Algebra

Problem 24501

A dog groomer has a budget of \$400 and needs at least 40 shampoo and body wash bottles. Shampoo is \$6 and body wash is \$7. Write the inequalities and give one solution.

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Problem 24502

Estimate the distance a car travels at 100km/h100 \mathrm{km/h} during your reaction time before braking. Remember to convert!

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Problem 24503

Calculate the total cost for a 2-week car rental at \$170/week plus \$1/mile for 500 miles. Round to the nearest dollar.

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Problem 24504

Solve the equations: 8x1=2x338^{x-1}=\sqrt[3]{2^{x-3}} and 35x+5x+1=8533 \cdot 5^{x}+5^{x+1}=8 \cdot 5^{3}.

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Problem 24505

Solve for uu in the equation: 1213u=212 - \frac{1}{3} u = 2.

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Problem 24506

Find the number that gives a quotient of 18 when divided by 6. Solve for xx in the equation x/6=18x / 6 = 18.

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Problem 24507

Simplify the expression: -6(r + 3g - t). A. 6r18g+6t-6r - 18g + 6t B. 6r+18g6t-6r + 18g - 6t C. 6r18g+6t6r - 18g + 6t D. 6r+18g6t6r + 18g - 6t

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Problem 24508

Solve for rr in the equation: 18=52r+12-18=\frac{5}{2} r+12.

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Problem 24509

Calculate the expression using the order of operations: 4(46)27(23)3=4(4-6)^{2}-7(2-3)^{3}=

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Problem 24510

Mary buys an annuity with monthly payments of \$9 at 3.8% interest, compounded monthly. Find its value in 10 years.

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Problem 24511

Expand and simplify y2(32y3)y^{2}(3 - 2y^{3}).

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Problem 24512

Solve for yy in the equation 40=5y840=5y-8.

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Problem 24513

Divide the equation 12(x+9)=78x\frac{1}{2}(x+9)=\frac{7}{8} x by 12\frac{1}{2}. What is the simplified new equation?

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Problem 24514

Solve for xx in the equation 38x+2=0-\frac{3}{8} x + 2 = 0.

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Problem 24515

Expand and simplify:
1. 3x(7x4)-3x(7x - 4)
2. 4x(3x2x2+5x3)4x(3x - 2x^2 + 5x^3)

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Problem 24516

Evaluate the expression 7x22x5-7 x^{2}-2 x-5 for x=2x=-2. What is the result?

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Problem 24517

Solve the inequality: 8(x5)3x208(x-5)-3x \geq -20. What is the solution set? A. x3x \geq -3 B. x12x \leq 12 C. x4x \geq 4 D. x12x \leq -12

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Problem 24518

Simplify the expression: 3x3[3(53x)]3 x - 3[3 - (5 - 3 x)]. What is the simplified form?

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Problem 24519

Rafael represents "a number, nn, decreased by thirty-one" and evaluates it for n=29n=29. Which statements are true?

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Problem 24520

Simplify the expression: 2x(5x+3)5(2x+3)2 x(5 x+3)-5(2 x+3).

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Problem 24521

Find the point-slope form of the line with slope =6=6 through (4,9)(-4,9) and convert it to slope-intercept form.

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Problem 24522

Find the point-slope and slope-intercept forms of the line through (2,0)(-2,0) and (0,6)(0,6).

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Problem 24523

Evaluate the expression x22-x^{2}-2 for x=6x=-6. What is the result?

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Problem 24524

Rewrite the function f(x)=x24x+3f(x)=x^{2}-4 x+3 in vertex form by completing the square.

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Problem 24525

Solve the equation p+3=p7|p+3|=|p-7|.

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Problem 24526

Determine the parent function of the absolute value function h(x)=4x+10h(x)=-4|x|+10.

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Problem 24527

Solve the equation: 4x=20-4x = 20. What is the value of xx?

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Problem 24528

Multiply 42/351/64^{2/3} \cdot 5^{1/6}.

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Problem 24529

Simplify (65x)-(-6-5 x).

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Problem 24530

Simplify the expression: 3(7+w)5w-3(7+w)-5 w.

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Problem 24531

Evaluate 5(1+1)3(51)=[?]5(1+1)-3(5-1)=[?]

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Problem 24532

Factor the expression 4x+84x + 8.

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Problem 24533

Evaluate n(3n)n(3-n) for n=11n=11. What is the result?

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Problem 24534

Evaluate when x=2x=2: 3x2+4(x+2x)+10=[?]3x^{2}+4(x+2x)+10=[?]

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Problem 24535

Evaluate m+2(m5)m + 2(m - 5) for m=25m = 25. What is the result?

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Problem 24536

Factor the equation 2x2+42x^{2}+4.

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Problem 24537

Is 0 a solution to 2x+10=4x+102x + 10 = 4x + 10? Justify your answer.

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Problem 24538

Calculate the state income tax for a \30,000salaryusingtherates:2%for$02000,5%for$20019000,and5.4%for$9001+.30,000 salary using the rates: 2\% for \$0-2000, 5\% for \$2001-9000, and 5.4\% for \$9001+. tax=$[?]\operatorname{tax}=\$[?]$ Round to the nearest dollar.

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Problem 24539

Calculate the state income tax on a \50,000salaryusingtheprogressiverates:2%for$02000,5%for$20019000,and5.4%for$9001+.Roundtothenearestdollar.50,000 salary using the progressive rates: 2\% for \$0-2000, 5\% for \$2001-9000, and 5.4\% for \$9001+. Round to the nearest dollar. tax=$[?]\operatorname{tax}=\$[?]$

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Problem 24540

Express the interval (,9)(0,)(-\infty,-9) \cup(0, \infty) using inequalities.

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Problem 24541

Solve the equation: 2(x1)=5x+16-2(x-1)=5x+16. Find x=[?]x=[?].

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Problem 24542

Solve the equation: 2x3=9x+42x - 3 = 9x + 4. Find x=[?]x = [?].

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Problem 24543

Solve the equation 7x+12(4x5)=32+2(x3)7x + \frac{1}{2}(4x - 5) = \frac{3}{2} + 2(x - 3) and simplify your answer.

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Problem 24544

Solve and simplify: 2(3x1)=5(x+3)2(3x - 1) = 5 - (x + 3); find x=x =.

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Problem 24545

Solve for nn in the equation np+r=q\frac{n}{p} + r = q.

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Problem 24546

Evaluate: (a) ln(1)=\ln (1)=

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Problem 24547

Solve for bb in the equation: ab+54=c\frac{a b + 5}{4} = c.

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Problem 24548

A bag of dog food costs \$32 and treats cost \$7. With \$74, how many bags of treats can you buy after buying 1 bag of food?

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Problem 24549

Solve for bb in the equation: ab+5t=c\frac{a b+5}{t}=c.

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Problem 24550

Check if 4 satisfies the inequality 12x33\frac{1}{2} x - 3 \leq -3.

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Problem 24551

Find (f+g)(x)(f+g)(x) for f(x)=4x3x10f(x)=\frac{4 x-3}{x-10} and g(x)=2x8x10g(x)=\frac{2 x-8}{x-10}.

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Problem 24552

Is 0 a solution to the inequality 4<w+46-4 < w + 4 \leq 6?

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Problem 24553

Find the graph of (fg)(x)(f-g)(x) where f(x)=1xf(x)=\frac{1}{x} and g(x)=xg(x)=\sqrt{x}.

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Problem 24554

Determine where the function f(x)=x+1x3xf(x)=\frac{x+1}{x^{3}-x} is undefined by finding the values of xx.

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Problem 24555

Find xx such that g(x)=4xg(x)=\sqrt{4-x} is defined.

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Problem 24556

Find constants aa and bb for function f(x)f(x) to be continuous everywhere, defined as: f(x)={a+bx,x>23,x=2bax2,x<2 f(x) = \begin{cases} a + b x, & x > 2 \\ 3, & x = 2 \\ b - a x^2, & x < 2 \end{cases}

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Problem 24557

Find an equation for the highest and lowest weights a helicopter can lift, given it averages 2,600 lbs with a 1,400 lb variance. w+1,400=2,600 |w+1,400|=2,600 w1,400=2,600|w-1,400|=2,600 w+2,600=1,400|w+2,600|=1,400 w2,600=1,400|w-2,600|=1,400

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Problem 24558

Express the inequality 4 ≤ x ≤ 9 in interval notation.

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Problem 24559

Solve for cc in the equation a(bc)=da(b-c)=d. Which expression for cc is correct?

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Problem 24560

Solve for qq in the equation s=4p+4qs = 4p + 4q.

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Problem 24561

A plumber charges \80plus$25perhour.Ifthebillis$160,whichequationrepresentsthis?<br/>1.80 plus \$25 per hour. If the bill is \$160, which equation represents this? <br />1. 80 h + 25 = 160<br/>2. <br />2. 80 + 25 h = 160<br/>3. <br />3. 80(h + 25) = 160<br/>4. <br />4. 25(h + 80) = 160$

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Problem 24562

Solve for CC in the equation: a(bc)=da(b - c) = d.

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Problem 24563

Which expression means "3 less than kk"? A. 3k3-k B. k3k-3 C. 3+k3+k D. k+3k+3

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Problem 24564

Write the interval (,0)(-\infty, 0) as an inequality.

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Problem 24565

Express the inequality x<6x < -6 or x>2x > -2 in interval notation.

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Problem 24566

Express the inequality x<6x<-6 or x>7x>7 in interval notation.

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Problem 24567

Which expression is the same as a+aa+a? A. a2a^{2} B. a+2a+2 C. aaa-a D. 2a2 a

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Problem 24568

Find when your service hours y=15+5x42y = 15 + 5 \cdot \frac{x-4}{2} equal your friend's y=10+2xy = 10 + 2 \cdot x.

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Problem 24569

Given points of a linear function ff: (3,10)(-3, -10), (3,2)(3, -2), (6,2)(6, 2). Find f(13)f(13). Choices: (A) 4 (B) 294\frac{29}{4} (C) 283\frac{28}{3}.

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Problem 24570

Find all expressions equivalent to 45×1145 \times 11:
1. (11×40)+(11×5)(11 \times 40)+(11 \times 5)
2. (11×50)(11×5)(11 \times 50)-(11 \times 5)
3. (45×10)+(45×1)(45 \times 10)+(45 \times 1)
4. (40×10)+(11+5)(40 \times 10)+(11+5)

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Problem 24571

Is it true or false that the distributive property can be used to rewrite a multiplication problem?

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Problem 24572

Isolate xx in the equation 24=7x+314y24=7 x+3-14 y. What are the possible expressions for xx?

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Problem 24573

Find the domain and range of the function, where range is 0y300 \leq y \leq 30. Explain what they represent.

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Problem 24574

Find the cost of a car wash when 1.4(s+8)=4.2s+61.4(s+8) = 4.2s + 6. Round to the nearest dollar. Options: \$2, \$10, \$14, \$19.

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Problem 24575

Rewrite 15×3915 \times 39 using one of these forms: (15×3)+(15×9)(15 \times 3)+(15 \times 9), (39×15)+(9×15)(39 \times 15)+(9 \times 15), (15×30)(15×9)(15 \times 30)-(15 \times 9), or (15×40)(15×1)(15 \times 40)-(15 \times 1).

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Problem 24576

Find when the ball hits the ground and when it passes the building using S(t)=192+64t16t2S(t)=192+64t-16t^2.

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Problem 24577

Simplify: 7X3+6X3+2Y3Y22X2+x+2Y33Y27 X^{3}+6 X^{3}+2 Y^{3}-Y^{2}-2 X^{2}+x+2 Y^{3}-3 Y^{2}.

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Problem 24578

Find the zeros of the function f(x)=8x2+4x1f(x)=8x^{2}+4x-1 using the quadratic formula. What are the xx-intercepts?

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Problem 24579

Describe how the graph of f(x)=x2f(x) = x^2 transforms to become g(x)=(x2)2+3g(x) = (x-2)^2 + 3.

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Problem 24580

Find the value of bb for the continuous function f(x)={x2+bx,x55sin(π2x),x>5f(x)=\left\{\begin{array}{l}x^{2}+b x, x \leq 5 \\ 5 \sin \left(\frac{\pi}{2} x\right), x>5\end{array}\right..

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Problem 24581

Is yy a function of xx in the relation x=y3x=y^{3}?

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Problem 24582

Calculate f(2)f(-2) for the function f(x)=3x22x+1f(x)=3x^{2}-2x+1.

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Problem 24583

Is y=1xy=\sqrt{1-x} a function of xx? Determine if it meets the function criteria.

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Problem 24584

Sketch the graph of f(x)=2(x+3)21f(x)=2(x+3)^{2}-1. Find the axis of symmetry, domain, and range in interval notation.

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Problem 24585

Simplify the expression: 34(8x22x)43(6x312x21x2)\frac{3}{4}(8 x^{2}-2 x)-\frac{4}{3}(6 x^{3}-12 x-21 x^{2}).

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Problem 24586

Find the real zeros of the function f(x)=x2+8x+14f(x)=x^{2}+8x+14 using the quadratic formula. What are the xx-intercepts?

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Problem 24587

Solve the equation x22x+10=0x^{2}-2x+10=0 using the quadratic formula. Provide the solution set in simplified form.

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Problem 24588

Simplify the expression: (243y10)35(243 y^{10})^{\frac{3}{5}}.

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Problem 24589

If 3+2i3+2 i is a root of z2+pz+q=0z^{2}+p z+q=0, find the values of pp and qq where p,qRp, q \in \mathbb{R}.

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Problem 24590

Given the function ff, the average rate of change from x=ax=a to x=a+1x=a+1 is 2a+12a+1. Which statement is true?

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Problem 24591

Calculate the depth of a well if a bucket falls for 9.3 seconds. Round to the nearest tenth. Use d=12gt2d = \frac{1}{2}gt^2.

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Problem 24592

Calculate f(1)f(-1) for the function defined by f(x)=8x27x+3f(x)=8x^{2}-7x+3.

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Problem 24593

Determine the domain of the function x+5x+3\frac{x+5}{x+3} and express it in interval notation.

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Problem 24594

Find the intercepts of the line given by y=9x14y=-9x-14. No rounding needed. xx-intercept: yy-intercept:

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Problem 24595

Find the value of the function f(0)=8(0)27(0)+3f(0)=8(0)^{2}-7(0)+3.

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Problem 24596

Identify which points satisfy the inequalities: y>3x+3y > -3x + 3 and y>x+2y > x + 2. Check (2,5)(2,-5), (2,5)(-2,5), (2,5)(2,5), (2,5)(-2,-5).

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Problem 24597

Factor the polynomial 10x3y32x2y4+6xy410x^{3}y^{3}-2x^{2}y^{4}+6xy^{4}.

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Problem 24598

Factor the cubic polynomial 4x38x2x+24x^{3}-8x^{2}-x+2.

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Problem 24599

Factor the polynomial 4x38x2x24x^{3}-8x^{2}-x-2.

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Problem 24600

Find the number of solutions for the equation x=x9x = x - 9. A. 2 B. 1 C. 0 D. Infinitely many

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