Math Statement

Problem 13701

i) limx3x3+x25x21x3=\lim _{x \rightarrow 3} \frac{x^{3}+x^{2}-5 x-21}{x-3}=

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Problem 13702

Question
Solve the following inequality for rr. Write your answer in simplest form. 9r4(5r5)9r+10+59 r-4(-5 r-5) \leq-9 r+10+5
Answer Attempt 1 out of 3 rr \square Submit Answer

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Problem 13703

Use the Laws of Logarithms to combine the expression. log4(2)+2log4(9)\log _{4}(2)+2 \log _{4}(9) \square Need Help? Read It Master It Submit Answer

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Problem 13704

Points: 0 of 1 Save
Solve the logarithmic equation. x=log12123x=\log _{12} \sqrt[3]{12}
The solution set is \square B. (Simplify your answer. Type an integer or a fraction.)

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Problem 13705

Convert y=(x+3)26y=(x+3)^{2}-6 to standard form. y=x2+y=x^{2}+ \square x+x+

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Problem 13706

Let XX be a non-negative random variable with a distribution such that P(X>a)=e0.6aP(X>a)=e^{-0.6 a} for all a>0a>0. Calculate P(eX0.291)P\left(e^{X}-0.29 \leq 1\right).

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Problem 13707

Question Pat 1 of 2 Completed: 6 of 11 My score: 6/116 / 11 pts (54.55\%) Save
Use the figures to calculate the left and right Riemann sums for f on the given interval and for the given value of n. f(x)=2x on [1,5];n=4f(x)=\frac{2}{x} \text { on }[1,5] ; n=4
The left Riemann sum for f is \square . (Simplify your answer.)

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Problem 13708

Question 5
Which ordered pairs are solutions to the inequality 2x+3y3-2 x+3 y \geq 3 ? Choose all that ap (1,2)(-1,-2) (4,1)(4,1) (2,3)(2,3) (1,2)(-1,2) (0,1)(0,1) (2,3)(2,-3) (0,1)(0,-1)

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Problem 13709

10) g(n)=3n2h(n)=n3+n Find (gh)(n)\begin{array}{l} g(n)=3 n-2 \\ h(n)=n^{3}+n \\ \text { Find }(g \circ h)(n) \end{array}

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Problem 13710

Solve for xx. Express any solution as a reduced fraction or intege 5x+11=x+1x=\begin{array}{l} \sqrt{5 x+11}=x+1 \\ x= \end{array}

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Problem 13711

Find the inverse of the function g(x)=2x+21 g(x) = \frac{2}{x+2} - 1 .

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Problem 13712

Use a calculator to find the common logarithm. log(35)\log (35)
The answer is \square \square. (Round to four decimal places as needed.)

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Problem 13713

75y3250xy4(15xy)3=0\frac{75 y^{3}-250 x y^{4}}{(1-5 x y)^{3}}=0

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Problem 13714

Evaluate the integral. 3x3/2xdx3x3/2xdx=\frac{\int \frac{3}{x^{3 / 2}-\sqrt{x}} d x}{\int \frac{3}{x^{3 / 2}-\sqrt{x}} d x=\square} \square

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Problem 13715

1 Recall that for any geometric sequence starting at aa with a common ratio rr, the sum ss of the first nn terms is given by s=a1rn1rs=a \frac{1-r^{n}}{1-r}. Find the approximate sum of the first 50 terms of each sequence:
Type your answers in the boxes.
1. 12,14,18,116,.s=1\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots . s=1
2. 1,12,14,18,116,s=21, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots s=2

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Problem 13716

Find the value. log584log303log584log303\begin{array}{l} \log 584-\log 303 \\ \log 584-\log 303 \approx \square \end{array} \square (Round to four decimal places as needed.)

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Problem 13717

Add the integers. 4+(7)4+(7)=\begin{array}{l} -4+(-7) \\ -4+(-7)= \end{array}

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Problem 13718

(a) (15×25)+11125\left(\frac{1}{5} \times \frac{2}{5}\right)+1 \frac{11}{25}

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Problem 13719

37. 28+34=w5\frac{2}{8}+\frac{3}{4}=\frac{w}{5}

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Problem 13720

Combine like terms to form an equivalent expression. 7+6x+3zxz127+6 x+3 z-x-z-12 7+6x+3zxz12=7+6 x+3 z-x-z-12= \square (Simplify your answer.)

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Problem 13721

2) If b0=1.4,b1=8b_{0}=1.4, b_{1}=8 and bm=3bm2bm1b_{m}=\frac{3-b_{m-2}}{b_{m-1}}, then b3=b_{3}= (A) -25 (B) -3.57 (C) 0.20 (D) 0.82 (E) 1.40

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Problem 13722

Solve for xx. 3+log3(x8)=6x=\begin{array}{l} 3+\log _{3}(x-8)=6 \\ x=\square \end{array}

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Problem 13723

20. Write the following values in descencting orctiar: 170,58,403,4.025\sqrt{170}, 5 \sqrt{8}, \frac{40}{3}, 4.025

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Problem 13724

Find all intervals on which f(x)f(x) is decreasing. f(x)=x412x3+13f(x)=-x^{4}-12 x^{3}+13
Answer Attempt 1 out of 2

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Problem 13725

Determine whether the given numbers are solutions of the inequality. 8,20,138,-20,-13, 3-3 y9>2y2y-9>2 y-2
Is 8 a solution? Yes No
Is -20 a solution? No Yes
Is - 13 a solution? No Yes
Is -3 a solution? No Yes

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Problem 13726

Solve the inequality. (Enter your answer using interval notation.) x2ex7ex<0x^{2} e^{x}-7 e^{x}<0

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Problem 13727

3. Calculate slope from two points: a) (9,6)(-9,6) and (6,9)(-6,-9) b) (10,1)(-10,1) and (0,4)(0,-4) c) (2,2)(2,-2) and (9,3)(9,3) d) (1,7)(-1,-7) and (3,9)(3,9)

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Problem 13728

Find all zeros of the polynomial function given below. P(x)=2x515x4+29x325x2+27x10P(x)=2 x^{5}-15 x^{4}+29 x^{3}-25 x^{2}+27 x-10

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Problem 13729

Solve using the addition and multiplication principles. 64x13x6-4 x \leq 1-3 x
Select the correct choice below and fill in the answer box within your choice. (Simplify your answer.) A. The solution set is {xx\{x|x\rangle \square \}. B. The solution set is {xx<\{x \mid x< \square \}. C. The solution set is {xx\{x \mid x \leq \square \}. D. The solution set is {xx\{x \mid x \geq \square \}.

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Problem 13730

f(x)=xg(x)=x+2+4\begin{array}{l} f(x)=|x| \\ g(x)=|x+2|+4 \end{array}
We can think of gg as a translated (shifted) version of ff. Complete the description of the transformation. Use nonnegative numbers.
To get the function gg, shift ff \square \square units and to the \square left by \square units.

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Problem 13731

э a:b=2:5a: b=2: 5b:c=3:4b: c=3: 4, дьдпб a:b:c=a: b: c=

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Problem 13732

A small business estimates that the value V(t)\mathrm{V}(t) of a copy machine is decreasing according to the function V(t)=7000(4)0.12tV(t)=7000(4)^{-0.12 t} where tt is the number of years that have elapsed since the machine was purchased, and V(t)\mathrm{V}(\mathrm{t}) is in dollars. Use this information to answer parts (a)-(d). (a) What was the original value of the machine?
The original value was $7000\$ 7000. (Round to the nearest dollar as needed.) (b) What is the value of the machine 5 yr after purchase, to the nearest dollar?
The value of the machine 5 yr after purchase is approximately. $3047\$ 3047. (Round to the nearest dollar as needed.) (c) What is the value of the machine 10 yr after purchase, to the nearest dollar?
The value of the machine 10 yr after purchase is approximately $\$ \square (Round to the nearest dollar as needed.)

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Problem 13733

Question 3
What are the zeros of f(x)=(2x+4)(x1)2f(x)=(2 x+4)(x-1)^{2} ? What is its degree and leading coefficient?
Edit View Insert Format Tools Table

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Problem 13734

For the function, evaluate the given expression. f(x,y)=xeyyex, find f(4,4)f(4,4)=\begin{array}{l} f(x, y)=x e^{y}-y e^{x}, \text { find } f(4,-4) \\ f(4,-4)= \end{array}

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Problem 13735

Bimplincaf. 153\sqrt{15} \cdot \sqrt{3}

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Problem 13736

2. The equation of a circle is x2+y2=121x^{2}+y^{2}=121. Determine the radius. a. 10 units b. 12.1 units c. 11 units d. 22 units
3. Which point is on the circle with equation x2+v2=26?x^{2}+v^{2}=26 ?

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Problem 13737

 Area =b1+b22× height =20ft+15ft2×10ft=35ft2×10ft=17.5ft×10ft=ft2\begin{aligned} \text { Area } & =\frac{b_{1}+b_{2}}{2} \times \text { height } \\ & =\frac{20 \mathrm{ft}+15 \mathrm{ft}}{2} \times 10 \mathrm{ft} \\ & =\frac{35 \mathrm{ft}}{2} \times 10 \mathrm{ft} \\ & =17.5 \mathrm{ft} \times 10 \mathrm{ft} \\ & =\square \mathrm{ft}^{2}\end{aligned}

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Problem 13738

Monthly mortgage payment=($5.22)(170)=$887.40\text{Monthly mortgage payment} = (\$5.22)(170) = \$887.40 \text{(Type an integer or a decimal.)}
\text{To find the total mortgage payment, first determine the number of months.}
\text{The number of months is } \square \text{ (Type a whole number.)}

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Problem 13739

Multiplicar. 3(3614)\sqrt{3}(\sqrt{3}-6 \sqrt{14})
Simplificar la respuesta tanto como sea posible. \square [\sqrt{[ } \square

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Problem 13740

Hallar la pendiente yy la intersección con el eje yy de la recta. 8x+4y=12-8 x+4 y=-12
Escribir sus respuestas en su forma más simple. pendiente: \square ㅁ Indefinido intersecclón con el eje yy : \square

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Problem 13741

2.5(4x2)>102.5(4 x-2)>10 True False

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Problem 13742

Name: Date: November -25 Page 2 of 2
5. A store uses the equation C=7.50+1.75wC=7.50+1.75 w to calculate the cost CC (in dollars) to ship merchandise that weighs ww pounds. a. Find the cost of mailing a 5 pound package. Show your work. b. It costs Manny $21.50\$ 21.50 to ship a package. How much does this package weigh? Show your work.

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Problem 13743

Resolver para xx. y=2(xa)x=π\begin{array}{l} y=2(x-a) \\ x=\pi \end{array}

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Problem 13744

Factorizar. 4x2494 x^{2}-49

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Problem 13745

Simplify the expression. (z8)(z+8)(z8)\frac{(z-8)(z+8)}{(z-8)} (z8)(z+8)(z8)=\frac{(z-8)(z+8)}{(z-8)}= \square (Simplify your answer.)

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Problem 13746

The events AA and BB satisfy: P(AB)=2/3P(A \cup B)=2 / 3 and P(AB)=1/2P\left(A^{\prime} \mid B^{\prime}\right)=1 / 2. The value of P(B)P(B) is a. 35\frac{3}{5} b. 12\frac{1}{2} C. 23\frac{2}{3} d. 19\frac{1}{9} e. none of them f. 15\frac{1}{5} g. 13\frac{1}{3}

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Problem 13747

Factoring Quiz B Factor each completely. 1) x2+9xx^{2}+9 x

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Problem 13748

1. Solve this DE using Exact Technique dydx=yy22xy+1,y>1\frac{d y}{d x}=\frac{y-y^{2}}{2 x y+1}, \quad y>1

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Problem 13749

Solve for xx. logx=log(x3)log2x=\begin{array}{l} \log x=\log (x-3)-\log 2 \\ x=\square \end{array}

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Problem 13750

Question 3 of 5
Subtract the following rational expressions f+g16fg16\frac{f+g}{16}-\frac{f-g}{16}

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Problem 13751

2. Flächeninhalt
Die Funktion f(x)=(x1)ex(sf(x)=(x-1) \cdot e^{x}(s. Bild oben) beschreibt den Verlauf eines Flusses, der von zwei Straßen überbrückt wird, die längs der Koordinatenachsen laufen. (1 LE = 1 km ) Die beiden Straßen und der Fluss schließen im 4. Quadranten ein Grundstück A ein, welches für 8080 € pro m2\mathrm{m}^{2} zum Kauf angeboten wird. a) Zeigen Sie, dass F(x)=(x2)exF(x)=(x-2) \cdot e^{x} eine Stammfunktion von ff ist.

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Problem 13752

Determine the number of solutions for the following linear equation: 28x16=4(7x4)28 x-16=4(7 x-4) No Solution Infinitely Many Solutions One Solution

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Problem 13753

Complete the square to re-write the quadratic function in vertex form: y=x2+4x9y=x^{2}+4 x-9

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Problem 13754

Use a rational exponent to write a43\sqrt[3]{a^{4}}. a43=\sqrt[3]{a^{4}}=

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Problem 13755

Solve the rational inequality. 3x20x290\frac{3 x-20}{x^{2}-9} \geq 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \square \square. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There are no real solutions.

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Problem 13756

The function gg is defined by g(x)=x2+9g(x)=x^{2}+9. For which value of xx is g(x)=25g(x)=25 ? A) 4 B) 5 C) 9 D) 13

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Problem 13757

Complete the square to re-write the quadratic function in vertex form: y=x24x+6y=x^{2}-4 x+6

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Problem 13758

y=cos(2θ),x=tan(θ)y=\cos (2 \theta), x=\tan (\theta) find dydx\frac{d y}{d x}.

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Problem 13759

7
The function ff is defined by the equation f(x)=7x+2f(x)=7 x+2. What is the value of f(x)f(x) when x=4x=4 ?

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Problem 13760

Unit 4: Trigonometric Functions Activity 8: Trigonometric Identities
Assignment Prove each of the following trigonometric identities.
1. sinxsin2x+cosxcos2x=cosx\sin x \sin 2 x+\cos x \cos 2 x=\cos x
2. cotx=sinxsin(π2x)+cos2xcotx\cot x=\sin x \sin \left(\frac{\pi}{2}-x\right)+\cos ^{2} x \cot x
3. 2csc2x=secxcscx2 \csc 2 x=\sec x \csc x

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Problem 13761

Factor completely. 4x2+12x274 x^{2}+12 x-27

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Problem 13762

x+4y=4x+3y=1\begin{array}{l} -x+4 y=4 \\ -x+3 y=1 \end{array}
Is (8,3)(8,3) a solution of the system?

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Problem 13763

2x+7y=1y=4x8\begin{array}{l} 2 x+7 y=1 \\ y=4 x-8 \end{array}
Is (4,8)(4,8) a solution of the system?

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Problem 13764

y=5x+24xy=0\begin{array}{l} y=5 x+2 \\ 4 x-y=0 \end{array}
Is (2,12)(2,12) a solution of the system?

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Problem 13765

nlist 0 Points: 0 of 1
For the given functions, find (fg)(x)(f \circ g)(x) and (gf)(x)(g \circ f)(x) and the domain of each. f(x)=3x+1,g(x)=xf(x)=3 x+1, g(x)=\sqrt{x} 36 (fg)(x)=(f \circ g)(x)= \square

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Problem 13766

Find the solution to the system of equations. You can use the interactive graph below to find the solution. {8x4y=168x+4y=16x=y=\begin{array}{l} \left\{\begin{array}{l} 8 x-4 y=16 \\ 8 x+4 y=16 \end{array}\right. \\ x=\square \\ y=\square \end{array}

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Problem 13767

14 z2+10z24=0z^{2}+10 z-24=0
What is one of the solutions to the given equation?

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Problem 13768

Find the solution to the system of equations. You can use the interactive graph below to find the ss {y=4x3y=2x+1x=\begin{array}{l} \left\{\begin{array}{l} y=-4 x-3 \\ y=-2 x+1 \end{array}\right. \\ x=\square \end{array} \square y=y= \square

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Problem 13769

Use identities to find an expression equivalent to 1+sin(6x)1sin(6x)1sin(6x)1+sin(6x)\frac{1+\sin (6 x)}{1-\sin (6 x)}-\frac{1-\sin (6 x)}{1+\sin (6 x)}

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Problem 13770

Fully factorise 24a232a24 a^{2}-32 a

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Problem 13771

{3x2+4x=6y6y=60+12x\left\{\begin{array}{l}3 x^{2}+4 x=6 y \\ 6 y=60+12 x\end{array}\right.

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Problem 13772

Simplify. 12+475\sqrt{12}+4 \sqrt{75}

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Problem 13773

2. f(6)f(6) if f(x)=4xf(x)=4 x a. 10 b. 20 c. 24 d. 30 A в c D

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Problem 13774

implify. 218+8-2 \sqrt{18}+\sqrt{8}

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Problem 13775

4) 320102213102151021\frac{320 \cdot 10^{-22}}{13 \cdot 10^{-21}-5 \cdot 10^{-21}}

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Problem 13776

Multiply. 7(8+3)\sqrt{7}(8+\sqrt{3})
Simplify your answer as much as possible.

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Problem 13777

Rationalize: 11312\quad \frac{11}{3 \sqrt{12}}

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Problem 13778

f(x,y)=x9ey2fx=\begin{array}{c}f(x, y)=x^{9} e^{y^{2}} \\ f_{x}=\square\end{array}

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Problem 13779

Simplify. v9\sqrt{v^{9}}
Assume that the variable represents a positive real number.

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Problem 13780

Itemi Daca F(x)=2x+1.(6)5xF(x)=\frac{2 x+1 .(6)}{5-x}, atunci F(0)=F(0)= Rezolvare:

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Problem 13781

Simplify. with an odd exponent x13\sqrt{x^{13}}
Assume that the variable represents a positive real number. \square \sqrt{\square}

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Problem 13782

CLEAR CHECK 1.5+0.7(2.6)(0.9)1.5+0.7-(-2.6)-(-0.9) 0.7(2.60.9)0.7-(-2.6-0.9)
1.5+0.7(2.60.9)1.5+0.7-(-2.6-0.9) 1.5+0.7+(2.6)+(0.9)1.5+0.7+(-2.6)+(-0.9)

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Problem 13783

aabab2bab\frac{a-\sqrt{a b}}{\sqrt{a b}} \cdot \frac{2}{b-\sqrt{a b}}

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Problem 13784

y=3/x,y=6/x2,x=4y=3 / x, \quad y=6 / x^{2}, \quad x=4

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Problem 13785

Find (fg)(2)(f \circ g)(2) for the following functions. f(x)=x2+1 and g(x)=x3+x2f(x)=x^{2}+1 \text { and } g(x)=x^{3}+x^{2}
Answer How to enter your:answer (opens in new window) (fg)(2)=(f \circ g)(2)= \square

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Problem 13786

Simplify the expression using synthetic division or the division algorithm. (4x23x1)(2x+5)\frac{\left(4 x^{2}-3 x-1\right)}{(2 x+5)}

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Problem 13787

difference of radical expressions:...
Simplify. 50x+8x\sqrt{50 x}+\sqrt{8 x}
Assume that the variable represents a positive real number. \square

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Problem 13788

Simplify. 48×327\sqrt{48} \times 3 \sqrt{27}

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Problem 13789

An iterative formula is shown below. xn+1=8xn5x_{n+1}=\sqrt{8 x_{n}-5}
Starting with x1=3x_{1}=3, calculate the values of x2,x3x_{2}, x_{3} and x4x_{4}. Give your answers to 3 d.p.

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Problem 13790

3(2x4)+1>2(2y3)83(2 x-4)+1>2(2 y-3)-8

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Problem 13791

Determine whether the function is one-to-one. f(x)=x+4f(x)=|x+4|
Is the function one-to-one? Yes No

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Problem 13792

Find a formula for f1(x)f^{-1}(x). Identify the domain and range of f1f^{-1}. Verify that ff and f1f^{-1} are inverses. f(x)=x+5,x5f(x)=\sqrt{x+5}, x \geq-5 f1(x)=f^{-1}(x)= \square (Simplify your answer.)

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Problem 13793

Simplify. 220×182 \sqrt{20} \times \sqrt{18}

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Problem 13794

Simplify. 27×412\sqrt{27} \times 4 \sqrt{12}

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Problem 13795

Part 2 of 4
Use f(x)f(x) to complete the table for f1(x)f^{-1}(x). f(x)=x+6f(x)=x+6
What is f1(2)?8f^{-1}(-2) ?-8 What is f1(1)f^{-1}(1) ?

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Problem 13796

Multiply and simplify completely: (4x3)(4x5)(4 x-3)(4 x-5)

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Problem 13797

Multiply and add like terms: (4w+5)(4w5)(4 w+5)(4 w-5)

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Problem 13798

0t3S(3S22)ds\int_{0}^{t} 3 S\left(\frac{3 S^{2}}{2}\right) d s

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Problem 13799

36.logx=3\begin{array}{l}36 . \log x=-3\end{array}

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Problem 13800

(suite)
7 Trouve la valeur des expressions algébriques suivantes. a) (2x24x+3)÷3\left(2 x^{2}-4 x+3\right) \div 3, si x=9x=9 b) 8ab+11b308 a b+11 b-30, si a=2a=2 et b=3b=-3

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