Algebra

Problem 28601

Find and simplify $f(3x)$ for $f(x) = x^2 - 11$ . What is $f(3x) = \square$ ?

See Solution

Problem 28602

Simplify $f(3+h)-f(3)$ for $f(x)=x^{2}-12$ .

See Solution

Problem 28603

Find and simplify for $f(x)=7x-2$ : (A) $f(x+h)$ , (B) $f(x+h)-f(x)$ , (C) $\frac{f(x+h)-f(x)}{h}$ .

See Solution

Problem 28604

Find the function with domain $\{-5,-3,0,3,11\}$ and range $\{-4,0,2\}$ from the given sets of pairs.

See Solution

Problem 28605

Let the price of a carton of juice be $j$ , a fruit cup be $f$ , and a bowl of soup be $s$ . Given:
1. $9j = 5f$
2. $f = w + 0.50$
3. $s = j + 0.50$
Find the prices $j$ , $f$ , and $s$ .

See Solution

Problem 28606

Count the terms in the expression: $4(x) + 4(3)$ .

See Solution

Problem 28607

East's score was $\frac{2}{3}$ of West's in the first meet. In the second meet, East scored 7 more and West scored 7 less, with West's score being 3 less than East's. Find the scores for both teams in each meet.

See Solution

Problem 28608

Solve the system: $x^{2}+2=y$ and $y=-3x^{2}+1$ .

See Solution

Problem 28609

Find a function $f(x)$ that passes through the points (0,-2), (1,0), and (-1,0). Options are: $f(x)=-2x-2$ , $f(x)=2x-2$ , $f(x)=2\sqrt{x}-2$ .

See Solution

Problem 28610

Find the total charge $C$ for a car rental with insurance, given $C = S + I$ where $S = 18.95 + 0.60M$ and $I = 5.80 + 0.15M$ .

See Solution

Problem 28611

Find $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$ for $f(x)=3x^2-7x+6$ .

See Solution

Problem 28612

Find the meaning of $f(6)=113$ for the function $f(x)=-x^{3}+8 x^{2}+6 x+5$ .

See Solution

Problem 28613

What does $f(6)=113$ mean for the function $f(x)=-x^{3}+8 x^{2}+6 x+5$ ?

See Solution

Problem 28614

If $\frac{x}{3y} = 3$ , find the value of $\frac{y}{x}$ .

See Solution

Problem 28615

A block of mass $m=36 \mathrm{~kg}$ has forces $F_{1}=12 \mathrm{~N}$ (left) and $F_{2}=19 \mathrm{~N}$ at $\theta=11^{\circ}$ . Find $F_{\text{netx}}$ and $a_{\mathrm{x}}$ .

See Solution

Problem 28616

Find the revenue function for the price-demand $p(x)=85-3x$ where $1 \leq x \leq 20$ . What is $R(x)$ ?

See Solution

Problem 28617

Create an absolute value equation with solutions $x=8$ and $x=18$ .

See Solution

Problem 28618

Solve the equation $|4n - 15| = |n|$ .

See Solution

Problem 28619

Solve the inequality $\frac{3}{x-4}>0$ . What are the valid ranges for $x$ ?

See Solution

Problem 28620

Solve the inequality $\frac{x+2}{x-4}<0$ and find the valid intervals for $x$ .

See Solution

Problem 28621

Find the revenue function $R(x)=85x-3x^{2}$ and its domain from options A. $[1,20]$ , B. $[0,592]$ , C. $[0,85]$ , D. $[0,20]$ .

See Solution

Problem 28622

Find $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$ for $f(x)=3x-5$ . What is $f(x+h)$ ?

See Solution

Problem 28623

Find the profit function $P(x)$ using the revenue $R(x)=80x-3x^2$ and cost $C(x)=120+15x$ for $1 \leq x \leq 20$ .

See Solution

Problem 28624

Given revenue $R(x)=80x-3x^2$ and cost $C(x)=120+15x$ , find the profit function and its domain. A. $[1,20]$ B. $[0,80]$ C. $[0,228]$ D. $[0,20]$

See Solution

Problem 28625

Find the expected aptitude test score for a 16-year-old using the formula: Aptitude = 109.7 - 1.10 * Age. Round to the nearest whole number.

See Solution

Problem 28626

Solve the equation: $-3 x^{2}-2 x+1=x^{2}-2 x-3$ .

See Solution

Problem 28627

What percent of peanuts is in a mixture of $9 \mathrm{lbs}$ (55% peanuts) and $6 \mathrm{lbs}$ (40% peanuts)?

See Solution

Problem 28628

Solve the equation $P=R-C$ for $C$ .

See Solution

Problem 28629

Solve for $x$ in the equation: $x=(8.4 \times 10^{3} M^{-2} \cdot s^{-1})(0.36 M)^{3}$ . Include units.

See Solution

Problem 28630

Which graph represents the solution for $\frac{x^{2}+9 x-22}{x+4} \geq 0$ ?

See Solution

Problem 28631

Solve the equation $4 x^{2}-2 x+1=2 x^{2}-5 x+3$ .

See Solution

Problem 28632

Solve the inequality: $6x + 1 \geq 2x - 3(6x - 5)$ . Express the solution in interval notation.

See Solution

Problem 28633

Calculate $x$ using the formula $x=\left(8.4 \times 10^{3} M^{-2} \cdot \mathrm{s}^{-1}\right)(0.36 M)^{3}$ .

See Solution

Problem 28634

What does a duck do when flying upside down? Solve these to find the answer:
1. If $I+5=6$ , then $I=?$
2. If $2U=S$ , then $S=?$
3. If $2C=12$ , then $C=?$
4. If $Q+2=7-T$ , then $Q=?$
5. If $5-A=0$ , then $A=?$
6. If $3Q=P$ , then $P=?$
7. If $2T+2=6$ , then $T=?$
8. If $K-A+T=C-2$ , then $K=?$
9. If $U-3=T-1$ , then $U=?$
Riddle Answer: (substitute numbers for letters)

See Solution

Problem 28635

Find $f(-3)$ for the piecewise function $f(x)=\begin{cases}8 x+1 & \text{if } x<3 \\ 3 x & \text{if } 3 \leq x \leq 5 \\ 3-3 x & \text{if } x>5\end{cases}$ .

See Solution

Problem 28636

Frank can type a report in 7 hours, James in 6 hours. How long for both together?

See Solution

Problem 28637

Solve the inequality: $7(x+3) \leq 0$ .

See Solution

Problem 28638

Solve and graph the inequalities: $x+y > -8$ , $x-y < 3$ , $y < 3$ .

See Solution

Problem 28639

Solve |3k - 2| = 2|k + 2|.

See Solution

Problem 28640

Two hoses fill a pool: one at $x$ g/min, the other at $x-15$ g/min. Solve the inequality $\frac{1}{x}+\frac{1}{x-15} \geq \frac{1}{10}$ for viable rates. Which intervals work?

See Solution

Problem 28641

A flight averages 460 mph and the return flight 500 mph. Total time is 4 hours 48 minutes. Find the duration of each flight.

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Problem 28642

Solve the system: 2x + 3y = 2 and 4x + 6y = 4.

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Problem 28643

A mother invests \$9,000, with part in a CD at 4% and the rest in a bond at 7%. Total interest after 1 year is \$540. Find the CD investment.

See Solution

Problem 28644

Solve for $t$ in the equation: $\frac{2}{5} = \frac{2t}{3} + 3$ .

See Solution

Problem 28645

Two hoses fill a pool: one at $x$ gallons/min, the other at $x-15$ . Find intervals for combined rate $\frac{1}{x}+\frac{1}{x-15} \geq \frac{1}{10}$ . Options: $(0,5] \cup(15,30]$ ; $(0,5] \cup(15,30]$ ; $(-\infty, 0) \cup[5,15) \cup[30, \infty)$ ; $(-\infty, 0) \cup[5,15) \cup[30, \infty)$ .

See Solution

Problem 28646

In 2003, card usage was $41\%$ and is projected to be $61\%$ in 2011.
(a) Find a linear function $P(x)$ for percentage over years. (b) Estimate when percentage was between $46\%$ and $56\%$ .

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Problem 28647

In 2003, card use was $37\%$ of purchases, projected to be $57\%$ in 2011.
(a) Find a linear function $P(x)$ for year $x$ . (b) Estimate when $P(x)$ was between $42\%$ and $52\%$ .

See Solution

Problem 28648

Bill wants to save for a café by depositing monthly into an annuity at $3.6\%$ interest. How much to deposit monthly for \$25,000 in 9 years? Round to the nearest cent.

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Problem 28649

Find the minutes where Plan A ( $29 + 0.09m$ ) equals Plan B ( $0.14m$ ) and the cost at that point.

See Solution

Problem 28650

A small business had \$16,500 this year, which is 34% less than last year. What was last year's revenue?

See Solution

Problem 28651

A house increased by $29\%$ to a current value of \$129,000. What was its original purchase value?

See Solution

Problem 28652

Write a function for the arithmetic sequence of Kaia's savings: $\$ 525$ , $\$ 580$ , $\$ 635$ , $\$ 690$ .

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Problem 28653

Find the domain and $(f+g)(x)$ for $f(x)=\sqrt{2 x}$ and $g(x)=3 x-2$ . Simplify your answer.

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Problem 28654

Evaluate the function $f(x)=\frac{3 x+8}{5 x-3}$ for: (a) $f(0)$ , (b) $f(1)$ , (c) $f(-1)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(7 x)$ , (h) $f(x+h)$ .

See Solution

Problem 28655

Given functions $f(x)=\sqrt{2x}$ and $g(x)=3x-2$ , find $(f+g)(x)$ and its domain.

See Solution

Problem 28656

Solve the inequality: $2|x+4|+8 \geq 18$ .

See Solution

Problem 28657

Solve the inequality: $5|x-7|+8 \leq 43$ .

See Solution

Problem 28658

Solve the equation $|m+3|=7$ .

See Solution

Problem 28659

Solve the inequality $3|x+9|-5 \leq 10$ .

See Solution

Problem 28660

Solve the inequality $5|x+6|-2 \geq 28$ .

See Solution

Problem 28661

Solve the equation |3k - 2| = 2|k + 2|.

See Solution

Problem 28662

Rewrite $4 x + 7 y = 28$ in slope-intercept form, find the slope, $y$ -intercept, and graph the line.

See Solution

Problem 28663

Solve the inequality $2|x-7|-4<14$ .

See Solution

Problem 28664

Solve the inequality: $-|3 + 3x| - 7 > -16$ .

See Solution

Problem 28665

Find the value of $k$ for a line with slope $-\frac{2}{3}$ passing through points A(2-k, 5) and B(-2k, -1).

See Solution

Problem 28666

Solve the inequality: $-2|1+2x|-4>-18$ .

See Solution

Problem 28667

Find the value of $k$ for a line with slope $-\frac{2}{3}$ that passes through points A(2-k, 5) and B(-2k, -1).

See Solution

Problem 28668

Find the standard form equation of the line through points $(8,3)$ and $(-4,7)$ .

See Solution

Problem 28669

Find the value not in the range of $f(g(x))$ where $f(x)=5-2x$ and $g(x)=\frac{x^{2}}{4}$ .

See Solution

Problem 28670

Solve $|4n - 15| = |n|$ .

See Solution

Problem 28671

Rewrite the term $a^{\frac{2}{8}}$ as a radical without reducing it.

See Solution

Problem 28672

Twenty times a number plus six equals 366. Write the equation and solve for $x$ .
Equation: $20x + 6 = 366$ Number: $x = 18$

See Solution

Problem 28673

Find the secret value, $k$ , of a 4-digit pin code $abcd$ : $k = \frac{c - 3b}{\frac{1}{2}(a + d)}$ . What is $k$ ?

See Solution

Problem 28674

Calculate: $1 \sqrt{28} + 4 \sqrt{150} - 1 \sqrt{63} - 4 \sqrt{6}$ .

See Solution

Problem 28675

Find $x - 3y$ for $x = 3$ and $y = -2$ .

See Solution

Problem 28676

A library has 474 books, with twice as many new books as old. How many new books are there?

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Problem 28677

Define a linear equation for the cost $(C)$ of Rhythym Nation based on minutes $(m)$ used: $C = 6 + 0.04m$ . If $C = 28.50$ , find $m$ .

See Solution

Problem 28678

Calculate (a) $f(g(0))$ and (b) $g(f(0))$ for $f(x)=2x+9$ and $g(x)=6-x^2$ .

See Solution

Problem 28679

Express $h(x)=\frac{1}{x-5}$ as $f \circ g$ with $g(x)=(x-5)$ . Find $f(x)$ . Your answer is $f(x)=$

See Solution

Problem 28680

Find the domain of the composite function $f(g(x))$ where $f(x)=\sqrt{42-x}$ and $g(x)=x^{2}-x$ .

See Solution

Problem 28681

Define a linear equation for monthly cost $C$ based on minutes $m$ for Rhythym Nation's plan. If $C = 28.50$ , find $m$ .

See Solution

Problem 28682

Multiply and simplify: $(4 \sqrt{5}+2)(\sqrt{35}+4)=$

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Problem 28683

Solve for $y$ in the equation $y + 45 = \frac{5}{2} x + 20$ . What is $y$ ?

See Solution

Problem 28684

Find the rectangle's width and length, where length is 10 less than twice the width and perimeter is 166 yards.

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Problem 28685

Find the point-slope form of the line that fits the points: (-16, -18), (-8, -14), (0, -10), (8, -6), (16, -2).

See Solution

Problem 28686

Solve for $p$ using the square root property: $(p-5)^{2}=2$ . Enter your answers as a list separated by commas.

See Solution

Problem 28687

Calculate: $3(5-9)^{2}-2(3-5)^{3}=$

See Solution

Problem 28688

Rationalize the denominator of the expression: $\frac{55}{12 \sqrt{11}}$ .

See Solution

Problem 28689

Estimate the day when a pond, holding 400 water lilies, will be full if the number doubles every 7 days.

See Solution

Problem 28690

Use the quadratic formula to find the solutions of $12 x^{2}+3 x-15=0$ . List them, separated by commas. $x=$

See Solution

Problem 28691

Write the point-slope equation for the point (-3, 1) with a slope of 2.

See Solution

Problem 28692

Solve $k^{2}-10 k-15=-8$ by completing the square. Find the value to add, the equation $(k-a)^{2}=b$ , and solutions.

See Solution

Problem 28693

Write the point-slope form of a line with slope 4 that goes through the point $(-9,2)$ .

See Solution

Problem 28694

Write the point-slope form of the line with slope $\frac{1}{5}$ that goes through the point $(-3,-7)$ .

See Solution

Problem 28695

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

See Solution

Problem 28696

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

See Solution

Problem 28697

Find $(f \cdot g)(x)$ for $f(x)=2x+3$ and $g(x)=3x^2+5x$ . Simplify the expression.

See Solution

Problem 28698

Find the function $\left(\frac{f}{g}\right)(x)$ where $f(x)=x^{2}-3x+2$ and $g(x)=x-2$ . What is the domain?

See Solution

Problem 28699

Calculate $f(g(12))$ and $g(f(12))$ for $f(x)=14x+2$ and $g(x)=\sqrt{x-7}$ .

See Solution

Problem 28700

Clare bought 4 rosebushes for \$96, each \$12 less than full price. Find the full price of each rosebush.

See Solution

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Algebra

Problem 28601

Find and simplify f(3x)f(3x)f(3x) for f(x)=x2−11f(x) = x^2 - 11f(x)=x2−11. What is f(3x)=□f(3x) = \squaref(3x)=□?

Problem 28602

Simplify f(3+h)−f(3)f(3+h)-f(3)f(3+h)−f(3) for f(x)=x2−12f(x)=x^{2}-12f(x)=x2−12.

Problem 28603

Find and simplify for f(x)=7x−2f(x)=7x-2f(x)=7x−2: (A) f(x+h)f(x+h)f(x+h), (B) f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x), (C) f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​.

Problem 28604

Find the function with domain {−5,−3,0,3,11}\{-5,-3,0,3,11\}{−5,−3,0,3,11} and range {−4,0,2}\{-4,0,2\}{−4,0,2} from the given sets of pairs.

Problem 28605

Let the price of a carton of juice be jjj, a fruit cup be fff, and a bowl of soup be sss. Given: 1. 9j=5f9j = 5f9j=5f2. f=w+0.50f = w + 0.50f=w+0.503. s=j+0.50s = j + 0.50s=j+0.50Find the prices jjj, fff, and sss.

Problem 28606

Count the terms in the expression: 4(x)+4(3)4(x) + 4(3)4(x)+4(3).

Problem 28607

East's score was 23\frac{2}{3}32​ of West's in the first meet. In the second meet, East scored 7 more and West scored 7 less, with West's score being 3 less than East's. Find the scores for both teams in each meet.

Problem 28608

Solve the system: x2+2=yx^{2}+2=yx2+2=y and y=−3x2+1y=-3x^{2}+1y=−3x2+1.

Problem 28609

Find a function f(x)f(x)f(x) that passes through the points (0,-2), (1,0), and (-1,0). Options are: f(x)=−2x−2f(x)=-2x-2f(x)=−2x−2, f(x)=2x−2f(x)=2x-2f(x)=2x−2, f(x)=2x−2f(x)=2\sqrt{x}-2f(x)=2x​−2.

Problem 28610

Find the total charge CCC for a car rental with insurance, given C=S+IC = S + IC=S+I where S=18.95+0.60MS = 18.95 + 0.60MS=18.95+0.60M and I=5.80+0.15MI = 5.80 + 0.15MI=5.80+0.15M.

Problem 28611

Find f(x+h)f(x+h)f(x+h), f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x), and f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=3x2−7x+6f(x)=3x^2-7x+6f(x)=3x2−7x+6.

Problem 28612

Find the meaning of f(6)=113f(6)=113f(6)=113 for the function f(x)=−x3+8x2+6x+5f(x)=-x^{3}+8 x^{2}+6 x+5f(x)=−x3+8x2+6x+5.

Problem 28613

What does f(6)=113f(6)=113f(6)=113 mean for the function f(x)=−x3+8x2+6x+5f(x)=-x^{3}+8 x^{2}+6 x+5f(x)=−x3+8x2+6x+5?

Problem 28614

If x3y=3\frac{x}{3y} = 33yx​=3, find the value of yx\frac{y}{x}xy​.

Problem 28615

A block of mass m=36 kgm=36 \mathrm{~kg}m=36 kg has forces F1=12 NF_{1}=12 \mathrm{~N}F1​=12 N (left) and F2=19 NF_{2}=19 \mathrm{~N}F2​=19 N at θ=11∘\theta=11^{\circ}θ=11∘. Find FnetxF_{\text{netx}}Fnetx​ and axa_{\mathrm{x}}ax​.

Problem 28616

Find the revenue function for the price-demand p(x)=85−3xp(x)=85-3xp(x)=85−3x where 1≤x≤201 \leq x \leq 201≤x≤20. What is R(x)R(x)R(x)?

Problem 28617

Create an absolute value equation with solutions x=8x=8x=8 and x=18x=18x=18.

Problem 28618

Solve the equation ∣4n−15∣=∣n∣|4n - 15| = |n|∣4n−15∣=∣n∣.

Problem 28619

Solve the inequality 3x−4>0\frac{3}{x-4}>0x−43​>0. What are the valid ranges for xxx?

Problem 28620

Solve the inequality x+2x−4<0\frac{x+2}{x-4}<0x−4x+2​<0 and find the valid intervals for xxx.

Problem 28621

Find the revenue function R(x)=85x−3x2R(x)=85x-3x^{2}R(x)=85x−3x2 and its domain from options A. [1,20][1,20][1,20], B. [0,592][0,592][0,592], C. [0,85][0,85][0,85], D. [0,20][0,20][0,20].

Problem 28622

Find f(x+h)f(x+h)f(x+h), f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x), and f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=3x−5f(x)=3x-5f(x)=3x−5. What is f(x+h)f(x+h)f(x+h)?

Problem 28623

Find the profit function P(x)P(x)P(x) using the revenue R(x)=80x−3x2R(x)=80x-3x^2R(x)=80x−3x2 and cost C(x)=120+15xC(x)=120+15xC(x)=120+15x for 1≤x≤201 \leq x \leq 201≤x≤20.

Problem 28624

Given revenue R(x)=80x−3x2R(x)=80x-3x^2R(x)=80x−3x2 and cost C(x)=120+15xC(x)=120+15xC(x)=120+15x, find the profit function and its domain. A. [1,20][1,20][1,20] B. [0,80][0,80][0,80] C. [0,228][0,228][0,228] D. [0,20][0,20][0,20]

Problem 28625

Find the expected aptitude test score for a 16-year-old using the formula: Aptitude = 109.7 - 1.10 * Age. Round to the nearest whole number.

Problem 28626

Solve the equation: −3x2−2x+1=x2−2x−3-3 x^{2}-2 x+1=x^{2}-2 x-3−3x2−2x+1=x2−2x−3.

Problem 28627

What percent of peanuts is in a mixture of 9lbs9 \mathrm{lbs}9lbs (55% peanuts) and 6lbs6 \mathrm{lbs}6lbs (40% peanuts)?

Problem 28628

Solve the equation P=R−CP=R-CP=R−C for CCC.

Problem 28629

Solve for xxx in the equation: x=(8.4×103M−2⋅s−1)(0.36M)3x=(8.4 \times 10^{3} M^{-2} \cdot s^{-1})(0.36 M)^{3}x=(8.4×103M−2⋅s−1)(0.36M)3. Include units.

Problem 28630

Which graph represents the solution for x2+9x−22x+4≥0\frac{x^{2}+9 x-22}{x+4} \geq 0x+4x2+9x−22​≥0?

Problem 28631

Solve the equation 4x2−2x+1=2x2−5x+34 x^{2}-2 x+1=2 x^{2}-5 x+34x2−2x+1=2x2−5x+3.

Problem 28632

Solve the inequality: 6x+1≥2x−3(6x−5)6x + 1 \geq 2x - 3(6x - 5)6x+1≥2x−3(6x−5). Express the solution in interval notation.

Problem 28633

Calculate xxx using the formula x=(8.4×103M−2⋅s−1)(0.36M)3x=\left(8.4 \times 10^{3} M^{-2} \cdot \mathrm{s}^{-1}\right)(0.36 M)^{3}x=(8.4×103M−2⋅s−1)(0.36M)3.

Problem 28634

Problem 28635

Find f(−3)f(-3)f(−3) for the piecewise function f(x)={8x+1if x<33xif 3≤x≤53−3xif x>5f(x)=\begin{cases}8 x+1 & \text{if } x<3 \\ 3 x & \text{if } 3 \leq x \leq 5 \\ 3-3 x & \text{if } x>5\end{cases}f(x)=⎩⎨⎧​8x+13x3−3x​if x<3if 3≤x≤5if x>5​.

Problem 28636

Frank can type a report in 7 hours, James in 6 hours. How long for both together?

Problem 28637

Solve the inequality: 7(x+3)≤07(x+3) \leq 07(x+3)≤0.

Problem 28638

Solve and graph the inequalities: x+y>−8x+y > -8x+y>−8, x−y<3x-y < 3x−y<3, y<3y < 3y<3.

Problem 28639

Solve |3k - 2| = 2|k + 2|.

Problem 28640

Two hoses fill a pool: one at xxx g/min, the other at x−15x-15x−15 g/min. Solve the inequality 1x+1x−15≥110\frac{1}{x}+\frac{1}{x-15} \geq \frac{1}{10}x1​+x−151​≥101​ for viable rates. Which intervals work?

Find and simplify $f(3x)$ for $f(x) = x^2 - 11$ . What is $f(3x) = \square$ ?

Simplify $f(3+h)-f(3)$ for $f(x)=x^{2}-12$ .

Find and simplify for $f(x)=7x-2$ : (A) $f(x+h)$ , (B) $f(x+h)-f(x)$ , (C) $\frac{f(x+h)-f(x)}{h}$ .

Find the function with domain $\{-5,-3,0,3,11\}$ and range $\{-4,0,2\}$ from the given sets of pairs.

Let the price of a carton of juice be $j$ , a fruit cup be $f$ , and a bowl of soup be $s$ . Given:
1. $9j = 5f$
2. $f = w + 0.50$
3. $s = j + 0.50$
Find the prices $j$ , $f$ , and $s$ .

Count the terms in the expression: $4(x) + 4(3)$ .

East's score was $\frac{2}{3}$ of West's in the first meet. In the second meet, East scored 7 more and West scored 7 less, with West's score being 3 less than East's. Find the scores for both teams in each meet.

Solve the system: $x^{2}+2=y$ and $y=-3x^{2}+1$ .

Find a function $f(x)$ that passes through the points (0,-2), (1,0), and (-1,0). Options are: $f(x)=-2x-2$ , $f(x)=2x-2$ , $f(x)=2\sqrt{x}-2$ .

Find the total charge $C$ for a car rental with insurance, given $C = S + I$ where $S = 18.95 + 0.60M$ and $I = 5.80 + 0.15M$ .

Find $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$ for $f(x)=3x^2-7x+6$ .

Find the meaning of $f(6)=113$ for the function $f(x)=-x^{3}+8 x^{2}+6 x+5$ .

What does $f(6)=113$ mean for the function $f(x)=-x^{3}+8 x^{2}+6 x+5$ ?

If $\frac{x}{3y} = 3$ , find the value of $\frac{y}{x}$ .

A block of mass $m=36 \mathrm{~kg}$ has forces $F_{1}=12 \mathrm{~N}$ (left) and $F_{2}=19 \mathrm{~N}$ at $\theta=11^{\circ}$ . Find $F_{\text{netx}}$ and $a_{\mathrm{x}}$ .

Find the revenue function for the price-demand $p(x)=85-3x$ where $1 \leq x \leq 20$ . What is $R(x)$ ?

Create an absolute value equation with solutions $x=8$ and $x=18$ .

Solve the equation $|4n - 15| = |n|$ .

Solve the inequality $\frac{3}{x-4}>0$ . What are the valid ranges for $x$ ?

Solve the inequality $\frac{x+2}{x-4}<0$ and find the valid intervals for $x$ .

Find the revenue function $R(x)=85x-3x^{2}$ and its domain from options A. $[1,20]$ , B. $[0,592]$ , C. $[0,85]$ , D. $[0,20]$ .

Find $f(x+h)$ , $f(x+h)-f(x)$ , and $\frac{f(x+h)-f(x)}{h}$ for $f(x)=3x-5$ . What is $f(x+h)$ ?

Find the profit function $P(x)$ using the revenue $R(x)=80x-3x^2$ and cost $C(x)=120+15x$ for $1 \leq x \leq 20$ .

Given revenue $R(x)=80x-3x^2$ and cost $C(x)=120+15x$ , find the profit function and its domain. A. $[1,20]$ B. $[0,80]$ C. $[0,228]$ D. $[0,20]$

Solve the equation: $-3 x^{2}-2 x+1=x^{2}-2 x-3$ .

What percent of peanuts is in a mixture of $9 \mathrm{lbs}$ (55% peanuts) and $6 \mathrm{lbs}$ (40% peanuts)?

Solve the equation $P=R-C$ for $C$ .

Solve for $x$ in the equation: $x=(8.4 \times 10^{3} M^{-2} \cdot s^{-1})(0.36 M)^{3}$ . Include units.

Which graph represents the solution for $\frac{x^{2}+9 x-22}{x+4} \geq 0$ ?

Solve the equation $4 x^{2}-2 x+1=2 x^{2}-5 x+3$ .

Solve the inequality: $6x + 1 \geq 2x - 3(6x - 5)$ . Express the solution in interval notation.

Calculate $x$ using the formula $x=\left(8.4 \times 10^{3} M^{-2} \cdot \mathrm{s}^{-1}\right)(0.36 M)^{3}$ .

Find $f(-3)$ for the piecewise function $f(x)=\begin{cases}8 x+1 & \text{if } x<3 \\ 3 x & \text{if } 3 \leq x \leq 5 \\ 3-3 x & \text{if } x>5\end{cases}$ .

Solve the inequality: $7(x+3) \leq 0$ .

Solve and graph the inequalities: $x+y > -8$ , $x-y < 3$ , $y < 3$ .

Two hoses fill a pool: one at $x$ g/min, the other at $x-15$ g/min. Solve the inequality $\frac{1}{x}+\frac{1}{x-15} \geq \frac{1}{10}$ for viable rates. Which intervals work?

Solve for $t$ in the equation: $\frac{2}{5} = \frac{2t}{3} + 3$ .

In 2003, card usage was $41\%$ and is projected to be $61\%$ in 2011.
(a) Find a linear function $P(x)$ for percentage over years. (b) Estimate when percentage was between $46\%$ and $56\%$ .

In 2003, card use was $37\%$ of purchases, projected to be $57\%$ in 2011.
(a) Find a linear function $P(x)$ for year $x$ . (b) Estimate when $P(x)$ was between $42\%$ and $52\%$ .

Bill wants to save for a café by depositing monthly into an annuity at $3.6\%$ interest. How much to deposit monthly for \$25,000 in 9 years? Round to the nearest cent.

Find the minutes where Plan A ( $29 + 0.09m$ ) equals Plan B ( $0.14m$ ) and the cost at that point.

A house increased by $29\%$ to a current value of \$129,000. What was its original purchase value?

Write a function for the arithmetic sequence of Kaia's savings: $\$ 525$ , $\$ 580$ , $\$ 635$ , $\$ 690$ .

Find the domain and $(f+g)(x)$ for $f(x)=\sqrt{2 x}$ and $g(x)=3 x-2$ . Simplify your answer.

Evaluate the function $f(x)=\frac{3 x+8}{5 x-3}$ for: (a) $f(0)$ , (b) $f(1)$ , (c) $f(-1)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(7 x)$ , (h) $f(x+h)$ .

Given functions $f(x)=\sqrt{2x}$ and $g(x)=3x-2$ , find $(f+g)(x)$ and its domain.

Solve the inequality: $2|x+4|+8 \geq 18$ .

Solve the inequality: $5|x-7|+8 \leq 43$ .

Solve the equation $|m+3|=7$ .

Solve the inequality $3|x+9|-5 \leq 10$ .

Solve the inequality $5|x+6|-2 \geq 28$ .

Rewrite $4 x + 7 y = 28$ in slope-intercept form, find the slope, $y$ -intercept, and graph the line.

Solve the inequality $2|x-7|-4<14$ .

Solve the inequality: $-|3 + 3x| - 7 > -16$ .

Find the value of $k$ for a line with slope $-\frac{2}{3}$ passing through points A(2-k, 5) and B(-2k, -1).

Solve the inequality: $-2|1+2x|-4>-18$ .

Find the value of $k$ for a line with slope $-\frac{2}{3}$ that passes through points A(2-k, 5) and B(-2k, -1).

Find the standard form equation of the line through points $(8,3)$ and $(-4,7)$ .

Find the value not in the range of $f(g(x))$ where $f(x)=5-2x$ and $g(x)=\frac{x^{2}}{4}$ .

Solve $|4n - 15| = |n|$ .

Rewrite the term $a^{\frac{2}{8}}$ as a radical without reducing it.

Twenty times a number plus six equals 366. Write the equation and solve for $x$ .
Equation: $20x + 6 = 366$ Number: $x = 18$

Find the secret value, $k$ , of a 4-digit pin code $abcd$ : $k = \frac{c - 3b}{\frac{1}{2}(a + d)}$ . What is $k$ ?

Calculate: $1 \sqrt{28} + 4 \sqrt{150} - 1 \sqrt{63} - 4 \sqrt{6}$ .