Problem 23863

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 23864

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

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Problem 23865

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 23866

Exercise (2) Write each of the following sets in roster notation (extension): $A=\left\{x / x \in N\right.$ , where $\left.0 \leq x^{2} \leq 28\right\}$ . $B=\{x / x$ is prime and $4 \leq 2 x<15\}$ . $C=\{x / x \in \mathbb{Z}$ , where $1 \leq \sqrt{x} \leq 3\}$ . $\mathrm{D}=\left\{x / x \in \mathbb{Z}\right.$ , where $x$ is a solution of the equation $\left.\left(x^{2}-5\right)(2 x+3)=0\right\}$ . $E=\left\{x / x \in \mathbb{Q}\right.$ , where $x$ is a solution of the equation $\left.\left(x^{2}-5\right)(x+3)=0\right\}$ . $\mathrm{F}=\{x / x \in \mathrm{~N}$ ,where $x$ is a power of 2 and less than 40 $\}$ . $G=\left\{x / x \in \mathbb{N}\right.$ , where $x$ is a multiple of 3 and $\left.\frac{\sqrt{2 x}}{3} \leq 2\right\}$ .

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Problem 23867

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

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Problem 23868

2. Determine the phase shift and the vertical displacement with respect to $y=\cos x$ for each function. Sketch a graph of each function. a) $y=\cos \left(x-30^{\circ}\right)+12$ b) $y=\cos \left(x-\frac{\pi}{3}\right)$ c) $y=\cos \left(x+\frac{5 \pi}{6}\right)+16$ d) $y=4 \cos \left(x+15^{\circ}\right)+3$ e) $y=4 \cos (x-\pi)+4$ f) $y=3 \cos \left(2 x-\frac{\pi}{6}\right)+7$

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Problem 23869

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

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Problem 23870

Find the following limit or state that it does not exist. $\lim _{x \rightarrow 2} 5$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\lim _{x \rightarrow 2} 5=\square$ (Simplify your answer.) B. The limit does not exist.

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Problem 23871

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 23872

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

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Problem 23873

$\lim _{x \rightarrow 5} \frac{x^{3}-125}{x-5}$

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Problem 23874

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 23875

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 23876

$f(x) = c - x$
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 23877

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 23878

$A=(22.5 \times 18)+(25 \times 13.75)+(8.5 \times 8.5)$

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Problem 23879

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

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Problem 23880

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 23881

$\frac{2}{9} \times \frac{3}{4}$

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Problem 23882

$f(x) = x^2 e^x - 5$
Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema.
Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. There are no relative minima. The function has a relative maximum of $\qquad$ at $x = \qquad$ . (Use a comma to separate answers as needed. Type exact answers in terms of $e$ .)
B. The function has a relative maximum of $\qquad$ at $x = \qquad$ and a relative minimum of $\qquad$ at $x = \qquad$ . (Use a comma to separate answers as needed. Type exact answers in terms of $e$ .)
C. There are no relative maxima. The function has a relative minimum of $\qquad$ at $x = \qquad$ . (Use a comma to separate answers as needed. Type exact answers in terms of $e$ .)
D. There are no relative extrema.

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Problem 23883

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 23884

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 23885

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 23886

Use inequality symbols (<, > or =) to complete the sentence.
1) $\frac{2}{3} > \frac{2}{5}$ 2) $-\frac{2}{3}$ $-\frac{2}{5}$ 3) $|{-2.3}|$ $-2.8$ 4) $-0.7$ $-0.65$ 5) $\frac{3}{4}$ $|{ -0.8 }|$ 6) $\frac{1}{8}$ $\frac{1}{9}$ 7) $-1\frac{3}{4}$ $-1.75$ 8) $-\frac{5}{2}$ $-3$ 9) $|{ -0.6 }| < |{ -0.55 }|$ 10) $\frac{3}{4}$ $|-\frac{3}{5}|$ 11) $-\frac{3}{4}$ $-\frac{3}{5}$ 12) $|{ -4\frac{1}{2} }|$ $\frac{9}{2}$ 13) $\frac{7}{4}$ $\frac{3}{2}$ 14) $|{ 0.82 }|$ $-0.9$ 15) $\frac{1}{3}$ $0.375$ 16) $-0.27$ $-0.5$ 17) $1\frac{2}{3}$ $8\frac{}{2}$ 18) $|{ -2.3 }|$ $|{ -\frac{5}{2} }|$ 19) $-0.36$ $-0.2$ 20) $\frac{1}{4}$ $\frac{5}{20}$

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Problem 23887

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 23888

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 23889

$V(x) = x^3 + 3x^2 - 11x - 33$ 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 23890

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 23891

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

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Problem 23892

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 23893

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 23894

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 23895

$7t - 14 - 16r + 9c + (-14c)$ $8 - 8c - 8c - 4b - 12b$ $10n - 15 - 5n + 6 + 2c$ $3x + (-17) + 21f + 3x - (-21f)$ $-19m + 5 - (-m) + c - 7c$ $y - 14 + 30c - 2y + 16c$ $10 + (-4g) + 10 - 13x - 2g + 5x$ $20j + 20j - 16m - 16m + 16$ $-25d + 2s - 7 + 15s - 20d$ $9m - 14 - 6m + 4r + 12r$ $m + 15c + (-3m) - 4$ 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 23896

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 23897

[10 Marks] 8) Given function $y(x)$ below product rule $y(x) = x^2 \ln(x) + 5$ a) Write the equation of the tangent to $y(x)$ at $(1,5)$ . b) Calculate $y''(1)$ . $\ln x'=$

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Problem 23898

```latex \text{Berechnen Sie die folgenden Wahrscheinlichkeiten für eine binomialverteilte Zufallsgröße } X \text{ mit den Parametern:}
\begin{itemize} \item \text{A) } n = 50 \text{ und } p = 0,05 \item \text{B) } n = 100 \text{ und } p = 0,03 \end{itemize}
\begin{align} &P(X = 4) \\ &P(X < 4) \\ &P(X > 3) \\ &P(1 < X < 5) \\ &P(X < 1 \text{ oder } X < 5) \end{align} ```

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Problem 23899

Find the square root. $\sqrt{\frac{1}{4}}$ $\sqrt{\frac{1}{4}}=$ $\square$ (Type a whole number or a simplified fraction.)

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Problem 23900

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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Math Statement

Problem 23801

5. Find the longest interval in which the initial value problem (x−3)y′′+xy′+(ln⁡x)ey=0(x-3)y'' + xy' + (\ln{x})e^y = 0(x−3)y′′+xy′+(lnx)ey=0, y(1)=3y(1) = 3y(1)=3 and y′(1)=0y'(1) = 0y′(1)=0

Problem 23802

Problem 23803

13. (a) Expand (2a+3b)2(2 a+3 b)^{2}(2a+3b)2. (b) Hence or otherwise, expand (2a+3b−4c)2(2 a+3 b-4 c)^{2}(2a+3b−4c)2.

Problem 23804

Subtract. (9u+6)−(u+1)(9 u+6)-(u+1)(9u+6)−(u+1)

Problem 23805

2(4y−5)=702(4 y-5)=702(4y−5)=70Simplify your answer as much as possible. y=y=y=

Problem 23806

ch expression to an equivalent expression by using ra b. 64x3\sqrt[4]{6} x^{3}46​x3

Problem 23807

Solve the following quadratic function by utilizing the square root method. Simplify your answer completely. f(x)=49x2−144x=±[?]□\begin{array}{c} f(x)=49 x^{2}-144 \\ x= \pm \frac{[?]}{\square} \end{array}f(x)=49x2−144x=±□[?]​​

Problem 23808

27. x2−4x−13=0x^2 - 4x - 13 = 0x2−4x−13=030. x2−8x−65=0x^2 - 8x - 65 = 0x2−8x−65=0

Problem 23809

The graphs of y=x+1y = x + 1y=x+1 intersects the graph of y=5cos⁡(x−π3)y = 5\cos\left(x - \frac{\pi}{3}\right)y=5cos(x−3π​) at the point AAA in the first quadrant. By using Newton-Raphson method, find the coordinates of AAA correct to four decimal places.

Problem 23810

Find the intersection of the line and the circle given below. y=−x−3x2+y2=17\begin{aligned} y & =-x-3 \\ x^{2}+y^{2} & =17 \end{aligned}yx2+y2​=−x−3=17​Provide your answer below: □\square□ □\square□ □\square□ □\square□ )

Problem 23811

Problem 23812

The polynomial p(x)=x3+7x2−36p(x)=x^{3}+7 x^{2}-36p(x)=x3+7x2−36 has a known factor of (x+3)(x+3)(x+3). Rewrite p(x)p(x)p(x) as a product of linear factors. p(x)=p(x)=p(x)= □\square□

Problem 23813

1 Find the slant asymptote of the function f(x)=x2+4x−8x+3f(x)=\frac{x^{2}+4 x-8}{x+3}f(x)=x+3x2+4x−8​ ?

Problem 23814

4. y=(x2+1)y = (x^2 + 1)y=(x2+1) arccot xxx 9

Problem 23815

Problem 23816

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 23817

Problem 23818

Find the distance from point A(−9,−3)A(-9,-3)A(−9,−3) to the line y=x−6y=x-6y=x−6. Round your answer to the nearest tenth.The distance is about □\square□ units.

Problem 23819

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

Problem 23820

Problem 23821

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 23822

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

Problem 23823

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

Problem 23824

What is the diameter of the circle (x+3)2+y2=100(x + 3)^2 + y^2 = 100(x+3)2+y2=100? Write your answer in simplified, rationalized form.

Problem 23825

Problem 23826

Problem 23827

Problem 23828

2. ddxx2sin⁡(x)\frac{d}{dx} x^2 \sin(x)dxd​x2sin(x).

Problem 23829

Problem 23830

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

Problem 23831

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 23832

(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 23833

3. ddxx+2cos⁡(x)⋅\frac{d}{dx} \frac{x+2}{\cos(x)} \cdotdxd​cos(x)x+2​⋅ 4 pts.

Problem 23834

Problem 23835

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

Problem 23836

Identify the greatest common factor of 36z36 z36z and 12 .Answer Attempt 1 out of 2

Problem 23837

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

Problem 23838

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 23839

Problem 23840

Problem 23841

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 23842

Evaluate. 79+16÷37\frac{7}{9} + \frac{1}{6} \div \frac{3}{7}97​+61​÷73​ Write your answer in simplest form.

Problem 23843

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 23844

c. lim⁡x→2−x+2x−2\lim_{x \to 2^{-}} \frac{x+2}{x-2}limx→2−​x−2x+2​ =20−= \frac{2}{0^{-}}=0−2​ 2 marks =−∞= -\infty=−∞ 1 mark

Problem 23845

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

Problem 23846

5. Find the longest interval in which the initial value problem $(x-3)y'' + xy' + (\ln{x})e^y = 0$ , $y(1) = 3$ and $y'(1) = 0$

13. (a) Expand $(2 a+3 b)^{2}$ . (b) Hence or otherwise, expand $(2 a+3 b-4 c)^{2}$ .

Subtract. $(9 u+6)-(u+1)$

$2(4 y-5)=70$
Simplify your answer as much as possible. $y=$

ch expression to an equivalent expression by using ra b. $\sqrt[4]{6} x^{3}$

Solve the following quadratic function by utilizing the square root method. Simplify your answer completely. $\begin{array}{c} f(x)=49 x^{2}-144 \\ x= \pm \frac{[?]}{\square} \end{array}$

27. $x^2 - 4x - 13 = 0$
30. $x^2 - 8x - 65 = 0$

The graphs of $y = x + 1$ intersects the graph of $y = 5\cos\left(x - \frac{\pi}{3}\right)$ at the point $A$ in the first quadrant. By using Newton-Raphson method, find the coordinates of $A$ correct to four decimal places.

Find the intersection of the line and the circle given below. $\begin{aligned} y & =-x-3 \\ x^{2}+y^{2} & =17 \end{aligned}$
Provide your answer below: $\square$ $\square$ $\square$ $\square$ )

The polynomial $p(x)=x^{3}+7 x^{2}-36$ has a known factor of $(x+3)$ . Rewrite $p(x)$ as a product of linear factors. $p(x)=$ $\square$

1 Find the slant asymptote of the function $f(x)=\frac{x^{2}+4 x-8}{x+3}$ ?

4. $y = (x^2 + 1)$ arccot $x$ 9

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

Find the distance from point $A(-9,-3)$ to the line $y=x-6$ . Round your answer to the nearest tenth.
The distance is about $\square$ units.

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

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. $1.9$

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

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

What is the diameter of the circle $(x + 3)^2 + y^2 = 100$ ? Write your answer in simplified, rationalized form.

2. $\frac{d}{dx} x^2 \sin(x)$ .

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. $\frac{x-5}{x^2 + 9x + 18}$

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

3. $\frac{d}{dx} \frac{x+2}{\cos(x)} \cdot$ 4 pts.

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

Identify the greatest common factor of $36 z$ and 12 .
Answer Attempt 1 out of 2

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

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) $\{3\}$

Evaluate. $\frac{7}{9} + \frac{1}{6} \div \frac{3}{7}$ Write your answer in simplest form.

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.

c. $\lim_{x \to 2^{-}} \frac{x+2}{x-2}$ $= \frac{2}{0^{-}}$ 2 marks $= -\infty$ 1 mark

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 $E^{0}_{Ag^{+} | Ag} = 0.80 V$

$\int_{0}^{\pi / 2} \cos (3 x) \sin (3 x) d x$

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

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

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

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

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

$\lim _{x \rightarrow 5} \frac{x^{3}-125}{x-5}$

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