Browse Algebra problems Studdy Solved!

Problem 29601

Joe's age is 3 times Aaron's. Aaron is 6 years older than Christina. Their ages sum to 149. Find Christina's, Joe's, and Aaron's ages.

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Problem 29602

Tìm tích các giá trị của tham số $m$ sao cho $g(x_{1})+g(x_{2})+g(x_{3})+g(x_{4})=0$ với $f(x)=x^{4}+4 x^{3}-2 x^{2}-4 m^{2} x+1$ .

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Problem 29603

Find the value of $\square$ in the equations: $63.85 \times \square = 63,850$ and $63.85 \times \square = 638,500$ .

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Problem 29604

Simplify the expression: $\frac{20 \sqrt{3}}{5 \sqrt{3}}$ .

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Problem 29605

Solve for $y$ in the equation: $-5=9+y$ .

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Problem 29606

Simplify the expression: $\frac{2}{1-\sqrt{2}}$ .

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Problem 29607

Solve for $n$ in the equation $\frac{n+2}{4}=1$ .

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Problem 29608

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the $x$ -axis and distance on the $y$ -axis? Distance in 45 seconds is (45, ).

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Problem 29609

Solve the inequality: $\frac{(x-6)^{2}}{x^{2}-25} \geq 0$ . List intervals and signs in interval notation.

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Problem 29610

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

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Problem 29611

Solve the inequality: $\frac{(x-4)^{2}}{x^{2}-4} \geq 0$ . List intervals and signs in interval notation.

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Problem 29612

Solve the inequality $(x-7)^{2}/(x^{2}-36) \geq 0$ and list intervals with signs in each. Use interval notation.

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Problem 29613

Rearrange the equation $\frac{-3 r+2}{-6 r+5}=4 s$ to solve for $r$ .

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Problem 29614

Alyssa wants to know her fuel savings by traveling to the Moon vs. Mars. Round trip distances: $d_{1} = 1.22 \times 10^{8} \mathrm{~km}$ , $d_{2} = 8.12 \times 10^{5} \mathrm{~km}$ . Fuel efficiency: $1.54 \times 10^{3} \mathrm{~km/L}$ , cost: \$3.23 \times 10^{2} per liter. Calculate savings.

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Problem 29615

Solve the inequality: $\frac{x+8}{x-3} \leq 1$ . List intervals and signs in each interval in interval notation.

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Problem 29616

Find the sum of the coefficients of $P(x) + Q(x)$ where $P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3$ and $Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7$ .

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Problem 29617

Solve the inequality $\frac{x+8}{x-3} \leq 1$ . List intervals and signs. Provide the solution in interval notation.

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Problem 29618

Solve the inequality $\frac{x+4}{x-2} \leq 1$ and list intervals with signs in interval notation.

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Problem 29619

Find the number of positive real solutions for the equation $5 x^{3}+x^{2}+7 x-28=0$ . Options: A. Two B. Three or one C. Two or zero D. One

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Problem 29620

Solve the inequality:
$\frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0$
Identify intervals and their signs, then list in interval notation.

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Problem 29621

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

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Problem 29622

Solve the inequality:
$\frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0$
List intervals and their signs in ascending order.

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Problem 29623

Find the slope-intercept form of the line passing through $(-1,1)$ with a slope of $0$ .

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Problem 29624

Find the slope-intercept form of the line that passes through the points $(2,3)$ and $(4,2)$ .

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Problem 29625

Find the real zeros of $f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3$ and factor $f$ over the reals.

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Problem 29626

Calculate the future value $A$ of a loan with principal $P=\$2000$ , interest rate $r=3.0\%$ , and time $t=3$ months.

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Problem 29627

Solve the equation $3 x^{4}-58 x^{3}+280 x^{2}-438 x+117=0$ . What are the real solutions? A. $x=$ ; B. No real solutions.

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Problem 29628

Analyze the polynomial $f(x)=(x+8)^{2}(1-x)$ :
(a) End behavior: $y=\square$ for large $|x|$ . (b) Find $x$ - and $y$ -intercepts. (c) Determine zeros and their multiplicity. (d) Max turning points? (e) Graph $f$ . Choose A, B, C, or D.

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Problem 29629

Analyze the function $R(x)=\frac{x^{2}-121}{x^{4}-81}$ :
(a) Find the domain. (b) Identify vertical asymptote(s). (c) Find horizontal/oblique asymptote. (d) Choose the correct graph.

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Problem 29630

Analyze the polynomial $f(x)=x^{3}+2x^{2}-15x$ . Answer parts (a) to (e). Factor first.

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Problem 29631

Rewrite $x(x-y)^{5}-y(x-y)^{5}$ as $(x-y)^{a}$ and find the value of $a$ .

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Problem 29632

1. Find $F_{30}$ .
2. Calculate $F_{10} + F_{20} + F_{5}$ .
3. Solve $3 F_{18} - 2 F_{10}$ .
4. Determine $F_{21} - 5 F_{7}$ .
5. Find $\frac{4 F_{5} + F_{11}}{2}$ .
6. Calculate $\frac{3 F_{13}}{6}$ .
7. What is $\mathrm{F}_{75} * 0$ ?
8. Compute $10 \mathrm{~F}_{6} * 3$ .
9. Find $\frac{F_{35}}{2}$ .
10. Calculate $\frac{F_{29}}{3} * 3$ .

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Problem 29633

Analyze the function $H(x)=\frac{4x-12}{9-x^{2}}$ . Find its domain and asymptotes.

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Problem 29634

Find the complex zeros of $f(x)=x^{3}-15 x^{2}+79 x-145$ . Provide exact answers using radicals and $i$ .

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Problem 29635

Write an inequality for: The product of $2x$ and $16$ is at most $9$ .

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Problem 29636

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

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Problem 29637

Find the value of $y$ for the equation $y=-5 x^{2}-10 x-15$ .

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Problem 29638

Find $\mathrm{n}$ using the future value of an annuity formula with $\mathrm{A}=\$ 18,500$ , $R=\$ 800$ , $r=8.0\%$ . $n=\square$

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Problem 29639

For the polynomial $f(x)=-4 x^{2}(x^{2}-5)$ , find its real zeros, their multiplicities, max turning points, and end behavior.

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Problem 29640

Analyze the function $R(x)=\frac{x^{2}}{x^{2}+x-42}$ for vertical and horizontal asymptotes. What are they?

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Problem 29641

Analyze the function $R(x)=\frac{11 x+11}{4 x+8}$ : find domain, vertical and horizontal asymptotes, and the correct graph.

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Problem 29642

Find the explicit formula for the arithmetic sequence starting with $a_{1}=26$ and the terms $26,33,40,47,54,61,\ldots$ .

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Problem 29643

Analyze the function $R(x)=\frac{11 x+11}{5 x+10}$ . Find its domain, vertical asymptote, and horizontal asymptote.

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Problem 29644

How much to invest now at 12% simple interest to have \$2,000 in 6 years? Round up to the nearest cent.

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Problem 29645

$\frac{5 x-3}{2}=6$

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Problem 29646

4. A paper airplane is thrown from the top of a building. The graph shows the relationship between the time, in seconds, after the paper airplane is thrown ( $x$ ) and the height of the paper airplane above the ground.
What does the $x$ -intercept of the graph indicate? (a) The height from which the airplane is thrown. (b) The speed at which the airplane is traveling. (c) The maximum height that the airplane reaches. (d) The number of seconds the airplane is in the air.

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Problem 29647

Multiply. $(z+8)(z-8)$
Simplify your answer.

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Problem 29648

Muliplying conjugate binomials: Univariate
Multiply. $(4-d)(4+d)$
Simplify your answer.

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Problem 29649

Cuotient of expressions involving expon
Simplify. $\frac{z^{3} x^{6}}{z^{5} x^{6}}$

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Problem 29650

Simplify. $\frac{x^{5} y^{4}}{x^{3} y^{6}}$

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Problem 29651

www-awu.aleks.com/alekscgi/x/lsl.exe/1o_u
Exponants and Pefyromials Introduction to the power rules of exponente
Simplifi. $\left(x^{2}\right)^{3}$
Write your answer without parentheses.

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Problem 29652

Tho number of bacteria growing in an incubation culture increases with time according to $n(t)=6900(2) t$ , where is time in days. Find the number of bacteria when $x=0$ and $x=3$ .

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Problem 29653

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

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Problem 29654

Find a linearly independent set of vectors that spans the same subspace of $\mathbb{R}^{4}$ as that spanned by the vectors $\left[\begin{array}{l} 2 \\ 2 \\ 0 \\ 1 \end{array}\right], \quad\left[\begin{array}{c} -4 \\ -2 \\ 2 \\ -5 \end{array}\right], \quad\left[\begin{array}{c} 3 \\ 2 \\ -1 \\ 3 \end{array}\right], \quad\left[\begin{array}{c} 7 \\ 6 \\ -1 \\ 5 \end{array}\right]$
A linearly independent spanning set for the subspace is: $\left\{\begin{array}{l} {\left[\begin{array}{l} \square \\ \square \\ \square \\ \square \end{array}\right],\left[\begin{array}{l} {\left[\begin{array}{l} \square \\ \square \\ \square \\ \square \end{array}\right]} \end{array}\right\} . . . . . . . . . . . ~} \\ \square \end{array}\right]$

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Problem 29655

Evaluate the expression when $x=-3$ . $x^{2}+8 x-7$

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Problem 29656

Evaluate the expression when $y=4$ . $y^{2}-5 y+6$

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Problem 29657

Rewrite the following without an exponent. $\left(\frac{8}{9}\right)^{-1}$

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Problem 29658

26.
Simplify the expression $\frac{6 n^{2}+36 n^{2}}{6 n^{3}-54 n^{2}}$ . A. $\frac{2}{3}$ $\equiv \quad \frac{2}{3} n \neq 0$ c. $\frac{n 16}{n-9}, n \neq 0$ $2 \frac{n+6}{n-9}, n \neq 9$

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Problem 29659

Multiply. $2 x-2 w^{9} \cdot 7 x^{6} w^{9}$
Simplify your answer as much as possible.

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Problem 29660

A company that manufactures small canoes has a fixed cost of $\$ 14,000$ . It costs $\$ 40$ to produce each canoe. The selling price is $\$ 80$ per canoe. (In solving this exercise, let $x$ represent the number of canoes produced and sold.) a. Write the cost function. $C(x)=14000+40 \cdot x \quad$ (Type an expression using $x$ as the variable.) b. Write the revenue function. $R(x)=$ $\square$ (Type an expression using $x$ as the variable.)

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Problem 29661

11. The partial fractional decomposition of the expression $\frac{3 x^{2}-2 x+1}{x^{4}-16}$ is (a) $\frac{A}{x+2}+\frac{B}{x-2}+\frac{C}{x^{2}+4}$ . (b) $\frac{A}{x+2}+\frac{B}{x-2}+\frac{C x+D}{x^{2}+4}$ . (c) $\frac{A x+B}{x^{2}-4}+\frac{C x+D}{x^{2}+4}$ . (d) $\frac{B}{x+2}+\frac{B}{x-2}+\frac{C}{(x+2)^{2}}+\frac{D}{(x-2)^{2}}$ . (e) $\frac{A+B x+C x^{2}+D x^{3}}{x^{4}-16}$ .

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Problem 29662

Simplify $\frac{5}{2 a+b}+\frac{5}{2 a-b}$

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Problem 29663

5. Simplify (a) $l(A, B, C, D)=\pi(0,2,5,7,8,10,13,15)$ (0.5 mark) (b) $T(A, B, C, D)=\Sigma(1,3,4,6,9,11,12,14)$ ( 0.5 mark)
6. (a) An alternating current is defined by the equation: $i=25 \operatorname{Sin} 100 \pi t m A$ . Determine its mean value over half-a-cycle and the root-mean square values over a cycle. (0.5 mark) (b) A body has an initial velocity of $100 \mathrm{~m} / \mathrm{s}$ and it is subjected to a retardation of $25 \mathrm{~m} / \mathrm{s}^{2}$ .
Find the mean value of the velocity of the body during its forward motion. (0.5 mark) Scanned with OKEN Scan
7. (a) Find the position of the centroid of the area bounded by the curve $y=3 x^{2}$ , and the $x$ -axis and the ordinates $x=0$ and $x=2$ (0.5 mark) (b) For the first quadrant area bounded by the curve $y=10-x^{2}$ . Find the moment of inertia w.r.t. the $y$ -axis (0.5 mark)
8. (a) Determine the co-ordinates of the centroid of the area lying between the curve $y=5 x-x^{2}$ and the $x$ -axis (0.5 mark) (b) Find the moment of inertia about the $x$ -axis of the region bounded by $y=x^{2}$ and $y=x-1$ (0.5 mark)
9. A d.c circuit comprises four closed loops. Applying Kirchhoff's laws to the closed loops give the following equations for the current flow in milliamperes: $\begin{aligned} 4 i_{1}+3 i_{2}+i_{3}-i_{4} & =14 \\ 2 i_{1}+5 i_{2}+2 i_{3}+i_{4} & =17 \\ i_{1}+4 i_{2}+4 i_{3}+6 i_{4} & =20 \\ 3 i_{1}+i_{2}-i_{3}+5 i_{4} & =12 \end{aligned}$
Use the Gaussian elimination method to Solve for $i_{1}, i_{2}, i_{3}$ , and $i_{4}$ . (1 mark)
10. Use simplex method to solve $\begin{aligned} \text { Maximize } z & =7 x_{1}+5 x_{2} \\ \text { Subjected to } & 2 x_{1}+x_{2} \leq 10 \\ & 4 x_{1}+3 x_{2} \leq 24 \\ & x_{1} \geq 0, x_{2} \geq 0 \end{aligned}$ (1 mark)

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Problem 29664

Find the vertical asymptotes of the function $f(x) = \frac{2}{x^2 + x - 3}$ .

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Problem 29665

Systems of Linear Equations: Tutorial 13 of 26 ? Question Plane $A$ is descending toward the local airport at a rate of 2,500 feet/minute. It is currently at an altitude of 12,000 feet. Plane $B$ is ascending from the same airport at a rate of 4,000 feet/minute. It is currently at an altitude of 1,000 feet. This system of equations models this real-world situation, where $x$ represents the time in minutes and $y$ represents the altitude in thousands of feet: $\begin{array}{l} y=12-2.5 x \\ y=1+4 x \end{array}$
Graph the lines of the two equations, and mark the point of intersection for the two lines. In approximately how many minutes will the two planes be at the same altitude? At what altitude will they be?

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Problem 29666

The product of two consecutive, nonnegative integers is 342 . Find the integers and separate them with a comma.

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Problem 29667

List the eigenvalues of A . The transformation $\mathrm{x} \mapsto \mathrm{Ax}$ is the composition of a rotation and a scaling. Give the angle $\varphi$ of the rotation, where $-\pi<\varphi \leq \pi$ , and give the scale factor $r$ . $A=\left[\begin{array}{rr} -8 \sqrt{3} & 8 \\ -8 & -8 \sqrt{3} \end{array}\right]$
The eigenvalues of A are $\lambda=-8 \sqrt{3}+8 \boldsymbol{i},-8 \sqrt{3}-8 \boldsymbol{i}$ . (Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals and $i$ as needed.) $\varphi=$ $\square$ (Simplify your answer. Type an exact answer, using $\pi$ as needed.)

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Problem 29668

6. A producer can sell 2000 items at a price of $10 \$$ for each one. For each decrease in price of $2 \$$ , the producer can sell an additional 100 items. The demand equation is a) $p=0.02 x+50$ . b) $p=-0.002 x+14$ . (c) $p=-0.02 x+50$ . d) $p=0.02 x-14$ .

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Problem 29669

Aufgaben zum Einsetzungsverfahren 1) Lose wie in Beispiel 1: a) $\left\lvert\, \begin{array}{l}4 x+2 y=8 \\ y=8 x-1\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}2 x+y=6 \\ y=-4 x\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}6 x+y=-4 \\ y=-3 x+2\end{array}\right.$ 2) Lóse wie in Beispiel 2: a) $\left\lvert\, \begin{array}{l}x+y=11 \\ x=-3\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}x-5 y=-16 \\ -5 x+20 y=40\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}2 x+3 y=-30 \\ x=-2 y-30\end{array}\right.$ 3) Lơse wie in Beispiel 3: a) $\left\lvert\, \begin{array}{l}4 x+7 y=-8 \\ 4 x+3 y=8\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}3 x+8 y=9 \\ 5 x-8 y=15\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}7 x+19 y=-3 \\ 12 x+19 y=22\end{array}\right.$ (mache jeweils die Probe und überprüfe somit dein Ergebnis!)

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Problem 29670

K12 K12 K12 OLS Login My Info K12 Customer Supp... Newrow Support 5 of 5
Match the simplified expression with the correct problem. $\begin{array}{c} \frac{3}{4}(8 x+16) \\ 2 x-5 x+5-4 \\ \hline x+x+x+3+5-2 \\ \hline 3+2(2 x+5) \end{array}$ $9 x-2$ $4 x+13$ $-3 x+1$ $6 x+12$ $3 x+6$

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Problem 29671

Simplify $5 b^{4} \times 5 b$

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Problem 29672

P'education nationale Oujda Angad Lycée Salam Oujda En Mathématiques Exercice 1 : (2points) Factoriser les expressions suivantes : 1 pt $A=4 x^{2}-(x-1)^{2}$ 1 pt $B=x^{2}-27$

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Problem 29673

A business owner pays $\$ 1,200$ per month in rent and a total of $\$ 120$ per hour in employee salary for each hour the store is open. On average, the store brings in $\$ 200$ in net sales per hour. Which equations can be solved to determine the break-even point if $C(x)$ represents the cost function, $R(x)$ represents the revenue function, and $x$ the number of hours per month the store is open? $C(x)=1,200+120 x R(x)=200 x$ $C(x)=1,200+120 R(x)=200 x$ $C(x)=200 x R(x)=1,200+120 x$ $C(x)=200 x R(x)=1,200+120$

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Problem 29674

Backspace
A stone fall from a railroad overpass which is 36 ft high into the path of a train which is approaching the overpass with uniporm speced It the stone falls when the train is 50 ft away from the overpass and thestome hit the gmind just as the train anives at that spot, how fast is the train movin

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Problem 29675

14. Given the following complex numbers find $z_{1}+z_{2}, z_{1} \cdot z_{2}$ and $\frac{z_{1}}{z_{2}}$ : $\begin{array}{l} z_{1}=-3-4 i \\ z_{2}=-2 \sqrt{3}+2 i \end{array}$

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Problem 29676

線分 $A B$ 上に 2 点 $\mathrm{P}, \mathrm{Q}$ がある。 $A P: P B=\frac{\sqrt{14}}{3}: \sqrt{\frac{7}{2}}$ , $\mathrm{AQ}: \mathrm{QB}=\sqrt{\frac{5}{3}}: \sqrt{\frac{3}{5}}$ であるとき, $\mathrm{AP}: \mathrm{PQ}$ を最も簡単な整数比で表せ。

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Problem 29677

fare lo stesso per $(\sqrt{2}-\sqrt{3})^{-1}$ .

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Problem 29678

Question 2: solve the system of equations by graphical method: $\begin{array}{l} \mathrm{x}+2 \mathrm{y}=4 \\ \mathrm{y}=\frac{-1}{2} x+2 \end{array}$

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Problem 29679

Question 1 (a) Kapil opened a recurring deposit account in a bank. He deposits ₹ 1500 every month [3] for 2 years at $5 \%$ simple interest per annum. Find the total interest earned by Kapil on maturity. b) If $A=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}1 & 4 \\ 2 & 3\end{array}\right]$ and $C=\left[\begin{array}{ll}-1 & 2 \\ -2 & 5\end{array}\right]$ , find $A(B-C)$ . [3]
The table below shows the daily expenditure on food of 50 house-holds in a locality. [4] \begin{tabular}{|c|c|c|c|c|c|c|} \hline \begin{tabular}{c} Daily \\ Expenditure \\ (in ₹) \end{tabular} & $0-100$ & $100-200$ & $200-300$ & $300-400$ & $400-500$ & $500-600$ \\ \hline \begin{tabular}{c} Number of \\ House-holds \end{tabular} & 5 & 8 & 15 & 10 & 7 & 5 \\ \hline \end{tabular}
Using graph paper, draw a histogram representing the above distribution and estimate the mode. Take along $x$ -axis $2 \mathrm{~cm}=₹ 100$ and along $y$ -axis $2 \mathrm{~cm}=2$ Households.
This paper consists of 8 printed pages. 11 Turn Ov yright reserved.

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Problem 29680

Copy and complete the table below for the graph of $y=2 x+1$ . What values should replace A and B? \begin{tabular}{c|c|c|c|c|c} $x$ & -1 & 0 & 1 & 2 & 3 \\ \hline $y$ & -1 & A & 3 & B & 7 \end{tabular}

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Problem 29681

The equation of a line is $y=2 x+8$ What is the $y$ -intercept of the line?

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Problem 29682

The equation of a line is $y+4=6 x+11$
What is the value of $y$ at the point where the line crosses the $y$ -axis?

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Problem 29683

Write as an exponential equation. $\log _{5} 5=1$

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Problem 29684

14. Solve. $x-9.5=-10.5$
Your answer

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Problem 29685

The Venn diagram below shows information about the number of items in sets $F$ and $G$ .
Given that there are fewer than 94 items in total, what is the largest possible number of items in set F?

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Problem 29686

$\begin{aligned} 3 v_{1}-2 v_{2}-3 v_{3} & =-6 \\ -12 v_{1}+19 v_{2}-3 v_{3} & =0 \\ -10 v_{1}-5 v_{2}+19 v_{3} & =140\end{aligned} \ldots$ (1)

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Problem 29687

$\begin{aligned} 3 v_{1}-2 v_{2}-3 v_{3} & =-6 \\ -12 v_{1}+19 v_{2}-3 v_{3} & =0 \\ -10 v_{1}-5 v_{2}+19 v_{3} & =140 \end{aligned} \ldots \text { (1) }$

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Problem 29688

ما الفرق بين فضاء المتجهات وفضاء المصفوفات؟

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Problem 29689

Question 3 Regina invests in a bond that increases in value based on the function $V(t)=470(2.003)^{\mathbf{s}}$ , where $t$ is the time elapsed in yeers and $V(t)$ is the value of the bond in dollars. 등 $x=\#$ of $y$ rs $y=$ value of ingnd
Estimate the amount of time it will take for Reoina's bond b- $\frac{13}{9}<t<\frac{14}{9}$ C- $13<t<14$ $=$ . .09 : $0: \frac{1}{9}$ d- $\frac{14}{9}<t<\frac{5}{3}$

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Problem 29690

Graph these equations: $\begin{array}{l} y=3 \\ y=4 \end{array}$
Click to select points on the graph. $y=3$ $y=4$
How many solutions does the system of equations have? no solution no solution one solution one solution infinitely many solutions Sctbmitit Work it out

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Problem 29691

and the logarithm fully using the properties of logs. Express is of $\log x, \log y$ , and $\log z$ . $\log \frac{x}{y^{3} z^{4}}$

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Problem 29692

$15-2(x+3)=x+9$

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Problem 29693

The polynomial of degree $3, P(x)$ , has a root of multiplicity 2 at $x=1$ and a root of multiplicity 1 at $x=-1$ . The $y$ -intercept is $y=-0.3$ : Find a formula for $P(x)$ . $P(x)=$ $\square$

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Problem 29694

Graph the function. Label the $x$ -intercept(s), vertex, and axis of symmetry.
21. $f(x)=(x-3)(x+1)$
22. $h(x)=x(x+6)$

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Problem 29695

Exercice 6 (3pts) Décomposer les fractions rationnelles suivantes; $f(x)=\frac{x}{x^{2}-4} \quad ; \quad g(x)=\frac{2 x^{3}+x^{2}-x+1}{x^{2}-2 x+1} \quad \text { et } h(x)=\frac{x^{5}+x^{4}+1}{x^{3}-x}$

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Problem 29696

¿Cuál es una ecuación de la relación lineal en la forma pendiente-intercepto? $y=\square x-\square$

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Problem 29697

r with a positive exponent. c) $\left(-9^{4}\right)^{-1}$ f) $\left[\left(7^{-3}\right)^{-2}\right]^{-2}$

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Problem 29698

1. Rewrite each expression as an equivalent expression with a positive exponen a) $5^{-4}$ c) $\frac{1}{2^{-4}}$ e) $\left(\frac{3}{11}\right)^{-1}$ b) $\left(-\frac{1}{10}\right)^{-3}$ d) $-\left(\frac{6}{5}\right)^{-3}$ f) $\frac{7^{-2}}{8^{-1}}$
2. Write each expression as a single power with a positive exponent. a) $(-10)^{8}(-10)^{-8}$ c) $\frac{2^{8}}{2^{-5}}$ e) $\left(-9^{4}\right)^{-1}$ b) $6^{-7} \times 6^{5}$ d) $\frac{11^{-3}}{11^{5}}$ f) $\left[\left(7^{-3}\right)^{-2}\right]^{-2}$
3. Which is the greater power, $2^{-5}$ or $\left(\frac{1}{2}\right)^{-5}$ ? Explain.

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Problem 29699

Solve the system below by interpreting it as the matrix equation $A X=B$ and finding the inverse coefficient matrix. $\begin{array}{c} x-2 y+z=33 \\ -2 x+7 y-4 z=-108 \\ 2 x+3 y-3 z=-35 \end{array}$
Calculate $A^{-1}$ . $\square$ Calculate $A^{-1} B$ . $\square$ What is $x$ ? Preview 11 11 $\qquad$
Not equivalent.

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Problem 29700

$\begin{aligned} x-7 y+5 z & =90 \\ -3 x+25 y-18 z & =-319 \\ x+6 y-5 z & =-71 \end{aligned}$
Calculate $A^{-1}$ . $\qquad$
Calculate $A^{-1} B$ . $\qquad$
What is $x$ ? $\qquad$
What is $y$ ? $\qquad$
What is $z$ ?

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Algebra

Problem 29601

Joe's age is 3 times Aaron's. Aaron is 6 years older than Christina. Their ages sum to 149. Find Christina's, Joe's, and Aaron's ages.

Problem 29602

Tìm tích các giá trị của tham số mmm sao cho g(x1)+g(x2)+g(x3)+g(x4)=0g(x_{1})+g(x_{2})+g(x_{3})+g(x_{4})=0g(x1​)+g(x2​)+g(x3​)+g(x4​)=0 với f(x)=x4+4x3−2x2−4m2x+1f(x)=x^{4}+4 x^{3}-2 x^{2}-4 m^{2} x+1f(x)=x4+4x3−2x2−4m2x+1.

Problem 29603

Find the value of □\square□ in the equations: 63.85×□=63,85063.85 \times \square = 63,85063.85×□=63,850 and 63.85×□=638,50063.85 \times \square = 638,50063.85×□=638,500.

Problem 29604

Simplify the expression: 20353\frac{20 \sqrt{3}}{5 \sqrt{3}}53​203​​.

Problem 29605

Solve for yyy in the equation: −5=9+y-5=9+y−5=9+y.

Problem 29606

Simplify the expression: 21−2\frac{2}{1-\sqrt{2}}1−2​2​.

Problem 29607

Solve for nnn in the equation n+24=1\frac{n+2}{4}=14n+2​=1.

Problem 29608

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the xxx-axis and distance on the yyy-axis? Distance in 45 seconds is (45, ).

Problem 29609

Solve the inequality: (x−6)2x2−25≥0\frac{(x-6)^{2}}{x^{2}-25} \geq 0x2−25(x−6)2​≥0. List intervals and signs in interval notation.

Problem 29610

Evaluate −73x+10-\frac{7}{3} x + 10−37​x+10 when x=6x = 6x=6.

Problem 29611

Solve the inequality: (x−4)2x2−4≥0\frac{(x-4)^{2}}{x^{2}-4} \geq 0x2−4(x−4)2​≥0. List intervals and signs in interval notation.

Problem 29612

Solve the inequality (x−7)2/(x2−36)≥0(x-7)^{2}/(x^{2}-36) \geq 0(x−7)2/(x2−36)≥0 and list intervals with signs in each. Use interval notation.

Problem 29613

Rearrange the equation −3r+2−6r+5=4s\frac{-3 r+2}{-6 r+5}=4 s−6r+5−3r+2​=4s to solve for rrr.

Problem 29614

Problem 29615

Solve the inequality: x+8x−3≤1\frac{x+8}{x-3} \leq 1x−3x+8​≤1. List intervals and signs in each interval in interval notation.

Problem 29616

Find the sum of the coefficients of P(x)+Q(x)P(x) + Q(x)P(x)+Q(x) where P(x)=3x4−2x3+4x2−6x+3P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3P(x)=3x4−2x3+4x2−6x+3 and Q(x)=−x4+5x3−2x2−3x+7Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7Q(x)=−x4+5x3−2x2−3x+7.

Problem 29617

Solve the inequality x+8x−3≤1\frac{x+8}{x-3} \leq 1x−3x+8​≤1. List intervals and signs. Provide the solution in interval notation.

Problem 29618

Solve the inequality x+4x−2≤1\frac{x+4}{x-2} \leq 1x−2x+4​≤1 and list intervals with signs in interval notation.

Problem 29619

Find the number of positive real solutions for the equation 5x3+x2+7x−28=05 x^{3}+x^{2}+7 x-28=05x3+x2+7x−28=0. Options: A. Two B. Three or one C. Two or zero D. One

Problem 29620

Solve the inequality: x2(2+x)(x+3)(x+7)(x−1)≥0 \frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0 (x+7)(x−1)x2(2+x)(x+3)​≥0 Identify intervals and their signs, then list in interval notation.

Problem 29621

Calculate the slope between the points (18,-12) and (-11,17). Use the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

Problem 29622

Solve the inequality: x2(4+x)(x+6)(x+7)(x−2)≥0 \frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0 (x+7)(x−2)x2(4+x)(x+6)​≥0 List intervals and their signs in ascending order.

Problem 29623

Find the slope-intercept form of the line passing through (−1,1)(-1,1)(−1,1) with a slope of 000.

Problem 29624

Find the slope-intercept form of the line that passes through the points (2,3)(2,3)(2,3) and (4,2)(4,2)(4,2).

Problem 29625

Find the real zeros of f(x)=7x4+6x3−22x2−18x+3f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3f(x)=7x4+6x3−22x2−18x+3 and factor fff over the reals.

Problem 29626

Calculate the future value AAA of a loan with principal P=$2000P=\$2000P=$2000, interest rate r=3.0%r=3.0\%r=3.0%, and time t=3t=3t=3 months.

Problem 29627

Solve the equation 3x4−58x3+280x2−438x+117=03 x^{4}-58 x^{3}+280 x^{2}-438 x+117=03x4−58x3+280x2−438x+117=0. What are the real solutions? A. x=x=x=; B. No real solutions.

Problem 29628

Analyze the polynomial f(x)=(x+8)2(1−x)f(x)=(x+8)^{2}(1-x)f(x)=(x+8)2(1−x): (a) End behavior: y=□y=\squarey=□ for large ∣x∣|x|∣x∣. (b) Find xxx- and yyy-intercepts. (c) Determine zeros and their multiplicity. (d) Max turning points? (e) Graph fff. Choose A, B, C, or D.

Problem 29629

Analyze the function R(x)=x2−121x4−81R(x)=\frac{x^{2}-121}{x^{4}-81}R(x)=x4−81x2−121​: (a) Find the domain. (b) Identify vertical asymptote(s). (c) Find horizontal/oblique asymptote. (d) Choose the correct graph.

Problem 29630

Analyze the polynomial f(x)=x3+2x2−15xf(x)=x^{3}+2x^{2}-15xf(x)=x3+2x2−15x. Answer parts (a) to (e). Factor first.

Problem 29631

Rewrite x(x−y)5−y(x−y)5x(x-y)^{5}-y(x-y)^{5}x(x−y)5−y(x−y)5 as (x−y)a(x-y)^{a}(x−y)a and find the value of aaa.

Problem 29632

Problem 29633

Analyze the function H(x)=4x−129−x2H(x)=\frac{4x-12}{9-x^{2}}H(x)=9−x24x−12​. Find its domain and asymptotes.

Problem 29634

Find the complex zeros of f(x)=x3−15x2+79x−145f(x)=x^{3}-15 x^{2}+79 x-145f(x)=x3−15x2+79x−145. Provide exact answers using radicals and iii.

Problem 29635

Write an inequality for: The product of 2x2x2x and 161616 is at most 999.

Problem 29636

Find the xxx-intercepts of the parabola with vertex (6,27)(6,27)(6,27) and yyy-intercept (0,−81)(0,-81)(0,−81). Round to the nearest hundredth.

Problem 29637

Find the value of yyy for the equation y=−5x2−10x−15y=-5 x^{2}-10 x-15y=−5x2−10x−15.

Problem 29638

Find n\mathrm{n}n using the future value of an annuity formula with A=$18,500\mathrm{A}=\$ 18,500A=$18,500, R=$800R=\$ 800R=$800, r=8.0%r=8.0\%r=8.0%. n=□n=\squaren=□

Problem 29639

For the polynomial f(x)=−4x2(x2−5)f(x)=-4 x^{2}(x^{2}-5)f(x)=−4x2(x2−5), find its real zeros, their multiplicities, max turning points, and end behavior.

Problem 29640

Analyze the function R(x)=x2x2+x−42R(x)=\frac{x^{2}}{x^{2}+x-42}R(x)=x2+x−42x2​ for vertical and horizontal asymptotes. What are they?

Problem 29641

Tìm tích các giá trị của tham số $m$ sao cho $g(x_{1})+g(x_{2})+g(x_{3})+g(x_{4})=0$ với $f(x)=x^{4}+4 x^{3}-2 x^{2}-4 m^{2} x+1$ .

Find the value of $\square$ in the equations: $63.85 \times \square = 63,850$ and $63.85 \times \square = 638,500$ .

Simplify the expression: $\frac{20 \sqrt{3}}{5 \sqrt{3}}$ .

Solve for $y$ in the equation: $-5=9+y$ .

Simplify the expression: $\frac{2}{1-\sqrt{2}}$ .

Solve for $n$ in the equation $\frac{n+2}{4}=1$ .

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the $x$ -axis and distance on the $y$ -axis? Distance in 45 seconds is (45, ).

Solve the inequality: $\frac{(x-6)^{2}}{x^{2}-25} \geq 0$ . List intervals and signs in interval notation.

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

Solve the inequality: $\frac{(x-4)^{2}}{x^{2}-4} \geq 0$ . List intervals and signs in interval notation.

Solve the inequality $(x-7)^{2}/(x^{2}-36) \geq 0$ and list intervals with signs in each. Use interval notation.

Rearrange the equation $\frac{-3 r+2}{-6 r+5}=4 s$ to solve for $r$ .

Solve the inequality: $\frac{x+8}{x-3} \leq 1$ . List intervals and signs in each interval in interval notation.

Find the sum of the coefficients of $P(x) + Q(x)$ where $P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3$ and $Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7$ .

Solve the inequality $\frac{x+8}{x-3} \leq 1$ . List intervals and signs. Provide the solution in interval notation.

Solve the inequality $\frac{x+4}{x-2} \leq 1$ and list intervals with signs in interval notation.

Find the number of positive real solutions for the equation $5 x^{3}+x^{2}+7 x-28=0$ . Options: A. Two B. Three or one C. Two or zero D. One

Solve the inequality:
$\frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0$
Identify intervals and their signs, then list in interval notation.

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Solve the inequality:
$\frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0$
List intervals and their signs in ascending order.

Find the slope-intercept form of the line passing through $(-1,1)$ with a slope of $0$ .

Find the slope-intercept form of the line that passes through the points $(2,3)$ and $(4,2)$ .

Find the real zeros of $f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3$ and factor $f$ over the reals.

Calculate the future value $A$ of a loan with principal $P=\$2000$ , interest rate $r=3.0\%$ , and time $t=3$ months.

Solve the equation $3 x^{4}-58 x^{3}+280 x^{2}-438 x+117=0$ . What are the real solutions? A. $x=$ ; B. No real solutions.

Analyze the polynomial $f(x)=(x+8)^{2}(1-x)$ :
(a) End behavior: $y=\square$ for large $|x|$ . (b) Find $x$ - and $y$ -intercepts. (c) Determine zeros and their multiplicity. (d) Max turning points? (e) Graph $f$ . Choose A, B, C, or D.

Analyze the function $R(x)=\frac{x^{2}-121}{x^{4}-81}$ :
(a) Find the domain. (b) Identify vertical asymptote(s). (c) Find horizontal/oblique asymptote. (d) Choose the correct graph.

Analyze the polynomial $f(x)=x^{3}+2x^{2}-15x$ . Answer parts (a) to (e). Factor first.

Rewrite $x(x-y)^{5}-y(x-y)^{5}$ as $(x-y)^{a}$ and find the value of $a$ .

Analyze the function $H(x)=\frac{4x-12}{9-x^{2}}$ . Find its domain and asymptotes.

Find the complex zeros of $f(x)=x^{3}-15 x^{2}+79 x-145$ . Provide exact answers using radicals and $i$ .

Write an inequality for: The product of $2x$ and $16$ is at most $9$ .

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

Find the value of $y$ for the equation $y=-5 x^{2}-10 x-15$ .

Find $\mathrm{n}$ using the future value of an annuity formula with $\mathrm{A}=\$ 18,500$ , $R=\$ 800$ , $r=8.0\%$ . $n=\square$

For the polynomial $f(x)=-4 x^{2}(x^{2}-5)$ , find its real zeros, their multiplicities, max turning points, and end behavior.

Analyze the function $R(x)=\frac{x^{2}}{x^{2}+x-42}$ for vertical and horizontal asymptotes. What are they?

Analyze the function $R(x)=\frac{11 x+11}{4 x+8}$ : find domain, vertical and horizontal asymptotes, and the correct graph.

Find the explicit formula for the arithmetic sequence starting with $a_{1}=26$ and the terms $26,33,40,47,54,61,\ldots$ .

Analyze the function $R(x)=\frac{11 x+11}{5 x+10}$ . Find its domain, vertical asymptote, and horizontal asymptote.

$\frac{5 x-3}{2}=6$

Multiply. $(z+8)(z-8)$
Simplify your answer.

Muliplying conjugate binomials: Univariate
Multiply. $(4-d)(4+d)$
Simplify your answer.

Cuotient of expressions involving expon
Simplify. $\frac{z^{3} x^{6}}{z^{5} x^{6}}$

Simplify. $\frac{x^{5} y^{4}}{x^{3} y^{6}}$

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Exponants and Pefyromials Introduction to the power rules of exponente
Simplifi. $\left(x^{2}\right)^{3}$
Write your answer without parentheses.

Tho number of bacteria growing in an incubation culture increases with time according to $n(t)=6900(2) t$ , where is time in days. Find the number of bacteria when $x=0$ and $x=3$ .

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

Evaluate the expression when $x=-3$ . $x^{2}+8 x-7$

Evaluate the expression when $y=4$ . $y^{2}-5 y+6$

Rewrite the following without an exponent. $\left(\frac{8}{9}\right)^{-1}$

Multiply. $2 x-2 w^{9} \cdot 7 x^{6} w^{9}$
Simplify your answer as much as possible.

Simplify $\frac{5}{2 a+b}+\frac{5}{2 a-b}$

Find the vertical asymptotes of the function $f(x) = \frac{2}{x^2 + x - 3}$ .

Simplify $5 b^{4} \times 5 b$

P'education nationale Oujda Angad Lycée Salam Oujda En Mathématiques Exercice 1 : (2points) Factoriser les expressions suivantes : 1 pt $A=4 x^{2}-(x-1)^{2}$ 1 pt $B=x^{2}-27$