Algebra

Problem 28101

Evaluate $b - 2y$ for $b = -3$ and $y = 3$ .

See Solution

Problem 28102

A cell phone plan costs \ $21 monthly plus \$5 per GB of data. Write the equation for cost$ C $in terms of data$ d$. If the bill is \$52, how many GB did you use?
$C = 21 + 5d$

See Solution

Problem 28103

Use the distributive property: $(7 \times 3)-(7 \times 2)=7 \times$ __.

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Problem 28104

Let the number of ten dollar bills be $x$ . Then, the number of five dollar bills is $2x$ . Solve for $x$ given $5(2x) + 10(x) = 720$ . How many ten's are there?

See Solution

Problem 28105

Define a linear equation for the monthly cost $C$ of a cell phone plan based on data usage $d$ in GB, given $C = 21 + 5d$ .

See Solution

Problem 28106

Juan rented a truck for \$18.99 plus \$0.76 per mile. He paid \$111.71 total. How many miles did he drive?

See Solution

Problem 28107

Solve for $t$ using the square root property: $2 t^{2}-45=-19$ . Find $t=$ .

See Solution

Problem 28108

Complete the square for the equation $p^{2}+14 p-33=10$ . Write it as $(p-a)^{2}=b$ and find $p=$ .

See Solution

Problem 28109

A truck goes 441 miles at 63 mph. Use $d = r t$ to find the travel time in hours.

See Solution

Problem 28110

Solve the equation $4 m^{2}-3 m-2=0$ using the quadratic formula and list solutions in simplest radical form.

See Solution

Problem 28111

Determine the nature of roots for a quadratic equation based on the discriminant values: 0, 4, 2, and -2.

See Solution

Problem 28112

If 1585 plasma TVs are sold, how many flatscreen TVs were sold if the ratio is 3:5? Also, for 27,360 total seats sold, find general admission seats if the ratio is 4:5.

See Solution

Problem 28113

Solve: $\sqrt{-1 x+68}=x-12$ . Find $x=$ (Separate answers with commas; use integers or reduced fractions. If none, enter DNE.)

See Solution

Problem 28114

Solve for $x$ : $x^{3/5} = 8$

See Solution

Problem 28115

Solve $a^{2}=15 a-56$ . Find $a=$ . If multiple solutions, separate with a comma.

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Problem 28116

Solve the equation $3 r^{3}-12 r=-2 r^{2}+8$ for real values of $r$ . Provide answers as integers or simplified fractions, separated by commas.

See Solution

Problem 28117

Solve for $x$ : $12 < -14(x+3) < 15$ . Type DNE if no solution exists. Provide your answer in interval notation.

See Solution

Problem 28118

Find three consecutive even integers where the smallest plus twice the median equals 20 more than the largest: $x + 2(x + 2) = (x + 4) + 20$ .

See Solution

Problem 28119

Find the intersection point of the lines defined by $y=3x$ and $y=-4x-49$ .

See Solution

Problem 28120

Solve the inequality: -6 ≤ x + 12. Provide the solution in interval notation.

See Solution

Problem 28121

Solve the quadratic $p^{2}+14 p-33=10$ by completing the square. Give the equation as $(p-a)^{2}=b$ and list solutions.

See Solution

Problem 28122

Jasmine earned $\$ 25.20$ for 6 hours and $\$ 16.80$ for 4 hours. Find the function for her earnings $(c)$ based on hours $(h)$ .

See Solution

Problem 28123

Solve the equation $4 m^{2}-3 m-2=0$ using the quadratic formula. Provide solutions in simplest radical form.

See Solution

Problem 28124

Find $f(64)$ given the function $f(x)=9 \sqrt{x}$ . What is $f(64)=?$

See Solution

Problem 28125

In Amanda's class, the ratio of students with widow's peaks to those without is 3:2. With 35 students, how many lack widow's peaks? $\frac{3}{2} w p=35$

See Solution

Problem 28126

Find $f(10)$ for the function $f(x)=5x+x^{2}+10$ . What is $f(10)$ ?

See Solution

Problem 28127

Find $f(5.75)$ using the function $f(x)=\frac{5.98}{x}$ . Provide the answer as a decimal or whole number.

See Solution

Problem 28128

In a class of 32 students with a junior to senior ratio of 5:3, how many are seniors? (A) 3 (B) 8 (C) 9 (D) 1 (E) 20

See Solution

Problem 28129

Find $f(34.58)$ using the rule $f(x)=0.07 \sqrt{38.58-x}$ . What is $f(34.58)$ ?

See Solution

Problem 28130

The environmental club has 450 pounds of cans and collects 14 pounds weekly.
(i) Find the slope $m$ of the linear model. (ii) Find the starting value $b$ of the linear model. (iii) Predict pounds of cans by week 44. (iv) Predict weeks to reach 725 pounds.

See Solution

Problem 28131

Graph the solution set for the system of inequalities:
1. $x^{2}-y \leq 3x-2$
2. $y+\frac{1}{2}x+2>x+2y-1$

See Solution

Problem 28132

Find the product and simplify: $(x+8)^{2}$ .

See Solution

Problem 28133

Find the time $t$ for a block to slide down an incline with base $a=12$ and angle $\theta=45^{\circ}$ using $t=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}$ .

See Solution

Problem 28134

Simplify the expression: $\sqrt[3]{\left(x^{2} y^{3} z^{4}\right)^{2}}$

See Solution

Problem 28135

Find the sum of the infinite geometric series with $a_{n}=64\left(\frac{1}{4}\right)^{n-1}$ .

See Solution

Problem 28136

Solve the system: 3x + 5y = -7 and 14x - 9y = 32. Choose from (2,1), (-2,1), (1,-2), (1,2).

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Problem 28137

Simplify the expression: $-5 r(r+s)^2$

See Solution

Problem 28138

Simplify and factor $-5\left(x^{2}+\frac{6}{5} x+\frac{5}{2}\right)-40+15$ .

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Problem 28139

Complete the square and find the vertex of the function $s(x)=-5 x^{2}-30 x-40$ .

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Problem 28140

Find the domain of the function $f(x)=\sqrt[4]{17-x}$ .

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Problem 28141

A car on a $2.6^{\circ}$ incline faces $124 \mathrm{lb}$ resistance. Find the car's weight to the nearest hundred pounds.

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Problem 28142

Find the domain of the function $f(x)=\frac{1}{x-2}$ .

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Problem 28143

Find the domain of the function $g(x)=\frac{8 x}{x^{2}-9}$ .

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Problem 28144

Simplify the expression: $\sqrt[3]{8 y^{27}}$

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Problem 28145

Find the grade resistance in pounds for a 2000-pound car on a $2.4^{\circ}$ uphill grade using $F=W \sin \theta$ .

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Problem 28146

Pham can work 15 hours weekly. Maximize earnings: Bookstore at \$9/hr, Café at \$12/hr (6 hrs), Garage at \$10/hr (5 hrs), Daycare at \$8.50/hr. How many hours at the bookstore? (Whole number answer)

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Problem 28147

A. How many pounds of potatoes can Janice buy with \$ 5, considering their value? Use values \$ 1.50, \$ 1.14, \$ 1.05, \$ 0.30.

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Problem 28148

Find the constant of variation for the point $(12,9)$ in a direct variation. Options: $\frac{1}{2}$ , $\frac{3}{4}$ , 1, 2.

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Problem 28149

What is the opportunity cost of buying one stapler if staplers are \$10 and pens are \$2.50, with a \$100 budget?

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Problem 28150

A. 3 B. 2

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Problem 28151

Find the vertex of the quadratic function $3 x^{2}+10 x-3$ .

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Problem 28152

Graph the function defined as: $f(x) = -3 - x$ for $x \leq 1$ and $f(x) = -3 + 2x$ for $x > 1$ .

See Solution

Problem 28153

Find the vertex of the quadratic function $2x^{2} - 2x - 4$ .

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Problem 28154

You have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?
A: Budget increases to \$150, prices same. increase
B: Budget \$100, books \$25, tickets rise to \$20. decrease
C: Budget \$100, tickets \$10, books drop to \$15. increase

See Solution

Problem 28155

Find the equation of the axis of symmetry for the function $2x^{2} - 2x - 4$ .

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Problem 28156

An employee's Medicare tax is given by a piecewise function. Find $f(0)$ , $f(200)$ , and $f(400)$ for $f(x)$ .
$f(x)=\left\{\begin{array}{ll} 13.5 x & \text { if } 0 \leq x \leq 200 \\ 2700+26.5(x-200) & \text { if } x>200 \end{array}\right.$

See Solution

Problem 28157

Calculate the Medicare tax function values for $x = 0$ , $200$ , and $400$ using the piecewise function defined for 2022.

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Problem 28158

Realiza la operación de $5 x^{3} y(2 x+3 y-4)$ .

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Problem 28159

Postage rates changed from 2006 to 2016.
(a) Let $f(x)$ be the cost of a first-class stamp in year $x$ . Find $f(2010)$ and $f(2015)$ given $f(2010)=\$0.36$ and $f(2015)=\$0.66$ .
(b) Why isn’t the graph of $f$ accurate? What changes are needed for accuracy?

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Problem 28160

Find the cost to rent a trailer for 3.3, 4, and 8.6 hours, given the rate of \$20 for 2 hours and \$10 per additional hour.

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Problem 28161

Renting a trailer costs \$20 for 2 hours, then \$10 per extra hour. Find costs for 3.3, 4, and 8.6 hours.

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Problem 28162

Simplify the expression $(2 x + 3 y)^{2}$ .

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Problem 28163

Find $f(x)=2$ . Calculate $f(7)$ , $f(-7)$ , $f(1.6)$ , $f(-1.3)$ . What is $f(7)$ ? A. $f(7)=$ B. $f(7)$ is undefined.

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Problem 28164

Evaluate the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ at $f(7)$ . Is it defined or undefined?

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Problem 28165

Evaluate the function $f(x)=14 x^{2}+7 x$ at these points: (a) $f(5)$ , (b) $f(-9)$ , (c) $f(4.5)$ , (d) $f(-3.5)$ .

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Problem 28166

For the function $f(x)=\sqrt{14-x}$ , calculate $f(5)$ , $f(-4)$ , $f(11.1)$ , and $f(-3.7)$ .

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Problem 28167

Given the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ , find $f(7)$ and $f(-6)$ . Are they defined?

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Problem 28168

Evaluate the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ for $f(7)$ , $f(-6)$ , and $f(4.3)$ .

See Solution

Problem 28169

Simplify $3^{8} \div 3^{4}$ or $\frac{3^{8}}{3^{4}}$ .

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Problem 28170

Evaluate for $x=2$ and $y=7$ : a. $9 x^{2} y^{0}+1$ , b. $\left(\frac{x^{9}}{x^{3}}\right)-y^{2}$ .

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Problem 28171

Rewrite $\frac{7^{8} \div 7^{2}}{7^{3}}$ as a single exponent.

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Problem 28172

Calculate $2^{16} \div 2^{4}$ and fill in the blanks: $2^{16} \square_{4} = \square$ .

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Problem 28173

Rearrange $2000=1000\left(1+\frac{R}{100}\right)^{D}$ to find $D=\frac{\log (2)}{\log \left(1+\frac{R}{100}\right)}$ .

See Solution

Problem 28174

Simplify $12^{9} \div 12^{3}$ .

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Problem 28175

Solve for the missing value in the equation $-2(2x-\square)+1=17-4x$ that makes it an identity, has one solution, or no solution.

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Problem 28176

If two lines are perpendicular, what is the relationship between their slopes $m_1$ and $m_2$ ?

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Problem 28177

In the formula $y=m x+b$ , what sign do you expect for $m$ regarding car prices over the years? Explain.

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Problem 28178

Calculate $6^{8} \div 3^{4}$ .

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Problem 28179

A family bought a jet ski for \$7,500 with a 10% down payment. What are the monthly installments at 696 simple interest for 12 months? Options: \$578.50, \$586.75, \$596.25, \$601.00, None of these choices.

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Problem 28180

Identify the means in the proportion $\frac{3}{5}=\frac{18}{30}$ . Choices: 18 & 30, 3 & 5, 3 & 30, 5 & 18.

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Problem 28181

Solve the inequality: $-\frac{2}{7}(3-4 x)+8<18$ .

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Problem 28182

Is Mateo correct that $6^{8} \div 3^{4} = 6^{4}$ ? Explain using the Quotient of Powers Law.

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Problem 28183

Find the values of $x$ for which $x^{0}+\left(x^{6} \div x^{3}\right) > 9$ .

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Problem 28184

Solve the inequality: $\frac{2.6 x-4.8}{-2}+3.2 < -8.7$

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Problem 28185

Ramon claims that $\left(\frac{1}{12}\right)^{4} = \frac{1}{12^{4}}$ . Jamal disagrees, saying both parts need the power. Who is right?

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Problem 28186

Solve the inequality: $\frac{2}{7}(3-4 x)+8>18$ .

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Problem 28187

Solve these inequalities for 'x':
1) $\frac{2.6x - 4.8}{-2} + 3.2 < x$
2) $\frac{2}{7}(3 - 4x) + 8 > x$

See Solution

Problem 28188

Graph the function $g(x)=f(x)-1$ using the graph of $y=f(x)$ .

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Problem 28189

Solve the inequality: $-3x + 4 < 5$ .

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Problem 28190

Identify expressions less than 2 for $x=5$ . Choose all that apply:
1. $\frac{x^{0}}{4}$
2. $\frac{x^{1}}{7^{0}}$
3. $\left(\frac{50}{x^{2}}\right)^{0}$
4. $2\left(\frac{10}{x}\right)^{0}$
5. $\frac{x^{0}}{x^{2}}$

See Solution

Problem 28191

Identify the properties in these equations:
1. $9 \cdot(7 \cdot 6)=(9 \cdot 7) \cdot 6$
2. $9 \cdot(7 \cdot 6)=9 \cdot(6 \cdot 7$
Options: A. Identity, B. Commutative, C. Distributive, D. Associative, E. Zero property.

See Solution

Problem 28192

Add parentheses to make these equations true: a. $4+3 \cdot 2=14$ b. $6 \div 2+1=4$ c. $5+4+9 \div 2=9$ d. $5+6 \div 2+2=10$ Choose the correct answer.

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Problem 28193

Find the compositions of functions $f(x)=5x+4$ and $g(x)=\frac{x-4}{5}$ : a. $(f \circ g)(x)$ , b. $(g \circ f)(x)$ , c. $(f \circ g)(5)$ , d. $(g \circ f)(5)$ .

See Solution

Problem 28194

Simplify: (a) $\frac{\frac{1}{a}}{\frac{1}{b}}$

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Problem 28195

If the oil should be changed every 3500 miles, when will the first three oil changes happen if you start at 0 miles?

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Problem 28196

Let $p$ : This is a turtle; $q$ : This is a reptile. Write "Not a turtle if not a reptile" in symbols.

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Problem 28197

Define $f(x)=x+4$ , $g(x)=2x+1$ , $h(x)=2x^2+9x+4$ . Find the formulas for: a. $\frac{f+g}{h}$ b. $\frac{fg}{h}$ c. $ff$ d. $gg$ e. $ff - gg$ $f \cdot (f+g)(f-g)$

See Solution

Problem 28198

Find the fixed point of the function where $f(x)=-2x+3$ . Solve for $x$ such that $f(x)=x$ .

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Problem 28199

Find the fixed point of the function where $f(x)=\frac{1}{2} x-3$ and $f(x)=x$ . What is $x$ ?

See Solution

Problem 28200

Find the fixed point of the function where $f(x)=\frac{2}{3} x-\frac{1}{2}$ , i.e., solve $f(x)=x$ .

See Solution

1 ...279 280 281 282 283 284 285 ...313

Algebra

Problem 28101

Evaluate b−2yb - 2yb−2y for b=−3b = -3b=−3 and y=3y = 3y=3.

Problem 28102

Problem 28103

Use the distributive property: (7×3)−(7×2)=7×(7 \times 3)-(7 \times 2)=7 \times(7×3)−(7×2)=7× __.

Problem 28104

Let the number of ten dollar bills be xxx. Then, the number of five dollar bills is 2x2x2x. Solve for xxx given 5(2x)+10(x)=7205(2x) + 10(x) = 7205(2x)+10(x)=720. How many ten's are there?

Problem 28105

Define a linear equation for the monthly cost CCC of a cell phone plan based on data usage ddd in GB, given C=21+5dC = 21 + 5dC=21+5d.

Problem 28106

Juan rented a truck for \$18.99 plus \$0.76 per mile. He paid \$111.71 total. How many miles did he drive?

Problem 28107

Solve for ttt using the square root property: 2t2−45=−192 t^{2}-45=-192t2−45=−19. Find t=t=t=.

Problem 28108

Complete the square for the equation p2+14p−33=10p^{2}+14 p-33=10p2+14p−33=10. Write it as (p−a)2=b(p-a)^{2}=b(p−a)2=b and find p=p=p=.

Problem 28109

A truck goes 441 miles at 63 mph. Use d=rtd = r td=rt to find the travel time in hours.

Problem 28110

Solve the equation 4m2−3m−2=04 m^{2}-3 m-2=04m2−3m−2=0 using the quadratic formula and list solutions in simplest radical form.

Problem 28111

Determine the nature of roots for a quadratic equation based on the discriminant values: 0, 4, 2, and -2.

Problem 28112

If 1585 plasma TVs are sold, how many flatscreen TVs were sold if the ratio is 3:5? Also, for 27,360 total seats sold, find general admission seats if the ratio is 4:5.

Problem 28113

Solve: −1x+68=x−12\sqrt{-1 x+68}=x-12−1x+68​=x−12. Find x=x=x= (Separate answers with commas; use integers or reduced fractions. If none, enter DNE.)

Problem 28114

Solve for xxx: x3/5=8x^{3/5} = 8x3/5=8

Problem 28115

Solve a2=15a−56a^{2}=15 a-56a2=15a−56. Find a=a=a=. If multiple solutions, separate with a comma.

Problem 28116

Solve the equation 3r3−12r=−2r2+83 r^{3}-12 r=-2 r^{2}+83r3−12r=−2r2+8 for real values of rrr. Provide answers as integers or simplified fractions, separated by commas.

Problem 28117

Solve for xxx: 12<−14(x+3)<1512 < -14(x+3) < 1512<−14(x+3)<15. Type DNE if no solution exists. Provide your answer in interval notation.

Problem 28118

Find three consecutive even integers where the smallest plus twice the median equals 20 more than the largest: x+2(x+2)=(x+4)+20x + 2(x + 2) = (x + 4) + 20x+2(x+2)=(x+4)+20.

Problem 28119

Find the intersection point of the lines defined by y=3xy=3xy=3x and y=−4x−49y=-4x-49y=−4x−49.

Problem 28120

Solve the inequality: -6 ≤ x + 12. Provide the solution in interval notation.

Problem 28121

Solve the quadratic p2+14p−33=10p^{2}+14 p-33=10p2+14p−33=10 by completing the square. Give the equation as (p−a)2=b(p-a)^{2}=b(p−a)2=b and list solutions.

Problem 28122

Jasmine earned $25.20\$ 25.20$25.20 for 6 hours and $16.80\$ 16.80$16.80 for 4 hours. Find the function for her earnings (c)(c)(c) based on hours (h)(h)(h).

Problem 28123

Solve the equation 4m2−3m−2=04 m^{2}-3 m-2=04m2−3m−2=0 using the quadratic formula. Provide solutions in simplest radical form.

Problem 28124

Find f(64)f(64)f(64) given the function f(x)=9xf(x)=9 \sqrt{x}f(x)=9x​. What is f(64)=?f(64)=?f(64)=?

Problem 28125

In Amanda's class, the ratio of students with widow's peaks to those without is 3:2. With 35 students, how many lack widow's peaks? 32wp=35 \frac{3}{2} w p=35 23​wp=35

Problem 28126

Find f(10)f(10)f(10) for the function f(x)=5x+x2+10f(x)=5x+x^{2}+10f(x)=5x+x2+10. What is f(10)f(10)f(10)?

Problem 28127

Find f(5.75)f(5.75)f(5.75) using the function f(x)=5.98xf(x)=\frac{5.98}{x}f(x)=x5.98​. Provide the answer as a decimal or whole number.

Problem 28128

In a class of 32 students with a junior to senior ratio of 5:3, how many are seniors? (A) 3 (B) 8 (C) 9 (D) 1 (E) 20

Problem 28129

Find f(34.58)f(34.58)f(34.58) using the rule f(x)=0.0738.58−xf(x)=0.07 \sqrt{38.58-x}f(x)=0.0738.58−x​. What is f(34.58)f(34.58)f(34.58)?

Problem 28130

The environmental club has 450 pounds of cans and collects 14 pounds weekly. (i) Find the slope mmm of the linear model. (ii) Find the starting value bbb of the linear model. (iii) Predict pounds of cans by week 44. (iv) Predict weeks to reach 725 pounds.

Problem 28131

Graph the solution set for the system of inequalities: 1. x2−y≤3x−2x^{2}-y \leq 3x-2x2−y≤3x−2 2. y+12x+2>x+2y−1y+\frac{1}{2}x+2>x+2y-1y+21​x+2>x+2y−1

Problem 28132

Find the product and simplify: (x+8)2(x+8)^{2}(x+8)2.

Problem 28133

Find the time ttt for a block to slide down an incline with base a=12a=12a=12 and angle θ=45∘\theta=45^{\circ}θ=45∘ using t=2agsin⁡θcos⁡θt=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}t=gsinθcosθ2a​​.

Problem 28134

Simplify the expression: (x2y3z4)23\sqrt[3]{\left(x^{2} y^{3} z^{4}\right)^{2}}3(x2y3z4)2​

Problem 28135

Find the sum of the infinite geometric series with an=64(14)n−1a_{n}=64\left(\frac{1}{4}\right)^{n-1}an​=64(41​)n−1.

Problem 28136

Solve the system: 3x + 5y = -7 and 14x - 9y = 32. Choose from (2,1), (-2,1), (1,-2), (1,2).

Problem 28137

Simplify the expression: −5r(r+s)2-5 r(r+s)^2−5r(r+s)2

Problem 28138

Simplify and factor −5(x2+65x+52)−40+15-5\left(x^{2}+\frac{6}{5} x+\frac{5}{2}\right)-40+15−5(x2+56​x+25​)−40+15.

Problem 28139

Complete the square and find the vertex of the function s(x)=−5x2−30x−40s(x)=-5 x^{2}-30 x-40s(x)=−5x2−30x−40.

Problem 28140

Find the domain of the function f(x)=17−x4f(x)=\sqrt[4]{17-x}f(x)=417−x​.

Evaluate $b - 2y$ for $b = -3$ and $y = 3$ .

Use the distributive property: $(7 \times 3)-(7 \times 2)=7 \times$ __.

Let the number of ten dollar bills be $x$ . Then, the number of five dollar bills is $2x$ . Solve for $x$ given $5(2x) + 10(x) = 720$ . How many ten's are there?

Define a linear equation for the monthly cost $C$ of a cell phone plan based on data usage $d$ in GB, given $C = 21 + 5d$ .

Solve for $t$ using the square root property: $2 t^{2}-45=-19$ . Find $t=$ .

Complete the square for the equation $p^{2}+14 p-33=10$ . Write it as $(p-a)^{2}=b$ and find $p=$ .

A truck goes 441 miles at 63 mph. Use $d = r t$ to find the travel time in hours.

Solve the equation $4 m^{2}-3 m-2=0$ using the quadratic formula and list solutions in simplest radical form.

Solve: $\sqrt{-1 x+68}=x-12$ . Find $x=$ (Separate answers with commas; use integers or reduced fractions. If none, enter DNE.)

Solve for $x$ : $x^{3/5} = 8$

Solve $a^{2}=15 a-56$ . Find $a=$ . If multiple solutions, separate with a comma.

Solve the equation $3 r^{3}-12 r=-2 r^{2}+8$ for real values of $r$ . Provide answers as integers or simplified fractions, separated by commas.

Solve for $x$ : $12 < -14(x+3) < 15$ . Type DNE if no solution exists. Provide your answer in interval notation.

Find three consecutive even integers where the smallest plus twice the median equals 20 more than the largest: $x + 2(x + 2) = (x + 4) + 20$ .

Find the intersection point of the lines defined by $y=3x$ and $y=-4x-49$ .

Solve the quadratic $p^{2}+14 p-33=10$ by completing the square. Give the equation as $(p-a)^{2}=b$ and list solutions.

Jasmine earned $\$ 25.20$ for 6 hours and $\$ 16.80$ for 4 hours. Find the function for her earnings $(c)$ based on hours $(h)$ .

Solve the equation $4 m^{2}-3 m-2=0$ using the quadratic formula. Provide solutions in simplest radical form.

Find $f(64)$ given the function $f(x)=9 \sqrt{x}$ . What is $f(64)=?$

In Amanda's class, the ratio of students with widow's peaks to those without is 3:2. With 35 students, how many lack widow's peaks? $\frac{3}{2} w p=35$

Find $f(10)$ for the function $f(x)=5x+x^{2}+10$ . What is $f(10)$ ?

Find $f(5.75)$ using the function $f(x)=\frac{5.98}{x}$ . Provide the answer as a decimal or whole number.

Find $f(34.58)$ using the rule $f(x)=0.07 \sqrt{38.58-x}$ . What is $f(34.58)$ ?

The environmental club has 450 pounds of cans and collects 14 pounds weekly.
(i) Find the slope $m$ of the linear model. (ii) Find the starting value $b$ of the linear model. (iii) Predict pounds of cans by week 44. (iv) Predict weeks to reach 725 pounds.

Graph the solution set for the system of inequalities:
1. $x^{2}-y \leq 3x-2$
2. $y+\frac{1}{2}x+2>x+2y-1$

Find the product and simplify: $(x+8)^{2}$ .

Find the time $t$ for a block to slide down an incline with base $a=12$ and angle $\theta=45^{\circ}$ using $t=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}$ .

Simplify the expression: $\sqrt[3]{\left(x^{2} y^{3} z^{4}\right)^{2}}$

Find the sum of the infinite geometric series with $a_{n}=64\left(\frac{1}{4}\right)^{n-1}$ .

Simplify the expression: $-5 r(r+s)^2$

Simplify and factor $-5\left(x^{2}+\frac{6}{5} x+\frac{5}{2}\right)-40+15$ .

Complete the square and find the vertex of the function $s(x)=-5 x^{2}-30 x-40$ .

Find the domain of the function $f(x)=\sqrt[4]{17-x}$ .

A car on a $2.6^{\circ}$ incline faces $124 \mathrm{lb}$ resistance. Find the car's weight to the nearest hundred pounds.

Find the domain of the function $f(x)=\frac{1}{x-2}$ .

Find the domain of the function $g(x)=\frac{8 x}{x^{2}-9}$ .

Simplify the expression: $\sqrt[3]{8 y^{27}}$

Find the grade resistance in pounds for a 2000-pound car on a $2.4^{\circ}$ uphill grade using $F=W \sin \theta$ .

Find the constant of variation for the point $(12,9)$ in a direct variation. Options: $\frac{1}{2}$ , $\frac{3}{4}$ , 1, 2.

Find the vertex of the quadratic function $3 x^{2}+10 x-3$ .

Graph the function defined as: $f(x) = -3 - x$ for $x \leq 1$ and $f(x) = -3 + 2x$ for $x > 1$ .

Find the vertex of the quadratic function $2x^{2} - 2x - 4$ .

You have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?
A: Budget increases to \$150, prices same. increase
B: Budget \$100, books \$25, tickets rise to \$20. decrease
C: Budget \$100, tickets \$10, books drop to \$15. increase

Find the equation of the axis of symmetry for the function $2x^{2} - 2x - 4$ .

Calculate the Medicare tax function values for $x = 0$ , $200$ , and $400$ using the piecewise function defined for 2022.

Realiza la operación de $5 x^{3} y(2 x+3 y-4)$ .

Simplify the expression $(2 x + 3 y)^{2}$ .

Find $f(x)=2$ . Calculate $f(7)$ , $f(-7)$ , $f(1.6)$ , $f(-1.3)$ . What is $f(7)$ ? A. $f(7)=$ B. $f(7)$ is undefined.

Evaluate the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ at $f(7)$ . Is it defined or undefined?

Evaluate the function $f(x)=14 x^{2}+7 x$ at these points: (a) $f(5)$ , (b) $f(-9)$ , (c) $f(4.5)$ , (d) $f(-3.5)$ .

For the function $f(x)=\sqrt{14-x}$ , calculate $f(5)$ , $f(-4)$ , $f(11.1)$ , and $f(-3.7)$ .

Given the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ , find $f(7)$ and $f(-6)$ . Are they defined?

Evaluate the function $f(x)=\frac{\sqrt{x-4}}{x^{2}-8}$ for $f(7)$ , $f(-6)$ , and $f(4.3)$ .

Simplify $3^{8} \div 3^{4}$ or $\frac{3^{8}}{3^{4}}$ .

Evaluate for $x=2$ and $y=7$ : a. $9 x^{2} y^{0}+1$ , b. $\left(\frac{x^{9}}{x^{3}}\right)-y^{2}$ .

Rewrite $\frac{7^{8} \div 7^{2}}{7^{3}}$ as a single exponent.

Calculate $2^{16} \div 2^{4}$ and fill in the blanks: $2^{16} \square_{4} = \square$ .

Rearrange $2000=1000\left(1+\frac{R}{100}\right)^{D}$ to find $D=\frac{\log (2)}{\log \left(1+\frac{R}{100}\right)}$ .

Simplify $12^{9} \div 12^{3}$ .