Math Statement

Problem 25501

d) $\lim _{x \rightarrow-\infty} \frac{3 x^{3}-2 x^{2}+1}{x^{2}+1}$

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Problem 25502

Write an equation in point-slope form of the line that passes through the given point and with the given slope $m$ . $(-6,5) ; m=7$
The equation of the line is $\square$ (Simplify your answer. Type your answer in point-slope form.)

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Problem 25503

6. The decimal equivalent of the rational number $\frac{28}{95}$ is $1.86666 \ldots$ . This can be expressed in bar notation as $\qquad$ - boli99 .001 A. $\overline{1.86}$ sold yd
8. $1 . \frac{86}{86}$ b vigislum C. $1.8 \overline{6}$ un ant gbivib D. 1.86 oj 5 nimongb

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Problem 25504

Solve for $y$ . $y^{2}-6 y+8=0$

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Problem 25505

Rewrite $x^{2}+14 x-10=0$ in the form $(x-p)^{2}=q$ by completing the square. Use the keypad to enter your answer in the box. Find more symbols by using the drop-down arrow at the top of the keypad. $x^{2}+14 x-10=0$ in the form $(x-p)^{2}=q$ is $\square$ 7.

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Problem 25506

Multiply. $(5 c-8)(-4 c+5)$

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Problem 25507

$900 \div 3=9$ hundreds $\div$

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Problem 25508

expression
1. $8 \times 8 \times 8 \times 8 \times 8 \times 8 \times$ 2.4 $4=4$
3. $-10 \times(-10) \times(-10) \times$
Evaluate each expressio $4.9^{2}=81$
6. $3,105^{\circ}$
8. $(-2)^{7}$

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Problem 25509

Solve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

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Problem 25510

Consider the following integral in $\int_{a}^{b} f(x) d x$ form. Find the value of $b$ such that $\int_{-2}^{b}(1-2 x) d x=0$
You may assume that $-2<b$ . $\square$

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Problem 25511

a. $\frac{1}{2} \div 4=$

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Problem 25512

For the compound inequality $5-2 x<7$ and $2(3 x-1) \leq 4 x+4$ , Find the solution set algebraically. $-2 \times 27^{\text {" }} x^{\prime \prime}$ is greater $\begin{array}{l} \frac{-2 x}{-2}<\frac{2}{-2} \quad x>-1 \quad 2(3 x-1) \leqslant 4 x+4 \\ \begin{array}{l} 6 x-2 \leqslant 4 x+4 \\ -4 x \end{array} \\ -4 x \\ \text { intersection: } \\ -12 x \leqslant 3 \\ x \leq 3 \quad x \text { is less than or } \\ \text { or }(-1,3) \end{array}$ b.) Graph the solution set.

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Problem 25513

QUESTION 4
Convert the following rectangular coordinates to cylindrical coordinates. Give angles in terms of Pi. If your answer is two-thirds Pi, you would type 2 pil3. It might look familiar. Keep the square root(s) in your answer- do not use decimals. Rectangular: $(2,-2,2 s q r t 2)=$ Cylindrical: $\square$ $\square$ $\square$

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Problem 25514

$y=x$

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Problem 25515

18. $m \div 3.54=1.5$ $m \div 3.54 \times$ $\square$ $=1.5 \times$ $\square$ $m=$ $\square$

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Problem 25516

$7(-6 f+1)-2(3 f-8)$

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Problem 25517

rms: $10(0.3 s+0.2)-9 s$

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Problem 25518

t terms: $9(0.7 a+0.3)+8 a$

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Problem 25519

e Divide. Check 7÷28 6599

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Problem 25520

$52249$

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Problem 25521

Exercice 2 Soit $X_{1}, X_{2}$ et $X_{3}$ , trois vecteurs de $I^{3}$ tels que : $X_{1}=(-1,5,2), X_{2}=(2,-1,2)$ et $X_{3}=(1,1,3)$ a. Calculer les combinaisons linéaires suivantes: $3 \mathrm{X}_{1}-2 \mathrm{X}_{2}+\mathrm{X}_{3} ; 3\left(\mathrm{X}_{1}-\mathrm{X}_{3}\right)+\mathrm{X}_{2}$ b. Trouver trois réels $\alpha, \beta$ et $\gamma$ non nuls, tels que $\alpha \mathrm{X}_{1}+\beta \mathrm{X}_{2}+\gamma \mathrm{X}_{3}$ ait ses deux premières composantes nulles .
Exercice 3
1. Soient $u_{1}=(1,1,1,1), u_{2}=(2,-1,2,-1), u_{3}=(4,1,4,1)$ trois vecteurs de $R^{4}$ La famille $\{\mathrm{u} 1, \mathrm{u} 2, \mathrm{u} 3\}$ est-elle libre?
2. Soient dans $\mathbb{R}^{3}$ les vecteurs $v 1=(1,1,0), v 2=(4,1,4)$ et $v 3=(2,-1,4)$ .
La famille $(v 1, v 2, v 3)$ est-elle libre ?

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Problem 25522

6. $-\frac{4}{22} t-\frac{5}{22} t+15+(-5)$

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Problem 25523

Calculate. $\left(7 \times 10^{5}\right)+\left(2 \times 10^{5}\right)$
Write your answer in scientific notation.

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Problem 25524

Evaluate $13+\frac{6}{y}$ when $y=6$

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Problem 25525

(2 points) Find all solutions to the system of nonlinear equations. $\begin{array}{c} y=x-7 \\ x^{2}+y^{2}=37 \end{array}$
Solution(s): $\square$ help (points)
Enter the solution as an ordered pair, $(a, b)$ or a list of ordered pairs, $(a, b),(c, d)$ .

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Problem 25526

(1 point) Find the augmented matrix for this system. $\begin{array}{r} -x+2 y=5 \\ 2 x+3 y=-9 \end{array}$
Augmented matrix: $\square$ $\square$ $\square$ $\square$ help (

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Problem 25527

$\begin{array}{l} \text { (1 point) } \\ x+4 y+7 z=9 \\ 9 x-5 y=4 \\ x-5 y+z=1 \end{array}$
Find the augmented matrix for this system.
Augmented matrix: $\square$ $\square$ $\square$ $\square$ 1 $\square$ $\square$ $\square$ $\square$

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Problem 25528

Solve for $X$ . $72=3 x$
Simplify your answer as much as possible. $x=$ $\square$

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Problem 25529

Evaluate the expression: $-\frac{3}{4}\left(-\frac{4}{9}\right)$ and simplify the result.

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Problem 25530

Evaluate the expression: $\frac{3}{8} \div \frac{3}{4}$ and simplify the result.

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Problem 25531

Evaluate the expression: $9\left(\frac{7}{15}\right)$ and write the result in simplest form.

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Problem 25532

Evaluate the expression and simplify: $-\frac{5}{12} \div \frac{45}{8}$ .

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Problem 25533

Evaluate the expression: $\frac{7}{3} \div \frac{7}{3}$ and simplify the result.

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Problem 25534

Evaluate and simplify the expression: $\frac{2}{7} \div \frac{9}{7}$ .

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Problem 25535

Solve the equation $(x-1)(x-3)=0$ for the values of $x$ .

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Problem 25536

Solve the equation: $(x-1)(x-3)=0$

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Problem 25537

Find the limit: $\lim _{x \rightarrow 0} \frac{\sin (6 x)}{\sin (2 x)}$ .

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Problem 25538

Solve the compound inequality: $2x \geq 7$ or $-\frac{4}{7}x - 1 > 6$ . What are the solution ranges for $x$ ?

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Problem 25539

Identify the sequence type: $10, 20, 30, \ldots$ - is it arithmetic, geometric, or neither?

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Problem 25540

Solve the equation $\frac{7}{x+2}-\frac{9}{2 x}=\frac{8}{2 x+4}$ for $x$ algebraically and graphically.

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Problem 25541

Identify the sequence: $6, 12, 18, \ldots$ as arithmetic, geometric, or neither.

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Problem 25542

Determine if the sequence defined by $f(1)=10, f(n)=f(n-1)-1.5$ for $n \geq 2$ is arithmetic, geometric, or neither.

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Problem 25543

Solve the equation: $\frac{3}{4} x + 3 - 2 x = -\frac{1}{4} + \frac{1}{2} x + 5$

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Problem 25544

Solve for $c$ in the equation $A = B + B c d$ .

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Problem 25545

Solve the equation $x^{2}-32=0$ to find $x$ algebraically and graphically.

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Problem 25546

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

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Problem 25547

Calculate $-\frac{3}{4}+\frac{5}{6}$ .

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Problem 25548

Solve the initial value problem $y' = 9ty^2$ , $y(0) = y_0$ , and find how the solution interval depends on $y_0$ .

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Problem 25549

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

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Problem 25550

Identify the sequence type: 4, 9, 16, ... Is it Arithmetic, Geometric, or Neither?

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Problem 25551

Simplify 20 - 6 + 8 ÷ 2^{3}. What is the result?

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Problem 25552

Find the derivative $f^{\prime}(x)$ of $f(x)=\frac{12}{x}$ and evaluate $f^{\prime}(-2), f^{\prime}(0), f^{\prime}(5)$ .

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Problem 25553

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

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Problem 25554

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

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Problem 25555

Find the derivative $f^{\prime}(x)$ for $f(x)=\frac{48}{x}$ and calculate $f^{\prime}(-4)$ , $f^{\prime}(0)$ , $f^{\prime}(3)$ .

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Problem 25556

Solve $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ . Options: $-0.45$ , $-0.25$ , $0.25$ , $0.45$ .

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Problem 25557

Find the derivative $g^{\prime}(x)$ for $g(x)=\sqrt{7 x}$ , then calculate $g^{\prime}(-3), g^{\prime}(0), g^{\prime}(4)$ .

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Problem 25558

Let $y$ be the total cost of publishing a book and $x$ the number of copies printed, related by $1250 + 25x = y$ .
1. What is the change in cost per book printed?
2. What is the initial cost before printing?

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Problem 25559

Solve the equation $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ .

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Problem 25560

Find the derivative $g^{\prime}(x)$ of $g(x)=\sqrt{15 x}$ , then compute $g^{\prime}(-3)$ , $g^{\prime}(0)$ , and $g^{\prime}(3)$ .

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Problem 25561

A pond's water amount $y$ in liters after $x$ minutes is given by $y=500+32x$ . Find the starting amount and change per minute.

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Problem 25562

Find the derivative $f^{\prime}(x)$ of $f(x)=4x^{3}+10$ using the limit definition, then calculate $f^{\prime}(-1)$ , $f^{\prime}(0)$ , and $f^{\prime}(4)$ .

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Problem 25563

Solve for $b$ in the equation $(2b + 88) + (-6b + 74) = 170$ .

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Problem 25564

Find the value of $x$ in the equation $x - 3x = 2(4 + x)$ .

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Problem 25565

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

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Problem 25566

Given the demand $p=900-10q$ and supply $p=20q$ , find: a. Price when demand is 0. b. Price when demand is 40 units. c. Supply at \$400. d. Demand at \$400. e. Surplus or shortage at \$400? f. Graph the curves. g. Equilibrium price and quantity.

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Problem 25567

Rewrite $x^{-3}$ as a fraction.

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Problem 25568

What is the value of $(\sqrt[3]{x})^{0}$ ?

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Problem 25569

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 25570

Analyze the function $R(x)=\frac{8x+8}{7x+21}$ for domain, vertical asymptote, and horizontal asymptote.

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Problem 25571

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

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Problem 25572

Find the secant line for $y=f(x)=x^{2}+x$ at $x=3$ and $x=7$ , and the tangent line at $x=3$ .

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Problem 25573

Find the maximum height of a projectile launched at $30^{\circ}$ with an initial speed of $50 \mathrm{~m/s}$ . Use $h(t)=v_{0} \sin (\theta) t-\frac{1}{2} g t^{2}$ , where $g=9.81 \mathrm{~m/s}^{2}$ .

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Problem 25574

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 25575

Convert $79^{\circ} \mathrm{C}$ to Fahrenheit and $90^{\circ} \mathrm{F}$ to Celsius using $y=\frac{5}{9}(x-32)$ .

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Problem 25576

Calculate $\left(\left(-6+\frac{5}{6}\right)-\left(2-\frac{4}{5}\right)\right):\left(\frac{5}{3}-0.5\right)-\frac{1}{35}$ .

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Problem 25577

Analyze the function $H(x)=\frac{2x-6}{9-x^{2}}$ for its domain, vertical, and horizontal asymptotes.

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Problem 25578

Analyze the function $R(x)=\frac{x^{2}-100}{x^{4}-81}$ : Find its domain, vertical asymptotes, and horizontal asymptote.

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Problem 25579

Find the equivalent expression for $x^{6} x^{2}$ . Options: $x^{4} x^{3}$ , $x^{5} x^{3}$ , $x^{7} x^{3}$ , $x^{9} x^{3}$ .

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Problem 25580

Determine the end behavior of $f(x)=-5 x^{2}(x^{2}-11)$ and find its real zeros and their multiplicities.

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Problem 25581

What is the probability that a General Manager works at a seafood restaurant, expressed as $P(S \mid G)$ ?

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Problem 25582

Solve for real solutions of $2 x^{4}-23 x^{3}+89 x^{2}-129 x+45=0$ . A: $\mathrm{x}=$ (exact answers); B: No real solutions.

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Problem 25583

Find the probability that a student studies daily given they passed the math test: $P(S | M)$ .

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Problem 25584

Simplify the expression $15 \times 10^{2}$ .

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Problem 25585

Find the probability of a cancer patient having elective surgery given they received chemotherapy: $P(E|C)$ .

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Problem 25586

Solve for $x$ in the equation: $8 - 2x = -8x + 14$ . Options: $x = -1$ , $x = -\frac{3}{5}$ , $x = \frac{3}{5}$ , $x = 1$ .

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Problem 25587

Solve the inequality: $9x - 9 \geq -4x^2$ . Provide the solution in interval notation.

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Problem 25588

Find $f(x+b)$ for $f(x)=3 x^{2}+5 x+20 x$ . Also, compute $f(x) g(x)$ for $f(x)=6 x^{3}+5 x$ and $g(x)=7 x+3$ .

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Problem 25589

Divide 7,200 by 10 raised to the power of 1. What is the result?

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Problem 25590

Find the complex zeros of the polynomial $f(x)=x^{3}-15 x^{2}+79 x-145$ .

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Problem 25591

What number can you multiply by to eliminate fractions in the equation $6-\frac{3}{4} x+\frac{1}{3}=\frac{1}{2} x+5$ ? Options: 2, 3, 6, 12.

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Problem 25592

Graph the supply $S(q)=p=\frac{3}{2} q$ and demand $D(q)=p=81-\frac{3}{4} q$ . Find equilibrium quantity and price.

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Problem 25593

Evaluate $4 + 2 \times [(29 - 15) \div 2]$ . Find values inside parentheses, brackets, and the entire expression.

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Problem 25594

Calculate $13,000 \div 10^{2}$ .

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Problem 25595

Solve the inequality: $\frac{x+1}{x-4}>0$ . Provide your answer in interval notation.

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Problem 25596

Find the product of the functions $f(x)=3 x^{2}+5 x$ and $g(x)=7 x+3$ . What is $f(x) g(x)$ ?

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Problem 25597

Find $f(3) g(3)$ for $f(x)=2 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

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Problem 25598

Solve for $y$ in the equation: $y + 6 = -3y + 26$ . Options: $-8$ , $-5$ , $5$ , $8$ .

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Problem 25599

Find the product $f(x) g(x)$ for $f(x)=3 x^{2}+4 x+5$ and $g(x)=x^{2}+x+1$ .

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Problem 25600

Find all real zeros of the polynomial $f(x)=2 x^{4}+x^{3}-7 x^{2}-3 x+3$ and factor it over the reals.

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1 ...253 254 255 256 257 258 259 ...269

Math Statement

Problem 25501

d) lim⁡x→−∞3x3−2x2+1x2+1\lim _{x \rightarrow-\infty} \frac{3 x^{3}-2 x^{2}+1}{x^{2}+1}limx→−∞​x2+13x3−2x2+1​

Problem 25502

Write an equation in point-slope form of the line that passes through the given point and with the given slope mmm. (−6,5);m=7(-6,5) ; m=7(−6,5);m=7The equation of the line is □\square□ (Simplify your answer. Type your answer in point-slope form.)

Problem 25503

Problem 25504

Solve for yyy. y2−6y+8=0y^{2}-6 y+8=0y2−6y+8=0

Problem 25505

Problem 25506

Multiply. (5c−8)(−4c+5)(5 c-8)(-4 c+5)(5c−8)(−4c+5)

Problem 25507

900÷3=9900 \div 3=9900÷3=9 hundreds ÷\div÷

Problem 25508

Problem 25509

Solve u2=16u^{2}=16u2=16, where uuu is a real numbe Simplify your answer as much as pcIf there is more than one solution, If there is no solution, click on "No u=u=u= □\square□

Problem 25510

Consider the following integral in ∫abf(x)dx\int_{a}^{b} f(x) d x∫ab​f(x)dx form. Find the value of bbb such that ∫−2b(1−2x)dx=0\int_{-2}^{b}(1-2 x) d x=0∫−2b​(1−2x)dx=0You may assume that −2<b-2<b−2<b. □\square□

Problem 25511

a. 12÷4=\frac{1}{2} \div 4=21​÷4=

Problem 25512

Problem 25513

Problem 25514

y=xy=xy=x

Problem 25515

18. m÷3.54=1.5m \div 3.54=1.5m÷3.54=1.5 m÷3.54×m \div 3.54 \timesm÷3.54× □\square□ =1.5×=1.5 \times=1.5× □\square□ m=m=m= □\square□

Problem 25516

7(−6f+1)−2(3f−8)7(-6 f+1)-2(3 f-8)7(−6f+1)−2(3f−8)

Problem 25517

rms: 10(0.3s+0.2)−9s10(0.3 s+0.2)-9 s10(0.3s+0.2)−9s

Problem 25518

t terms: 9(0.7a+0.3)+8a9(0.7 a+0.3)+8 a9(0.7a+0.3)+8a

Problem 25519

e Divide. Check 7÷28 6599

Problem 25520

522495224952249

Problem 25521

Problem 25522

6. −422t−522t+15+(−5)-\frac{4}{22} t-\frac{5}{22} t+15+(-5)−224​t−225​t+15+(−5)

Problem 25523

Calculate. (7×105)+(2×105)\left(7 \times 10^{5}\right)+\left(2 \times 10^{5}\right)(7×105)+(2×105)Write your answer in scientific notation.

Problem 25524

Evaluate 13+6y13+\frac{6}{y}13+y6​ when y=6y=6y=6

Problem 25525

Problem 25526

(1 point) Find the augmented matrix for this system. −x+2y=52x+3y=−9\begin{array}{r} -x+2 y=5 \\ 2 x+3 y=-9 \end{array}−x+2y=52x+3y=−9​Augmented matrix: □\square□ □\square□ □\square□ □\square□ help (

Problem 25527

Problem 25528

Solve for XXX. 72=3x72=3 x72=3xSimplify your answer as much as possible. x=x=x= □\square□

Problem 25529

Evaluate the expression: −34(−49)-\frac{3}{4}\left(-\frac{4}{9}\right)−43​(−94​) and simplify the result.

Problem 25530

Evaluate the expression: 38÷34\frac{3}{8} \div \frac{3}{4}83​÷43​ and simplify the result.

Problem 25531

Evaluate the expression: 9(715)9\left(\frac{7}{15}\right)9(157​) and write the result in simplest form.

Problem 25532

Evaluate the expression and simplify: −512÷458-\frac{5}{12} \div \frac{45}{8}−125​÷845​.

Problem 25533

Evaluate the expression: 73÷73\frac{7}{3} \div \frac{7}{3}37​÷37​ and simplify the result.

Problem 25534

Evaluate and simplify the expression: 27÷97\frac{2}{7} \div \frac{9}{7}72​÷79​.

Problem 25535

Solve the equation (x−1)(x−3)=0(x-1)(x-3)=0(x−1)(x−3)=0 for the values of xxx.

Problem 25536

Solve the equation: (x−1)(x−3)=0(x-1)(x-3)=0(x−1)(x−3)=0

Problem 25537

Find the limit: lim⁡x→0sin⁡(6x)sin⁡(2x)\lim _{x \rightarrow 0} \frac{\sin (6 x)}{\sin (2 x)}limx→0​sin(2x)sin(6x)​.

Problem 25538

Solve the compound inequality: 2x≥72x \geq 72x≥7 or −47x−1>6-\frac{4}{7}x - 1 > 6−74​x−1>6. What are the solution ranges for xxx?

Problem 25539

Identify the sequence type: 10,20,30,…10, 20, 30, \ldots10,20,30,… - is it arithmetic, geometric, or neither?

Problem 25540

Solve the equation 7x+2−92x=82x+4\frac{7}{x+2}-\frac{9}{2 x}=\frac{8}{2 x+4}x+27​−2x9​=2x+48​ for xxx algebraically and graphically.

Problem 25541

Identify the sequence: 6,12,18,…6, 12, 18, \ldots6,12,18,… as arithmetic, geometric, or neither.

Problem 25542

Determine if the sequence defined by f(1)=10,f(n)=f(n−1)−1.5f(1)=10, f(n)=f(n-1)-1.5f(1)=10,f(n)=f(n−1)−1.5 for n≥2n \geq 2n≥2 is arithmetic, geometric, or neither.

Problem 25543

Solve the equation: 34x+3−2x=−14+12x+5\frac{3}{4} x + 3 - 2 x = -\frac{1}{4} + \frac{1}{2} x + 543​x+3−2x=−41​+21​x+5

Problem 25544

d) $\lim _{x \rightarrow-\infty} \frac{3 x^{3}-2 x^{2}+1}{x^{2}+1}$

Write an equation in point-slope form of the line that passes through the given point and with the given slope $m$ . $(-6,5) ; m=7$
The equation of the line is $\square$ (Simplify your answer. Type your answer in point-slope form.)

Solve for $y$ . $y^{2}-6 y+8=0$

Multiply. $(5 c-8)(-4 c+5)$

$900 \div 3=9$ hundreds $\div$

Solve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

Consider the following integral in $\int_{a}^{b} f(x) d x$ form. Find the value of $b$ such that $\int_{-2}^{b}(1-2 x) d x=0$
You may assume that $-2<b$ . $\square$

a. $\frac{1}{2} \div 4=$

$y=x$

18. $m \div 3.54=1.5$ $m \div 3.54 \times$ $\square$ $=1.5 \times$ $\square$ $m=$ $\square$

$7(-6 f+1)-2(3 f-8)$

rms: $10(0.3 s+0.2)-9 s$

t terms: $9(0.7 a+0.3)+8 a$

$52249$

6. $-\frac{4}{22} t-\frac{5}{22} t+15+(-5)$

Calculate. $\left(7 \times 10^{5}\right)+\left(2 \times 10^{5}\right)$
Write your answer in scientific notation.

Evaluate $13+\frac{6}{y}$ when $y=6$

(1 point) Find the augmented matrix for this system. $\begin{array}{r} -x+2 y=5 \\ 2 x+3 y=-9 \end{array}$
Augmented matrix: $\square$ $\square$ $\square$ $\square$ help (

Solve for $X$ . $72=3 x$
Simplify your answer as much as possible. $x=$ $\square$

Evaluate the expression: $-\frac{3}{4}\left(-\frac{4}{9}\right)$ and simplify the result.

Evaluate the expression: $\frac{3}{8} \div \frac{3}{4}$ and simplify the result.

Evaluate the expression: $9\left(\frac{7}{15}\right)$ and write the result in simplest form.

Evaluate the expression and simplify: $-\frac{5}{12} \div \frac{45}{8}$ .

Evaluate the expression: $\frac{7}{3} \div \frac{7}{3}$ and simplify the result.

Evaluate and simplify the expression: $\frac{2}{7} \div \frac{9}{7}$ .

Solve the equation $(x-1)(x-3)=0$ for the values of $x$ .

Solve the equation: $(x-1)(x-3)=0$

Find the limit: $\lim _{x \rightarrow 0} \frac{\sin (6 x)}{\sin (2 x)}$ .

Solve the compound inequality: $2x \geq 7$ or $-\frac{4}{7}x - 1 > 6$ . What are the solution ranges for $x$ ?

Identify the sequence type: $10, 20, 30, \ldots$ - is it arithmetic, geometric, or neither?

Solve the equation $\frac{7}{x+2}-\frac{9}{2 x}=\frac{8}{2 x+4}$ for $x$ algebraically and graphically.

Identify the sequence: $6, 12, 18, \ldots$ as arithmetic, geometric, or neither.

Determine if the sequence defined by $f(1)=10, f(n)=f(n-1)-1.5$ for $n \geq 2$ is arithmetic, geometric, or neither.

Solve the equation: $\frac{3}{4} x + 3 - 2 x = -\frac{1}{4} + \frac{1}{2} x + 5$

Solve for $c$ in the equation $A = B + B c d$ .

Solve the equation $x^{2}-32=0$ to find $x$ algebraically and graphically.

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

Calculate $-\frac{3}{4}+\frac{5}{6}$ .

Solve the initial value problem $y' = 9ty^2$ , $y(0) = y_0$ , and find how the solution interval depends on $y_0$ .

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

Find the derivative $f^{\prime}(x)$ of $f(x)=\frac{12}{x}$ and evaluate $f^{\prime}(-2), f^{\prime}(0), f^{\prime}(5)$ .

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

Find the derivative $f^{\prime}(x)$ for $f(x)=\frac{48}{x}$ and calculate $f^{\prime}(-4)$ , $f^{\prime}(0)$ , $f^{\prime}(3)$ .

Solve $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ . Options: $-0.45$ , $-0.25$ , $0.25$ , $0.45$ .

Find the derivative $g^{\prime}(x)$ for $g(x)=\sqrt{7 x}$ , then calculate $g^{\prime}(-3), g^{\prime}(0), g^{\prime}(4)$ .

Let $y$ be the total cost of publishing a book and $x$ the number of copies printed, related by $1250 + 25x = y$ .
1. What is the change in cost per book printed?
2. What is the initial cost before printing?

Solve the equation $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ .

Find the derivative $g^{\prime}(x)$ of $g(x)=\sqrt{15 x}$ , then compute $g^{\prime}(-3)$ , $g^{\prime}(0)$ , and $g^{\prime}(3)$ .

A pond's water amount $y$ in liters after $x$ minutes is given by $y=500+32x$ . Find the starting amount and change per minute.

Find the derivative $f^{\prime}(x)$ of $f(x)=4x^{3}+10$ using the limit definition, then calculate $f^{\prime}(-1)$ , $f^{\prime}(0)$ , and $f^{\prime}(4)$ .

Solve for $b$ in the equation $(2b + 88) + (-6b + 74) = 170$ .

Find the value of $x$ in the equation $x - 3x = 2(4 + x)$ .

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

Given the demand $p=900-10q$ and supply $p=20q$ , find: a. Price when demand is 0. b. Price when demand is 40 units. c. Supply at \$400. d. Demand at \$400. e. Surplus or shortage at \$400? f. Graph the curves. g. Equilibrium price and quantity.

Rewrite $x^{-3}$ as a fraction.

What is the value of $(\sqrt[3]{x})^{0}$ ?

Simplify $(\sqrt[3]{x})^{6}$ .

Analyze the function $R(x)=\frac{8x+8}{7x+21}$ for domain, vertical asymptote, and horizontal asymptote.

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

Find the secant line for $y=f(x)=x^{2}+x$ at $x=3$ and $x=7$ , and the tangent line at $x=3$ .

Find the maximum height of a projectile launched at $30^{\circ}$ with an initial speed of $50 \mathrm{~m/s}$ . Use $h(t)=v_{0} \sin (\theta) t-\frac{1}{2} g t^{2}$ , where $g=9.81 \mathrm{~m/s}^{2}$ .

Simplify $(\sqrt[3]{x})^{6}$ .