Browse Math Statement problems Studdy Solved!

Problem 25401

4) Individua quali fra i seguenti punti non appartengono al grafico della funzione $f(x)=\frac{1-x^{2}}{x}$ [a] $(1 ; 0)$ (b) $(0 ; 1)$ [C] $\left(-2 ; \frac{3}{2}\right)$ (motiva la risposta) [i] $(-1 ; 0)$ [e) $\left(-3 ;-\frac{10}{3}\right)$

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Problem 25402

12. Risolvi l'equazione $2 \cos ^{2}(x)-3 \sin (x)-1=0$ nell'intervallo $[0,2 \pi]$ . (a) $x=\frac{\pi}{4}, \frac{5 \pi}{4}$ (b) $x=\frac{\pi}{6}, \frac{5 \pi}{6}$ (c) $x=\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{4 \pi}{3}, \frac{5 \pi}{3}$ (d) Nessuna soluzione (e) $x=\arcsin \left(-\frac{1}{3}\right), \pi-\arcsin \left(-\frac{1}{3}\right)$

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Problem 25403

4) Individua quali fra i seguenti punti non appartengono al grafico della funzione $f(x)=\frac{1-x^{2}}{x}$ [a] $(1 ; 0)$ $5(0 ; 1)$ E $\left(-2 ; \frac{3}{2}\right)$ (motiva la risposta) [] $(-1 ; 0)$ [e $\left(-3 ;-\frac{10}{3}\right)$

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Problem 25404

4. Исследовать функцию на экстремумы и промежутки монотонности; найти перегиба и указать промежутки выпуклости, нарисовать эскиз трафика ( 356 $y=x^{3}-6 x^{2}+121$

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Problem 25405

7(3). Используя метод Лагранжа, найдите условные локальные эхстремумы фунвия $z=x^{2} y$ при условин $x+y-2=0$ .

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Problem 25406

Find $\lim _{x \rightarrow 4} \frac{x^{2}-x-12}{x-4}$

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Problem 25407

1. Prove that $2+3 \sqrt{3}$ is an irrational number. It is given that $\sqrt{ } 3$ is an irrational number.

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Problem 25408

侪 $\sqrt{2}$ Write the equation in standard form for the hyperbola $-2 x^{2}+y^{2}+12 y-32=0$ $\square$ 믐 () 2 Submit

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Problem 25409

ame the Field Axiom that was use $x+(y+z)=(x+y)+z$

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Problem 25410

$-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$ . Find the value of $\theta$ in radians. $\sin (\theta)=\frac{1}{2}$
Write your answer in simplified, rationalized form. Do not round. $\theta=$ $\square$

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Problem 25411

For $y=48 x-3 x^{5}$ , determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; inflection points; symmetry; and those intercepts that can be obtained conveniently. Then sketch the graph.
On which interval(s) is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is increasing on $\left(-\frac{2}{\sqrt[4]{5}}, \frac{2}{\sqrt[4]{5}}\right)$ . (Type your answer in interval notation. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The function is never increasing.
On which interval(s) is the function concave down? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is concave down on $(0, \infty)$ . $\square$ (Type your answer in interval notation. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no interval on which the function is concave down.
On which interval(s) is the function concave up? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is concave up on $(-\infty, 0)$ . $\square$ (Type your answer in interval notation. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no interval on which the function is concave up.
Determine the relative minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The relative minimum/minima is/are $\square$ . (Type an ordered pair. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. There is no relative minimum.

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Problem 25412

$(-2 a)^{4}$

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Problem 25413

Determine the following indefinite integrals:
1. $\int_{2}^{5}(-3 v+4) d \dot{v}$
2. $\int_{-1}^{1}\left(t^{2}-2\right) d t$
3. $\int_{-1}^{1}\left(t^{3}-9 t\right) d t$
4. $\int_{1}^{2}\left(\frac{3}{x^{2}}-1\right) d x$
5. $\int_{-3}^{3} v^{1 / 3} d x$
6. $\int_{0}^{2} 6 x d x$

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Problem 25414

Determine the real roots of the cubic function $f(x)=x^{3}+3 x^{2}-13 x-15$ . Correctly plot the THREE roots on the coordinate plane.

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Problem 25415

6. For each equation below, find the value(s) of $x$ that $m$ (Lesson 2-18) a. $10=\frac{1+7 x}{7+x}$ b. $0.2=\frac{6+2 x}{12+x}$ c. $0.8=\frac{x}{0.5+x}$ d. $3.5=\frac{4+2 x}{0.5-x}$

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Problem 25416

9. What is $(2 i-5)(4+7 i)$ in simplest form? $14 i^{2}-27 i-20$ $57 i+20$ $-27 i-34$ $-27 i-6$ Clear All

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Problem 25417

15. What are the solutions for the quadratic function $y=3 x^{2}-8 x+7$ ? $x=\frac{4 \pm i \sqrt{5}}{3}$ $x=\frac{-4 \pm i \sqrt{5}}{3}$ $x=-6 ; x=14$ $x=\frac{8 \pm \sqrt{20}}{6}$

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Problem 25418

Factorise $7(5 x-y)^{2}-(y-5 x)$

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Problem 25419

6. Simplify $(9 m+n)^{2}-(9 m-n)^{2}$ .

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Problem 25420

17. Reflect the function $f(x)=x^{3}$ about the $x$ -axis and translate it 3 units to the left to produce $g(x)$ . Which equation represents the function $g(x)$ ?
$g(x)=-(x+3)^{3}$
$g(x)=-x^{3}-3$
$g(x)=-x^{3}+3$
$g(x)=-(x-3)^{3}$

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Problem 25421

$\int \frac{e^{1 / t}}{t^{2}} d t$

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Problem 25422

11. The function $g(x)=4(x-6)^{3}-2$ was created by transforming $f(x)=x^{3}$ . To create $g(x), f(x)$ was -Choose the correct answer - - , then was $\qquad$ and then was -Choose the correct answer - . - Choose the correct answer - stretched vertically by a factor of 4 Clear All compressed vertically by a factor 4

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Problem 25423

Simplify: $\log _{2} 16 d$ $4 \log _{2} d$ $\log _{2} 4 d$ $\log _{2}(4+d)$ $4+\log _{2} d$

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Problem 25424

solution. $\begin{array}{l} x+2 y=-8 \\ y=-\frac{3}{2} x-6 \end{array}$
Click to select points on the graph.

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Problem 25425

Vrite 5.79 in expanded form. $5.79=\quad \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}$

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Problem 25426

6. A bug walks along a straight path. For $t \geq 0$ , the position of the bug is modeded by $B(t)=t^{2}-3 t=28$ . (a) For what times does the bug have a positive velocity? (b) Is the bug speeding up or slowing down att $=1$ Give a reason for your answer. (c) Find the position of the bug when $v(t)=5$ . (d) At what time(s) $t$ does the bug turn around? Give a reason for your answer.
7. For $0 \leq t \leq 2 \pi$ , the position of a particle moving along the $x$ axis is given by $x(t)=\sin ^{2}(t)$ . (a) Find the velocity of the particle at $t=\frac{\pi}{3}$ . Is the particle moving toward or away from the origin when $t=$ Give a reason for your answer. (b) Find $a(\pi)$ .
8. Jevin rides his bike along a straight bike path. Jevin's velocity is modeled by $v(t)=e^{\frac{6}{2}}-t^{2}+20$ wher $0 \leq t \leq 5$ hours and $v(t)$ is measured in miles per hour. (a) Find a(4). Include units of measure.

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Problem 25427

Find the product. $\begin{array}{l} \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right) \\ \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right)= \end{array}$

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Problem 25428

$\{(a, m),(m, n),(t, n),(n, n)\}$
Function Not a function

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Problem 25429

Simplify. $-\left(-3+\frac{i}{5}\right)+\frac{i}{15}-\frac{3+3 i}{5}$
Write your answer in the form a + bi. Simplify all fractions. $\square$

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Problem 25430

Divide. $\begin{array}{l} \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}} \\ \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}}= \end{array}$

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Problem 25431

Addition and Subtraction $1\left(2 x^{2}-5 x+7\right)+\left(3 x^{2}+3 x-5\right)$
2. $\left(2 x^{2}-5 x+7\right)-\left(x^{2}+3 x-5\right)$
Multiplication and Division
1. $\left(3 x^{2} y^{2} z\right)\left(5 x^{2} y z^{2}\right)$
2. $\left(3 x y^{2}\right)\left(3 x^{2}+2 x y-5 y^{2}\right)$
3. $\frac{30 r^{2} y^{2} z}{6 x^{2} y^{2}}$
4. $\frac{5 x^{-3}}{2 y^{-1}}$ : $5 x^{2}+2 x+2$ $15 x^{6} y^{3} z^{3}$ $3 x^{2}-2 x+2$ $x^{2}-8 x+12$ $9 x^{3} y^{2}+6 x^{2} y^{3}-15 x y^{4}$ $5 x^{2}-2 x+2$ $6 x^{2} y^{2}+5 x y^{2}-8 x y^{4}$ : $\frac{5 x}{z^{4}}$ $=\frac{5 y^{2}}{2 x^{2}}$ $=\frac{2 y^{2}}{5 x^{2}}$

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Problem 25432

7. Let $f(x)=2 x^{4}-4 x^{3}-22 x^{2}+32 x+48$ . a. (2 points) Use your graphing calculator to find the integer zeros of $y=f(x)$ . b. (6 points) Use synthetic or polynomial division to find any remaining real zeros (if any exist). c. (4 points) Factor $f$ completely over the real numbers. Here, "completely factor" means that $f$ should be made up of only linear and/or irreducible quadratic factors. An irreducible quadratic is a quadratic function with no real zeros such as $x^{2}+1$ . $f(x)=$

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Problem 25433

Factor out the greatest com polynomial. $8 z-4$

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Problem 25434

Factor the expression completely. $392 x^{4}-128 x^{2} y^{2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $392 x^{4}-128 x^{2} y^{2}=$ $\square$ (Simplify your answer.) B. $392 x^{4}-128 x^{2} y^{2}$ is prime.

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Problem 25435

Solve. $\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}$ $\square$ (Use a comma to separate answers as needed.)

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Problem 25436

$5 x^{2}(x-2)-x(4 x+2)-9 x^{2}(-3 x)$

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Problem 25437

In the equation $\log _{3}(7 x-1)=\log _{3}(5 x+17)$ , what is the value of $x$ a) 7 b) 9 c) 11 d) 13 a b C d

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Problem 25438

The equation of a circle is $(x-9)^{2}+(y+8)^{2}=4$ . What are the center and radius of the circle?
Choose 1 answer: (A) The center is $(9,-8)$ and the radius is 2 .
B The center is $(-9,-8)$ and the radius is 2 . (C) The center is $(9,8)$ and the radius is 2 . (D) The center is $(9,-8)$ and the radius is 4 .

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Problem 25439

$\frac{1-2 \sin ^{2} x}{\sin x+\cos x}+2 \sin \frac{x}{2} \cos \frac{x}{2}=\cos x$

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Problem 25440

Quadratic Formula
Solve for x . $\begin{array}{c} x^{2}-5 x-24=0 \\ x=[?] \end{array}$
Remember the quadratic formula: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

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Problem 25441

b) $\sin 2 x=2 \sin x \cos x$ c) $\tan x=\frac{\sin x}{\cos x}$ d) all of these - The height of the tip of one blade of a wind turbine above the ground, $h(t)$ , can be modelled by $h(t)=18 \cos \left(\pi t+\frac{\pi}{4}\right)+2$ where $t$ is the time passed in seconds. Whic, time interval describes a period when the bl tip is at least 30 m above the ground? a) $5.24 \leq t \leq 7.33$ (c) $1.37 \leq t \leq 2$ . ) $0.42 \leq t \leq 1.08$ d) $0.08 \leq t \leq 1$ .
Iify $\cos \frac{\pi}{5} \cos \frac{\pi}{6}-\sin \frac{\pi}{5} \sin \frac{\pi}{6}$

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Problem 25442

e 0.05 in expanded form. $0.05=\square \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}$

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Problem 25443

1. Which of these is an equivalent trigonomerric ratio for $\sin \frac{2 \pi}{5}$ ? a) $\cos \frac{\pi}{10}$ c) $-\cos \frac{9 \pi}{10}$ b) $\sin \frac{3 \pi}{5}$ d) all of these $\alpha=\frac{12}{2}$ and

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Problem 25444

dessous. II) $\tan \frac{\pi}{4}+\tan \frac{\pi}{6} \tan \frac{\pi}{3}$

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Problem 25445

atic by factoring. $2 x^{2}+9 x-1=2 x-7$

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Problem 25446

5. Which of the following values of $x$ does not lie in the domain of $y=-2 \sqrt{5-2 x}$ ? (1) -3 (3) 2.5 (2) 2 (4) 4
COMMON CORE Algebra II, Final ASSESSMENTS (1)

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Problem 25447

-ite the expression as a decimal number. $3 \times \frac{1}{10}+7 \times \frac{1}{100}+2 \times \frac{1}{1000}=$

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Problem 25448

New! Multi Part Question - when you answer this question we'll mark each part individually Bookwork code: 1E Calculator allowed
Work out the solutions to these simultaneous equations: $\begin{aligned} x & =5-y \\ y^{2} & =3 x+28 \end{aligned}$
If any of your answers are decimals, give them to 2 d.p.

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Problem 25449

Write $(-5+10 i)^{2}$ in simplest $a+b i$ form.

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Problem 25450

$\cos x \sin x=0$

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Problem 25451

recelculus Q-s Propertes of matrices w. Ras bave gris
If $E=\left[\begin{array}{ccc}-3 & 1 & -1 \\ -3 & 3 & 1\end{array}\right], F=\left[\begin{array}{cc}5 & 1 \\ 4 & -1 \\ -3 & -3\end{array}\right]$ , and $G=\left[\begin{array}{cc}-5 & -1 \\ -2 & 1\end{array}\right]$ , is the following statement true or false? $E(F G)=(G) F$ true false Subm:

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Problem 25452

Math $2 A$ REVIEW SHOW ALL WORK Unit 5 Module 9 Linear Equations and Inequalities Name $\qquad$ Datel Per $\qquad$ LT SA: I can solve and write multi-step equations that intudo declmbls and froctions. I can solve the eral equaktons. 1) Solve the equation for $x$ . 2) Solve the equation for $x$ . $7 x+8(x-3)=12-3 x$ $14.3 h-6.5 h=10.3 h+9$

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Problem 25453

$\frac{5 \sqrt{6}}{-\sqrt{3}}$

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Problem 25454

Given $f(x)=-\csc (4 x)$ , find $f^{\prime}(x)$

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Problem 25455

If the range of a quadratic function is $5 \leq y<\infty$ , which of the following could be true? None of these are correct. The parabola has a maximum at $(2,5)$ . The parabola has a minimum at $(2,1)$ . The parabola has a maximum at $(5,1)$ .

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Problem 25456

a) Factorise $x^{2}+9 x+14$ . b) By sketching a graph, solve the inequality $x^{2}+9 x+14 \leq 0$ .

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Problem 25457

Factoring the following polynomial completely using the greatest common factor. If the expression cannot be factored enter the expression as is. $81 x^{5}-99 x^{4}+9 x^{2}$

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Problem 25458

Work out the lowest integer value that $k$ can take if $7+4 k>k+40$

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Problem 25459

$\begin{array}{r}3 x-4=8 \\ x=\end{array}$

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Problem 25460

quations below? $5 x-2=18$

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Problem 25461

Subtract the polynomials. See Example
49. $\left(3 a^{2}-2 a+4\right)-\left(a^{2}-3 a+7\right)$

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Problem 25462

1 Multiple Choice
1 point Add or subtract. $\frac{5}{x-2}+\frac{3}{x-5}$ $\frac{8 x+31}{(x-2)(x-5)}$ $\frac{-8 x-31}{(x-2)(x-5)}$ $\frac{8 x}{(x-2)(x-5)}$ $\frac{8 x-31}{(x-2)(x-5)}$

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Problem 25463

Divide: $\frac{-10}{-5}=\square$ subrit

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Problem 25464

Time left 0:29
The average value of the function $f(x)=-\left|x^{5}\right|$ on the interval $[-2,2]=$ Select one: a. $-\frac{1}{4} \int_{0}^{32} \sqrt[5]{y} d y$ b. $\frac{1}{4} \int_{2}^{-2} x^{5} \mathrm{~d} x$ c. Else d. $-\frac{1}{16} \int_{0}^{32} \sqrt[5]{y} \mathrm{~d} y$ e. $\frac{1}{2} \int_{32}^{0}(2-\sqrt[5]{y}) \mathrm{d} y$ Next p

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Problem 25465

one of the following integrals is improper a. $\int_{-1}^{1} \frac{1}{1+x^{2}} d x$ b. none C. $\int_{-1}^{1} \frac{1}{1+e^{x}} d x$ d. $\int_{-1}^{1} \frac{1}{1+\sqrt[3]{x}} d x$ $\int_{-1}^{1} \frac{1}{1+} d x$

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Problem 25466

$\int_{0}^{\infty} \frac{2}{1+x^{2}}$ a. none b. $\frac{\pi}{2}$ c. $-\pi$ d. $\pi$

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Problem 25467

Questions 1 through 3 refer to the following. The function $f$ is given by $f(x)=2.5 x^{4}+3 x^{3}-2.6 x^{2}-5.1 x-5.6$ .
2 2 Mark for Review Part B Find all real zeros of $f$ . Note On your AP Exam, you will handwrite your responses to free-response questions in a test booklet
B $\square$ I $\underline{u}$ U $\Omega$ $\checkmark$ do 国睨 $\leftrightarrows$ $\rightarrow$ $x^{2}$ $x_{2}$ I

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Problem 25468

The area of the region encloded by the curves $y=-\frac{1}{2} x^{2}$ and $y=-4 \sqrt{x}$ is given by:
Select one: a. $\int_{0}^{8}\left(\sqrt{2 y}-\frac{y^{2}}{16}\right) d y$ b. $\int_{0}^{4}\left(\sqrt{2 y}-\frac{y^{2}}{16}\right) d y$ c. $\int_{0}^{4}\left(8 \sqrt{x}-x^{2}\right) d x$ d. $\int_{0}^{4}\left(4 \sqrt{x}-\frac{1}{2} x^{2}\right) d x$ e. Else

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Problem 25469

$\log (3 x-7)+\log (3 x+1)=1+\log 2$

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Problem 25470

How many zeros does $f(x)=a(x-5)^{2}$ have if $a<0$ ? 1) It is impossible to determine. 2) 1 3) 0 4) 2

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Problem 25471

Frintrics
Question 3 Usten
You are given the following polynomials: $\begin{array}{l} f(x)=x^{4}-x^{2} \\ g(x)=x^{3}+x^{2} \\ h(x)=x^{4}+x^{2} \end{array}$
Determine the new polynomial and appropriate names for $f(x)+g(x)$ and $f(x)-n(x)$ . (Wress on an item in the answer box, and then press on the box under the corresponding category. To remove an item, you can press on the box and the trash icon to the right of the ltem you want to remove. $f(x)+g(x) \quad F(x)-h(x)$
Answer Bank binomial $x^{4}+x^{2}$ quadratic quartic $-2 x^{2}$

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Problem 25472

The derivative of $y=\cos ^{3}\left(\sin \left(x^{3}\right)\right) \text { is }$

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Problem 25473

Select all the correct answers.
Which vectors are unit vectors? $u=\left\langle-\frac{1}{3} \sqrt{\frac{7}{2}}, \frac{1}{3} \sqrt{\frac{13}{2}}\right\rangle$ $u=\left\langle\frac{1}{\sqrt{3}},-\sqrt{\frac{2}{3}}\right\rangle$ $u=\left\langle\frac{1}{2} \sqrt{\frac{5}{3}},-\frac{1}{2} \sqrt{\frac{7}{3}}\right\rangle$ $\mathbf{u}=\left\langle\frac{3}{\sqrt{7}},-\frac{2}{\sqrt{7}}\right\rangle$

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Problem 25474

(B) > (D) 1>2
9. Find lim 1-e* x+0 In (2-e*) (A) 210 (B) 1 (C) 0 (D) The limit does not exist. function given by f(x)=2 graph of fat

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Problem 25475

What are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

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Problem 25476

Select the correct answer.
Convert $\theta=\frac{3 \pi}{4}$ to rectangular form. A. $y=-1$ B. $y=1$ C. $y=x$ D. $y=-x$ E. $x=-1$

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Problem 25477

1. Solve each equation. a) $(2 x-5)(3 x+8)=0$

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Problem 25478

Solve using the quadratic formula. $k^{2}-k-4=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $k=$ $\square$ or $k=$ $\square$ Submit

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Problem 25479

Simplify: $-6(\sqrt{36 t}+3-\sqrt{t})$ $-48 \sqrt{t}$ $-30 \sqrt{t}+18$ None of these. $48 \sqrt{t}$ $-30 \sqrt{t}-18$

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Problem 25480

5/44
Combine like terms to simplify: $(5 x+2)+(4 x-5)$ $x+7$ $9 x+7$

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Problem 25481

Solve using the quadratic formula. $-2 t^{2}+9 t+7=0$
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $t=$ $\square$ or $t=$ $\square$

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Problem 25482

Select the correct answer. If $f(x)=\frac{2 x+1}{x-4}$ , what is the value of $f^{-1}(3)$ ? A. $\frac{22}{7}$ B. $\frac{19}{11}$ C. $\frac{8}{3}$ D. 13 E. 11

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Problem 25483

23. What is $\sqrt{-144}$ ?

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Problem 25484

2
Решите уравнение: $\log _{d}(3-2 x)=\log _{d}(2 x+5)$

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Problem 25485

Question: Convergence in Probability Let $X_{1}, X_{2}, \ldots$ be a sequence of independent and identically distributed (i.i.d.) random variables, where each $X_{i}$ has the following probability distribution: $P\left(X_{i}=0\right)=\frac{1}{2}, \quad P\left(X_{i}=1\right)=\frac{1}{2} .$ 1
Define the sample mean $\bar{X}_{n}$ as: $\bar{X}_{n}=\frac{1}{n} \sum_{i=1}^{n} X_{i} .$
We want to analyze the behavior of $\bar{X}_{n}$ as $n \rightarrow \infty$ . (a) Show that $E\left[X_{i}\right]=\frac{1}{2}$ and $\operatorname{Var}\left(X_{i}\right)=\frac{1}{4}$ . (b) Using the weak law of large numbers (WLLN), show that $\bar{X}_{n} \xrightarrow{P} \frac{1}{2}$ as $n \rightarrow \infty$ . That is, prove that $\bar{X}_{n}$ converges to $\frac{1}{2}$ in probability. (c) For a sequence $Y_{1}, Y_{2}, \ldots$ of independent random variables where $P\left(Y_{i}=\right.$ 1) $=1-\frac{1}{i}$ and $P\left(Y_{i}=0\right)=\frac{1}{i}$ , determine whether $Y_{n}$ converges in probability to 1 as $n \rightarrow \infty$ . Justify your answer using the definition of convergence in probability.

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Problem 25486

Soit le sinte $\mu_{n}$ sefin por $\left\{\begin{array}{l}\mu_{0}=4 \\ \mu_{n+1}=\frac{1}{2}\end{array} \mu_{n}+5\right.$ a) calculer $\mu_{1}, \mu_{2}, \mu_{3}$ . b) justifier que (un) ni erthimethique ni Gcométrique o) expore $v_{n}=\mu_{n}-10$ . a) Montre que $\left(v_{n}\right)(S \cdot G)$ . b) Exprimer $v_{n}$ puis $u_{n}$ enfonction den d) oxpose $S_{n}=\sum_{k=0}^{n-1} v_{k}$ et $S_{n}^{\prime}=\sum_{k=0}^{n-1} \mu_{k}$ a) experime $S_{n}$ pins sn'enfonction dek. b) aluiler $S_{325}$ et $S_{2024}$ .

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Problem 25487

Graph this line using the slope and $y$ -intercept: $y=x-6$
Click to select points on the graph.

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Problem 25488

(10) $\frac{2}{x^{2}-x}=\frac{1}{x-1}$

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Problem 25489

What are the co-vertices of the ellipse $\frac{x^{2}}{25}+\frac{(y-3)^{2}}{100}=1 ?$ Write your answer in simplified, rationalized form. $\square$ $\square$ and $\square$ $\square$

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Problem 25490

Calculer la longueur d'arc de la courbe définie par l'équation $y=\sqrt{25-x^{2}}$ pour $0 \leq x \leq \frac{5 \sqrt{2}}{2}$ .

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Problem 25491

Which of these statements is true? $\overleftrightarrow{W X} \perp \overleftrightarrow{Z Y}$ and $\overleftrightarrow{A B}|\mid \overleftrightarrow{U V}$ $\overleftrightarrow{U V}|\mid \overleftrightarrow{A B}$ and $\overleftrightarrow{U V}| \mid \overleftrightarrow{Z Y}$ $\overleftrightarrow{W X} \perp \overleftrightarrow{Z Y}$ and $\overleftrightarrow{W X} \| \overleftrightarrow{A B}$ $\overleftrightarrow{U V} \perp \overleftrightarrow{W X}$ and $\overleftrightarrow{A B} \perp \overleftrightarrow{W X}$

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Problem 25492

$708 \div 3$

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Problem 25493

Solve the inequality. $|x+8|>1$
Select the correct choice below and, if necessary, fill in the answ A. The solution is $\square$ (Type your answer in interval notation B. The solution set is $\varnothing$ .

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Problem 25494

Which of the following is the correct simplified difference quotient for $f(x)=\frac{2 x}{x-3} ?$ $-\frac{2}{(x+h-3)(x-3)}$ $\frac{2}{(x+h-3)(x-3)}$ $-\frac{2 h}{(x+h-3)(x-3)}$ $\frac{2 h}{(x+h-3)(x-3)}$ Nothing in this list is correct.

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Problem 25495

12. Use the elimination method by subtraction to solve for $x$ and $y$ .
Equation $1 \quad 4 x-3 y=-4$ Equation $2 \quad 4 x+5 y=28$
12a First solve for $y$ . Enter your next step here $12 b$ Submit step

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Problem 25496

Übung 3 Ortskurvennachweis Gegeben ist die $\operatorname{Schar}_{\mathrm{a}}(\mathrm{x})=\mathrm{ax}^{2}-\mathrm{x}(\mathrm{a}>0)$ . a) Untersuchen Sie $f_{a}$ auf Nullstellen und Extrema.

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Problem 25497

$475 \div 50$

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Problem 25498

6. Untersuchung von Funktionenscharen
Untersuchen Sie die Schar $f_{a}$ auf Nullstellen und Extrema. Zeichnen Sie $f_{a}$ . Es gelte $a>0$ . a) $f_{a}(x)=-\frac{1}{a} x^{2}+a x$ ,

See Solution

Problem 25499

CCA2 > Chapter 2 > Lesson 2.1.2 > Problem 2-24
Consider the equations $y=3(x-1)^{2}-5$ and $y=3 x^{2}-6 x-2$ . a. Verify that they are equivalent by creating a table or graph for each equation. $\square$ $\checkmark$ Hint (a): Here are a couple of points on the table. Make sure you get these points and continue both of your tables for at leas \begin{tabular}{c|c|} \hline $x$ & $y$ \\ \hline-2 & 22 \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & -5 \\ \hline 2 & \\ \hline \end{tabular}

See Solution

Problem 25500

6. $f(x)=4^{x}\left(\frac{2}{x^{5}}+\frac{1}{3 x}\right)$

See Solution

Math Statement

Problem 25401

Problem 25402

Problem 25403

Problem 25404

Problem 25405

7(3). Используя метод Лагранжа, найдите условные локальные эхстремумы фунвия z=x2yz=x^{2} yz=x2y при условин x+y−2=0x+y-2=0x+y−2=0.

Problem 25406

Find lim⁡x→4x2−x−12x−4\lim _{x \rightarrow 4} \frac{x^{2}-x-12}{x-4}limx→4​x−4x2−x−12​

Problem 25407

1. Prove that 2+332+3 \sqrt{3}2+33​ is an irrational number. It is given that 3\sqrt{ } 3​3 is an irrational number.

Problem 25408

侪 2\sqrt{2}2​ Write the equation in standard form for the hyperbola −2x2+y2+12y−32=0-2 x^{2}+y^{2}+12 y-32=0−2x2+y2+12y−32=0 □\square□ 믐 () 2 Submit

Problem 25409

ame the Field Axiom that was use x+(y+z)=(x+y)+zx+(y+z)=(x+y)+zx+(y+z)=(x+y)+z

Problem 25410

−π2≤θ≤π2-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}−2π​≤θ≤2π​. Find the value of θ\thetaθ in radians. sin⁡(θ)=12\sin (\theta)=\frac{1}{2}sin(θ)=21​Write your answer in simplified, rationalized form. Do not round. θ=\theta=θ= □\square□

Problem 25411

Problem 25412

(−2a)4(-2 a)^{4}(−2a)4

Problem 25413

Problem 25414

Determine the real roots of the cubic function f(x)=x3+3x2−13x−15f(x)=x^{3}+3 x^{2}-13 x-15f(x)=x3+3x2−13x−15. Correctly plot the THREE roots on the coordinate plane.

Problem 25415

6. For each equation below, find the value(s) of xxx that mmm (Lesson 2-18) a. 10=1+7x7+x10=\frac{1+7 x}{7+x}10=7+x1+7x​ b. 0.2=6+2x12+x0.2=\frac{6+2 x}{12+x}0.2=12+x6+2x​ c. 0.8=x0.5+x0.8=\frac{x}{0.5+x}0.8=0.5+xx​ d. 3.5=4+2x0.5−x3.5=\frac{4+2 x}{0.5-x}3.5=0.5−x4+2x​

Problem 25416

9. What is (2i−5)(4+7i)(2 i-5)(4+7 i)(2i−5)(4+7i) in simplest form? 14i2−27i−2014 i^{2}-27 i-2014i2−27i−20 57i+2057 i+2057i+20 −27i−34-27 i-34−27i−34 −27i−6-27 i-6−27i−6 Clear All

Problem 25417

15. What are the solutions for the quadratic function y=3x2−8x+7y=3 x^{2}-8 x+7y=3x2−8x+7 ? x=4±i53x=\frac{4 \pm i \sqrt{5}}{3}x=34±i5​​ x=−4±i53x=\frac{-4 \pm i \sqrt{5}}{3}x=3−4±i5​​ x=−6;x=14x=-6 ; x=14x=−6;x=14 x=8±206x=\frac{8 \pm \sqrt{20}}{6}x=68±20​​

Problem 25418

Factorise 7(5x−y)2−(y−5x)7(5 x-y)^{2}-(y-5 x)7(5x−y)2−(y−5x)

Problem 25419

6. Simplify (9m+n)2−(9m−n)2(9 m+n)^{2}-(9 m-n)^{2}(9m+n)2−(9m−n)2.

Problem 25420

Problem 25421

∫e1/tt2dt\int \frac{e^{1 / t}}{t^{2}} d t∫t2e1/t​dt

Problem 25422

Problem 25423

Simplify: log⁡216d\log _{2} 16 dlog2​16d 4log⁡2d4 \log _{2} d4log2​d log⁡24d\log _{2} 4 dlog2​4d log⁡2(4+d)\log _{2}(4+d)log2​(4+d) 4+log⁡2d4+\log _{2} d4+log2​d

Problem 25424

solution. x+2y=−8y=−32x−6\begin{array}{l} x+2 y=-8 \\ y=-\frac{3}{2} x-6 \end{array}x+2y=−8y=−23​x−6​Click to select points on the graph.

Problem 25425

Vrite 5.79 in expanded form. 5.79=×1+□×110+□×11005.79=\quad \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}5.79=×1+□×101​+□×1001​

Problem 25426

Problem 25427

Find the product. (6x−14)(6x+14)(6x−14)(6x+14)=\begin{array}{l} \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right) \\ \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right)= \end{array}(6x−41​)(6x+41​)(6x−41​)(6x+41​)=​

Problem 25428

{(a,m),(m,n),(t,n),(n,n)}\{(a, m),(m, n),(t, n),(n, n)\}{(a,m),(m,n),(t,n),(n,n)}Function Not a function

Problem 25429

Simplify. −(−3+i5)+i15−3+3i5-\left(-3+\frac{i}{5}\right)+\frac{i}{15}-\frac{3+3 i}{5}−(−3+5i​)+15i​−53+3i​Write your answer in the form a + bi. Simplify all fractions. □\square□

Problem 25430

Divide. 30y7−6y2+12y6y230y7−6y2+12y6y2=\begin{array}{l} \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}} \\ \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}}= \end{array}6y230y7−6y2+12y​6y230y7−6y2+12y​=​

Problem 25431

Problem 25432

Problem 25433

Factor out the greatest com polynomial. 8z−48 z-48z−4

Problem 25434

Problem 25435

Solve. y3−8y2−9y=0y=□\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}y3−8y2−9y=0y=□​ □\square□ (Use a comma to separate answers as needed.)

Problem 25436

5x2(x−2)−x(4x+2)−9x2(−3x)5 x^{2}(x-2)-x(4 x+2)-9 x^{2}(-3 x)5x2(x−2)−x(4x+2)−9x2(−3x)

Problem 25437

In the equation log⁡3(7x−1)=log⁡3(5x+17)\log _{3}(7 x-1)=\log _{3}(5 x+17)log3​(7x−1)=log3​(5x+17), what is the value of xxx a) 7 b) 9 c) 11 d) 13 a b C d

Problem 25438

Problem 25439

1−2sin⁡2xsin⁡x+cos⁡x+2sin⁡x2cos⁡x2=cos⁡x\frac{1-2 \sin ^{2} x}{\sin x+\cos x}+2 \sin \frac{x}{2} \cos \frac{x}{2}=\cos xsinx+cosx1−2sin2x​+2sin2x​cos2x​=cosx

Problem 25440

Quadratic FormulaSolve for x . x2−5x−24=0x=[?]\begin{array}{c} x^{2}-5 x-24=0 \\ x=[?] \end{array}x2−5x−24=0x=[?]​Remember the quadratic formula: x=−b±b2−4ac2ax=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}x=2a−b±b2−4ac​​

Problem 25441

Problem 25442

e 0.05 in expanded form. 0.05=□×1+□×110+□×11000.05=\square \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}0.05=□×1+□×101​+□×1001​

Problem 25443

1. Which of these is an equivalent trigonomerric ratio for sin⁡2π5\sin \frac{2 \pi}{5}sin52π​ ? a) cos⁡π10\cos \frac{\pi}{10}cos10π​ c) −cos⁡9π10-\cos \frac{9 \pi}{10}−cos109π​ b) sin⁡3π5\sin \frac{3 \pi}{5}sin53π​ d) all of these α=122\alpha=\frac{12}{2}α=212​ and

Problem 25444

dessous. II) tan⁡π4+tan⁡π6tan⁡π3\tan \frac{\pi}{4}+\tan \frac{\pi}{6} \tan \frac{\pi}{3}tan4π​+tan6π​tan3π​

Problem 25445

atic by factoring. 2x2+9x−1=2x−72 x^{2}+9 x-1=2 x-72x2+9x−1=2x−7

Problem 25446

5. Which of the following values of xxx does not lie in the domain of y=−25−2xy=-2 \sqrt{5-2 x}y=−25−2x​ ? (1) -3 (3) 2.5 (2) 2 (4) 4COMMON CORE Algebra II, Final ASSESSMENTS (1)

Problem 25447

7(3). Используя метод Лагранжа, найдите условные локальные эхстремумы фунвия $z=x^{2} y$ при условин $x+y-2=0$ .

Find $\lim _{x \rightarrow 4} \frac{x^{2}-x-12}{x-4}$

1. Prove that $2+3 \sqrt{3}$ is an irrational number. It is given that $\sqrt{ } 3$ is an irrational number.

侪 $\sqrt{2}$ Write the equation in standard form for the hyperbola $-2 x^{2}+y^{2}+12 y-32=0$ $\square$ 믐 () 2 Submit

ame the Field Axiom that was use $x+(y+z)=(x+y)+z$

$-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$ . Find the value of $\theta$ in radians. $\sin (\theta)=\frac{1}{2}$
Write your answer in simplified, rationalized form. Do not round. $\theta=$ $\square$

$(-2 a)^{4}$

Determine the real roots of the cubic function $f(x)=x^{3}+3 x^{2}-13 x-15$ . Correctly plot the THREE roots on the coordinate plane.

6. For each equation below, find the value(s) of $x$ that $m$ (Lesson 2-18) a. $10=\frac{1+7 x}{7+x}$ b. $0.2=\frac{6+2 x}{12+x}$ c. $0.8=\frac{x}{0.5+x}$ d. $3.5=\frac{4+2 x}{0.5-x}$

9. What is $(2 i-5)(4+7 i)$ in simplest form? $14 i^{2}-27 i-20$ $57 i+20$ $-27 i-34$ $-27 i-6$ Clear All

15. What are the solutions for the quadratic function $y=3 x^{2}-8 x+7$ ? $x=\frac{4 \pm i \sqrt{5}}{3}$ $x=\frac{-4 \pm i \sqrt{5}}{3}$ $x=-6 ; x=14$ $x=\frac{8 \pm \sqrt{20}}{6}$

Factorise $7(5 x-y)^{2}-(y-5 x)$

6. Simplify $(9 m+n)^{2}-(9 m-n)^{2}$ .

$\int \frac{e^{1 / t}}{t^{2}} d t$

Simplify: $\log _{2} 16 d$ $4 \log _{2} d$ $\log _{2} 4 d$ $\log _{2}(4+d)$ $4+\log _{2} d$

solution. $\begin{array}{l} x+2 y=-8 \\ y=-\frac{3}{2} x-6 \end{array}$
Click to select points on the graph.

Vrite 5.79 in expanded form. $5.79=\quad \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}$

Find the product. $\begin{array}{l} \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right) \\ \left(6 x-\frac{1}{4}\right)\left(6 x+\frac{1}{4}\right)= \end{array}$

$\{(a, m),(m, n),(t, n),(n, n)\}$
Function Not a function

Simplify. $-\left(-3+\frac{i}{5}\right)+\frac{i}{15}-\frac{3+3 i}{5}$
Write your answer in the form a + bi. Simplify all fractions. $\square$

Divide. $\begin{array}{l} \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}} \\ \frac{30 y^{7}-6 y^{2}+12 y}{6 y^{2}}= \end{array}$

Factor out the greatest com polynomial. $8 z-4$

Solve. $\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}$ $\square$ (Use a comma to separate answers as needed.)

$5 x^{2}(x-2)-x(4 x+2)-9 x^{2}(-3 x)$

In the equation $\log _{3}(7 x-1)=\log _{3}(5 x+17)$ , what is the value of $x$ a) 7 b) 9 c) 11 d) 13 a b C d

$\frac{1-2 \sin ^{2} x}{\sin x+\cos x}+2 \sin \frac{x}{2} \cos \frac{x}{2}=\cos x$

Quadratic Formula
Solve for x . $\begin{array}{c} x^{2}-5 x-24=0 \\ x=[?] \end{array}$
Remember the quadratic formula: $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

e 0.05 in expanded form. $0.05=\square \times 1+\square \times \frac{1}{10}+\square \times \frac{1}{100}$

1. Which of these is an equivalent trigonomerric ratio for $\sin \frac{2 \pi}{5}$ ? a) $\cos \frac{\pi}{10}$ c) $-\cos \frac{9 \pi}{10}$ b) $\sin \frac{3 \pi}{5}$ d) all of these $\alpha=\frac{12}{2}$ and

dessous. II) $\tan \frac{\pi}{4}+\tan \frac{\pi}{6} \tan \frac{\pi}{3}$

atic by factoring. $2 x^{2}+9 x-1=2 x-7$

5. Which of the following values of $x$ does not lie in the domain of $y=-2 \sqrt{5-2 x}$ ? (1) -3 (3) 2.5 (2) 2 (4) 4
COMMON CORE Algebra II, Final ASSESSMENTS (1)

-ite the expression as a decimal number. $3 \times \frac{1}{10}+7 \times \frac{1}{100}+2 \times \frac{1}{1000}=$

Write $(-5+10 i)^{2}$ in simplest $a+b i$ form.

$\cos x \sin x=0$

$\frac{5 \sqrt{6}}{-\sqrt{3}}$

Given $f(x)=-\csc (4 x)$ , find $f^{\prime}(x)$

If the range of a quadratic function is $5 \leq y<\infty$ , which of the following could be true? None of these are correct. The parabola has a maximum at $(2,5)$ . The parabola has a minimum at $(2,1)$ . The parabola has a maximum at $(5,1)$ .

a) Factorise $x^{2}+9 x+14$ . b) By sketching a graph, solve the inequality $x^{2}+9 x+14 \leq 0$ .

Factoring the following polynomial completely using the greatest common factor. If the expression cannot be factored enter the expression as is. $81 x^{5}-99 x^{4}+9 x^{2}$

Work out the lowest integer value that $k$ can take if $7+4 k>k+40$

$\begin{array}{r}3 x-4=8 \\ x=\end{array}$

quations below? $5 x-2=18$

Subtract the polynomials. See Example
49. $\left(3 a^{2}-2 a+4\right)-\left(a^{2}-3 a+7\right)$

Divide: $\frac{-10}{-5}=\square$ subrit

$\int_{0}^{\infty} \frac{2}{1+x^{2}}$ a. none b. $\frac{\pi}{2}$ c. $-\pi$ d. $\pi$

$\log (3 x-7)+\log (3 x+1)=1+\log 2$

How many zeros does $f(x)=a(x-5)^{2}$ have if $a<0$ ? 1) It is impossible to determine. 2) 1 3) 0 4) 2

The derivative of $y=\cos ^{3}\left(\sin \left(x^{3}\right)\right) \text { is }$

(B) > (D) 1>2
9. Find lim 1-e* x+0 In (2-e*) (A) 210 (B) 1 (C) 0 (D) The limit does not exist. function given by f(x)=2 graph of fat