Math Statement

Problem 17101

Write a conditional from $7 x-7=42$ implies $7 x=49$ . Choose the correct option: A, B, C, or D.

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Problem 17102

Find the inverse function $f^{-1}(x)$ for $f(x) = 2x + 16$ . What is $f^{-1}(x)$ ?

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Problem 17103

Find the cost to manufacture each additional Kinect using $C(x)=150x+30$ . Estimate the cost for 37 Kinects.

See Solution

Problem 17104

Find the inverse function $f^{-1}(x)$ if $f(x) = \frac{x}{4} - 5$ . What is $f^{-1}(x) = [?] x + []$ ?

See Solution

Problem 17105

Identify the pattern in the sequence $25, 18, 11, 4, \ldots$ and provide the next two terms: $25, 18, 11, 4, \square, \square$ .

See Solution

Problem 17106

Identify which function opens upward: $y=-2 x^{2}+x+3$ or $f(x)=0.5 x^{2}-x-1$ .

See Solution

Problem 17107

Identify which function opens downward: $f(x)=0.5 x^{2}-10 x-110$ or $f(x)=-x^{2}+33 x$ .

See Solution

Problem 17108

Find the axis of symmetry for the function $f(x)=2 x^{2}-3 x+6$ using $x=\frac{-b}{2 a}$ . What is the value?

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Problem 17109

Find the axis of symmetry for $f(x)=8 x^{2}+6 x+19$ using $x=\frac{-b}{2 a}$ . Enter $x=[?] \frac{[]}{[]}$ .

See Solution

Problem 17110

Calculate $\frac{734}{2}$ .

See Solution

Problem 17111

Demuestra que el producto de cuatro enteros consecutivos más uno es un cuadrado. Da 3 ejemplos y encuentra la expresión algebraica.

See Solution

Problem 17112

Factor the quadratic function $f(x)=x^{2}+14x+48$ and find the value of $x$ that fits: $x=-8 ; x=[?]$ .

See Solution

Problem 17113

Factor the quadratic function $f(x)=4x^{2}-9$ and find the values for $x$ in $x=-\frac{[?]}{2}; x=\frac{3}{[]}$ .

See Solution

Problem 17114

Solve the quadratic function $y=x^{2}-1$ using the square root method. Find $x= \pm[?]$ .

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Problem 17115

Complete the square to solve the quadratic: $y=x^{2}+10x+10$ . Steps: Set $y=0$ , adjust constants, add $(\frac{b}{2})^2$ , factor, solve for $x$ .

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Problem 17116

ISeeYou charges \$7,500.
(a) Create a linear function for the fee $p$ for $q$ contracts: $p(q)=$ . (b) Determine total revenue $R$ from $q$ contracts: $R(q)=$ . (c) Monthly costs: Fixed \ $150,000, Variable \$1,500 per contract. Find cost function:$ C(q)=$.

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Problem 17117

Complete the square to solve: $y=x^{2}-8x+5$ . Find $x$ values when $y=0$ .

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Problem 17118

Solve for $x$ in the equation $x^{2}-x-6=0$ . Use the quadratic formula and list the smallest solution first.

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Problem 17119

Solve for x in the equation x² - 5x - 24 = 0. Use the quadratic formula and list the smallest solution first.

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Problem 17120

Solve the equation $x=\sqrt{2 x+15}$ and find the value of $x$ .

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Problem 17121

Solve for $x$ in the equation $\sqrt{x}=12$ and verify your solution.

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Problem 17122

Find the starting point of the function $f(x)=\sqrt{x-4}+7$ on the coordinate plane. What is the ordered pair?

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Problem 17123

Prove by induction that for $n$ numbers $a_1, a_2, \ldots, a_n$ , $|a_1 + \cdots + a_n| \leq |a_1| + \cdots + |a_n|$ . Also, show $|b| < a$ iff $-a < b < a$ .

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Problem 17124

Find the inverse of the function $f(x)=3x+9$ . What is $f^{-1}(x)=\frac{x}{[?]}+$ ?

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Problem 17125

Find the inverse function $f^{-1}(x)$ for $f(x) = \frac{x}{9} + 1$ . What is $f^{-1}(x) = [?] x + []$ ?

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Problem 17126

Find the starting point of the function $f(x)=\sqrt{x+2}-2$ on the coordinate plane. $([?],[])$

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Problem 17127

Evaluate $6(12+4)$ .

See Solution

Problem 17128

Find the y-intercept of $f(x)=\frac{x^{2}-4}{x+2}$ .

See Solution

Problem 17129

Determine the oblique asymptote for the function $f(x)=\frac{x^{2}-4}{x+2}$ .

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Problem 17130

Determine the vertical asymptote of $f(x)=\frac{x^{2}-4}{x+2}$ .

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Problem 17131

Determine the horizontal asymptote for the function $f(x)=\frac{x^{2}-4}{x+2}$ .

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Problem 17132

Find the holes in the rational function $f(x)=\frac{x^{2}-4}{x+2}$ . If none, state 'none'.

See Solution

Problem 17133

Solve the equation $7+3(x-2)=2x+10$ by applying the distributive property. What is the first step?

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Problem 17134

Calculate the value of $\log _{5} 125$ .

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Problem 17135

Solve the equation: $\log _{3} x + \log _{3}(x-24) = 4$

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Problem 17136

Find the derivative of $f(x) = 5x^2$ .

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Problem 17137

Rewrite the equation $e^{x}=10$ using logarithms.

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Problem 17138

Evaluate $\log _{3} 25$ using the Change-of-Base Formula and round to two decimal places.

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Problem 17139

Solve the equation: $\log _{3}(x-5)+\log _{3}(x-11)=3$ .

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Problem 17140

Solve the equation: $\ln \sqrt{x+3} = 7$ .

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Problem 17141

Solve for $x$ in the equation: $2+\log _{3}(2x+5)-\log _{3}x=4$ .

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Problem 17142

Find the exact value of $\ln \mathrm{e}^{\sqrt{6}}$ using logarithm properties without a calculator.

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Problem 17143

Rewrite the expression as a sum/difference of logarithms: $\log_{6}\left(\frac{x-1}{x^{4}}\right)$ .

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Problem 17144

Find the domain of the function $f(x)=\log _{3}(x-9)^{2}$ .

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Problem 17145

Find the exact value of $\log _{2} 11 \cdot \log _{11} 8$ using logarithm properties without a calculator.

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Problem 17146

Convert the logarithm $\log _{2} \frac{1}{4}$ to its equivalent exponential form.

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Problem 17147

Find $\log_{b} B^{2}$ if $\log_{b} A = 5$ and $\log_{b} B = -4$ .

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Problem 17148

Solve for $x$ in the equation: $\log _{3}(x+4)=-2$ .

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Problem 17149

Convert the exponential equation $5^{3}=125$ to a logarithmic form.

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Problem 17150

Find $\log_{b} AB$ given that $\log_{b} A=5$ and $\log_{b} B=-2$ .

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Problem 17151

Rewrite the exponential equation $4^{3}=x$ using logarithms.

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Problem 17152

Find the value of $\log _{9} \frac{1}{729}$ .

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Problem 17153

Find the exact value of $7^{\log_{7} 0.499}$ using logarithm properties without a calculator.

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Problem 17154

Rewrite the exponential equation $4^{5 / 2}=32$ using a logarithm.

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Problem 17155

Rewrite the expression $3^{-3}$ using a logarithm.

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Problem 17156

Solve for $x$ in the equation: $e^{x+8}=2$ .

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Problem 17157

Solve the equation: $e^{3 x} = 5$

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Problem 17158

Convert the logarithmic expression to an exponent: $\ln \frac{1}{e^{4}}=-4$ .

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Problem 17159

Find the value of $\ln e^{4}$ .

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Problem 17160

Solve the equation $3^{x+8}=7$ and express the solution using natural logarithms.

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Problem 17161

Calculate the value of $\log _{8} \frac{1}{64}$ .

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Problem 17162

Find the exact value of $\ln \mathrm{e}$ .

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Problem 17163

Determine the domain of the function $f(x)=\log (x+6)$ .

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Problem 17164

Solve for $x$ in the equation: $\log_{2} x = 3$ .

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Problem 17165

Combine the logarithms: $\log_{c} q + \log_{c} r$ as a single logarithm.

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Problem 17166

Find the exact value of $2 \ln e^{4.2}$ using logarithm properties without a calculator.

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Problem 17167

Combine the expression into one logarithm: $2 \log_{c} m - \frac{4}{3} \log_{c} n + \frac{1}{6} \log_{c} j - 6 \log_{c} k$ .

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Problem 17168

Solve the equation $e^{x+7}=5$ and express the solution using natural logarithms.

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Problem 17169

Rewrite the logarithmic expression as an exponent: $\log_{4} x = 3$ .

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Problem 17170

Solve for $x$ in the equation $\log _{4} 64=x$ . Choose from: {16, 3, 256, 68}.

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Problem 17171

Find the integral of $\frac{1-x^{2}}{x(1-2 x)}$ and simplify to get the final expression.

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Problem 17172

Find the value of $x$ in the equation $\log _{4} 64=x$ .

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Problem 17173

Solve the equation $e^{5x} = 3$ and express the solution using natural logarithms.

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Problem 17174

Find the exact value of the expression using logarithm properties: $\log_{3} 6 - \log_{3} 2$ .

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Problem 17175

Simplify: $\frac{x^{2}-3 x-4}{x^{2}+x} \div \frac{x-4}{x^{2}}$

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Problem 17176

Simplify these expressions: 1) $\frac{x^{2}-3 x-4}{x^{2}+x} \div \frac{x-4}{x^{2}}$ 2) $\frac{x-1}{x+2}+\frac{x+1}{2 x+4}$

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Problem 17177

Solve for $x$ using the method of completing the square: $x^{2}-7 x=-12$ .

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Problem 17178

Find the $x$ intercept(s) of the function $f(x)=2 x^{2}-8 x+6$ .

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Problem 17179

Solve for $x$ by completing the square: $x^{2}-7 x=-12$ . Also, find $x$ and $y$ for $y-2 x+4=0$ and $x^{2}+y=4$ .

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Problem 17180

Solve for $x$ in the equation: $3^{2 x}=15^{x-6}$ .

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Problem 17181

Simplify $\left[\left(\frac{m}{n}\right)^{2}-1\right] \div\left(m/n + 1\right)$ .

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Problem 17182

Simplify the expression: $\left[\left(\frac{m}{n}\right)^{2}-(-m)^{0}\right] \div\left(m n^{-1}+1\right)$ .

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Problem 17183

Calculate the integral $\int_{0}^{3}(1-e^{-x}) \, dx$ with $h=2$ .

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Problem 17184

Calculate the integral $\int_{v}^{t} t \cdot \cos \left(\frac{t}{5}\right) \cdot d t$ .

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Problem 17185

Find the value of $a$ in the equation $f(x)=a \cdot x^{4}$ given $60=a \cdot 25^{4}$ .

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Problem 17186

Is the number 15 prime, composite, or neither?

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Problem 17187

Find the prime factors of 25.

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Problem 17188

Distribute 100 in the expression: $100(0.06 a + 0.09 b) =$

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Problem 17189

Simplify the expression: $1(2) - 3(-2) + (-3)(3) =$

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Problem 17190

Simplify the following expressions using order of operations: a. $(7+6)^{2}=$ b. $7^{2}+6^{2}=$ c. $7^{2}+2 \cdot 7 \cdot 6+6^{2}=$

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Problem 17191

Evaluate these expressions for $x = 3$ : a. $x^{2}+8x+16$ , b. $(x+4)^{2}$ , c. $x^{2}+4$ , d. $x^{2}-16$ .

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Problem 17192

Distribute in the expression: $x\left(1-\frac{4}{x}\right)=$

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Problem 17193

Simplify using properties: $1 - 2(5b - 5) + 3b =$

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Problem 17194

1. Calculate $5^{2}+9$ .
2. Factor $9 x^{2}-4$ .
3. Complete the square for $x^2+3x=18$ .

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Problem 17195

Find the elements of the set $A \cap B$ where $A=\{0,2,4,6\}$ and $B=\{1,2,3,4,5\}$ .

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Problem 17196

Solve for $m$ in the equation: $\sqrt{2 m-1}+\sqrt{2 m+1}-2=0$ .

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Problem 17197

Solve for $m$ in the equation $\sqrt{2 m+1}+\sqrt{2 m+1}-2=0$ .

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Problem 17198

Show that $f(x)=x^{2}-6x+1$ on [1,3] meets Lagrange's theorem. Find where the tangent is parallel to the line joining A(1,-4) and B(3,-8).

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Problem 17199

1/2 - 3/10 = ?

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Problem 17200

Solve the equation $2x = 2$ .

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Math Statement

Problem 17101

Write a conditional from 7x−7=427 x-7=427x−7=42 implies 7x=497 x=497x=49. Choose the correct option: A, B, C, or D.

Problem 17102

Find the inverse function f−1(x)f^{-1}(x)f−1(x) for f(x)=2x+16f(x) = 2x + 16f(x)=2x+16. What is f−1(x)f^{-1}(x)f−1(x)?

Problem 17103

Find the cost to manufacture each additional Kinect using C(x)=150x+30C(x)=150x+30C(x)=150x+30. Estimate the cost for 37 Kinects.

Problem 17104

Find the inverse function f−1(x)f^{-1}(x)f−1(x) if f(x)=x4−5f(x) = \frac{x}{4} - 5f(x)=4x​−5. What is f−1(x)=[?]x+[]f^{-1}(x) = [?] x + []f−1(x)=[?]x+[]?

Problem 17105

Identify the pattern in the sequence 25,18,11,4,…25, 18, 11, 4, \ldots25,18,11,4,… and provide the next two terms: 25,18,11,4,□,□25, 18, 11, 4, \square, \square25,18,11,4,□,□.

Problem 17106

Identify which function opens upward: y=−2x2+x+3y=-2 x^{2}+x+3y=−2x2+x+3 or f(x)=0.5x2−x−1f(x)=0.5 x^{2}-x-1f(x)=0.5x2−x−1.

Problem 17107

Identify which function opens downward: f(x)=0.5x2−10x−110f(x)=0.5 x^{2}-10 x-110f(x)=0.5x2−10x−110 or f(x)=−x2+33xf(x)=-x^{2}+33 xf(x)=−x2+33x.

Problem 17108

Find the axis of symmetry for the function f(x)=2x2−3x+6f(x)=2 x^{2}-3 x+6f(x)=2x2−3x+6 using x=−b2ax=\frac{-b}{2 a}x=2a−b​. What is the value?

Problem 17109

Find the axis of symmetry for f(x)=8x2+6x+19f(x)=8 x^{2}+6 x+19f(x)=8x2+6x+19 using x=−b2ax=\frac{-b}{2 a}x=2a−b​. Enter x=[?][][]x=[?] \frac{[]}{[]}x=[?][][]​.

Problem 17110

Calculate 7342\frac{734}{2}2734​.

Problem 17111

Demuestra que el producto de cuatro enteros consecutivos más uno es un cuadrado. Da 3 ejemplos y encuentra la expresión algebraica.

Problem 17112

Factor the quadratic function f(x)=x2+14x+48f(x)=x^{2}+14x+48f(x)=x2+14x+48 and find the value of xxx that fits: x=−8;x=[?]x=-8 ; x=[?]x=−8;x=[?].

Problem 17113

Factor the quadratic function f(x)=4x2−9f(x)=4x^{2}-9f(x)=4x2−9 and find the values for xxx in x=−[?]2;x=3[]x=-\frac{[?]}{2}; x=\frac{3}{[]}x=−2[?]​;x=[]3​.

Problem 17114

Solve the quadratic function y=x2−1y=x^{2}-1y=x2−1 using the square root method. Find x=±[?]x= \pm[?]x=±[?].

Problem 17115

Complete the square to solve the quadratic: y=x2+10x+10y=x^{2}+10x+10y=x2+10x+10. Steps: Set y=0y=0y=0, adjust constants, add (b2)2(\frac{b}{2})^2(2b​)2, factor, solve for xxx.

Problem 17116

Problem 17117

Complete the square to solve: y=x2−8x+5y=x^{2}-8x+5y=x2−8x+5. Find xxx values when y=0y=0y=0.

Problem 17118

Solve for xxx in the equation x2−x−6=0x^{2}-x-6=0x2−x−6=0. Use the quadratic formula and list the smallest solution first.

Problem 17119

Solve for x in the equation x² - 5x - 24 = 0. Use the quadratic formula and list the smallest solution first.

Problem 17120

Solve the equation x=2x+15x=\sqrt{2 x+15}x=2x+15​ and find the value of xxx.

Problem 17121

Solve for xxx in the equation x=12\sqrt{x}=12x​=12 and verify your solution.

Problem 17122

Find the starting point of the function f(x)=x−4+7f(x)=\sqrt{x-4}+7f(x)=x−4​+7 on the coordinate plane. What is the ordered pair?

Problem 17123

Problem 17124

Find the inverse of the function f(x)=3x+9f(x)=3x+9f(x)=3x+9. What is f−1(x)=x[?]+f^{-1}(x)=\frac{x}{[?]}+f−1(x)=[?]x​+?

Problem 17125

Find the inverse function f−1(x)f^{-1}(x)f−1(x) for f(x)=x9+1f(x) = \frac{x}{9} + 1f(x)=9x​+1. What is f−1(x)=[?]x+[]f^{-1}(x) = [?] x + []f−1(x)=[?]x+[]?

Problem 17126

Find the starting point of the function f(x)=x+2−2f(x)=\sqrt{x+2}-2f(x)=x+2​−2 on the coordinate plane. ([?],[])([?],[])([?],[])

Problem 17127

Evaluate 6(12+4)6(12+4)6(12+4).

Problem 17128

Find the y-intercept of f(x)=x2−4x+2f(x)=\frac{x^{2}-4}{x+2}f(x)=x+2x2−4​.

Problem 17129

Determine the oblique asymptote for the function f(x)=x2−4x+2f(x)=\frac{x^{2}-4}{x+2}f(x)=x+2x2−4​.

Problem 17130

Determine the vertical asymptote of f(x)=x2−4x+2f(x)=\frac{x^{2}-4}{x+2}f(x)=x+2x2−4​.

Problem 17131

Determine the horizontal asymptote for the function f(x)=x2−4x+2f(x)=\frac{x^{2}-4}{x+2}f(x)=x+2x2−4​.

Problem 17132

Find the holes in the rational function f(x)=x2−4x+2f(x)=\frac{x^{2}-4}{x+2}f(x)=x+2x2−4​. If none, state 'none'.

Problem 17133

Solve the equation 7+3(x−2)=2x+107+3(x-2)=2x+107+3(x−2)=2x+10 by applying the distributive property. What is the first step?

Problem 17134

Calculate the value of log⁡5125\log _{5} 125log5​125.

Problem 17135

Solve the equation: log⁡3x+log⁡3(x−24)=4 \log _{3} x + \log _{3}(x-24) = 4 log3​x+log3​(x−24)=4

Problem 17136

Find the derivative of f(x)=5x2f(x) = 5x^2f(x)=5x2.

Problem 17137

Rewrite the equation ex=10e^{x}=10ex=10 using logarithms.

Problem 17138

Evaluate log⁡325\log _{3} 25log3​25 using the Change-of-Base Formula and round to two decimal places.

Problem 17139

Solve the equation: log⁡3(x−5)+log⁡3(x−11)=3\log _{3}(x-5)+\log _{3}(x-11)=3log3​(x−5)+log3​(x−11)=3.

Problem 17140

Solve the equation: ln⁡x+3=7\ln \sqrt{x+3} = 7lnx+3​=7.

Problem 17141

Write a conditional from $7 x-7=42$ implies $7 x=49$ . Choose the correct option: A, B, C, or D.

Find the inverse function $f^{-1}(x)$ for $f(x) = 2x + 16$ . What is $f^{-1}(x)$ ?

Find the cost to manufacture each additional Kinect using $C(x)=150x+30$ . Estimate the cost for 37 Kinects.

Find the inverse function $f^{-1}(x)$ if $f(x) = \frac{x}{4} - 5$ . What is $f^{-1}(x) = [?] x + []$ ?

Identify the pattern in the sequence $25, 18, 11, 4, \ldots$ and provide the next two terms: $25, 18, 11, 4, \square, \square$ .

Identify which function opens upward: $y=-2 x^{2}+x+3$ or $f(x)=0.5 x^{2}-x-1$ .

Identify which function opens downward: $f(x)=0.5 x^{2}-10 x-110$ or $f(x)=-x^{2}+33 x$ .

Find the axis of symmetry for the function $f(x)=2 x^{2}-3 x+6$ using $x=\frac{-b}{2 a}$ . What is the value?

Find the axis of symmetry for $f(x)=8 x^{2}+6 x+19$ using $x=\frac{-b}{2 a}$ . Enter $x=[?] \frac{[]}{[]}$ .

Calculate $\frac{734}{2}$ .

Factor the quadratic function $f(x)=x^{2}+14x+48$ and find the value of $x$ that fits: $x=-8 ; x=[?]$ .

Factor the quadratic function $f(x)=4x^{2}-9$ and find the values for $x$ in $x=-\frac{[?]}{2}; x=\frac{3}{[]}$ .

Solve the quadratic function $y=x^{2}-1$ using the square root method. Find $x= \pm[?]$ .

Complete the square to solve the quadratic: $y=x^{2}+10x+10$ . Steps: Set $y=0$ , adjust constants, add $(\frac{b}{2})^2$ , factor, solve for $x$ .

Complete the square to solve: $y=x^{2}-8x+5$ . Find $x$ values when $y=0$ .

Solve for $x$ in the equation $x^{2}-x-6=0$ . Use the quadratic formula and list the smallest solution first.

Solve the equation $x=\sqrt{2 x+15}$ and find the value of $x$ .

Solve for $x$ in the equation $\sqrt{x}=12$ and verify your solution.

Find the starting point of the function $f(x)=\sqrt{x-4}+7$ on the coordinate plane. What is the ordered pair?

Find the inverse of the function $f(x)=3x+9$ . What is $f^{-1}(x)=\frac{x}{[?]}+$ ?

Find the inverse function $f^{-1}(x)$ for $f(x) = \frac{x}{9} + 1$ . What is $f^{-1}(x) = [?] x + []$ ?

Find the starting point of the function $f(x)=\sqrt{x+2}-2$ on the coordinate plane. $([?],[])$

Evaluate $6(12+4)$ .

Find the y-intercept of $f(x)=\frac{x^{2}-4}{x+2}$ .

Determine the oblique asymptote for the function $f(x)=\frac{x^{2}-4}{x+2}$ .

Determine the vertical asymptote of $f(x)=\frac{x^{2}-4}{x+2}$ .

Determine the horizontal asymptote for the function $f(x)=\frac{x^{2}-4}{x+2}$ .

Find the holes in the rational function $f(x)=\frac{x^{2}-4}{x+2}$ . If none, state 'none'.

Solve the equation $7+3(x-2)=2x+10$ by applying the distributive property. What is the first step?

Calculate the value of $\log _{5} 125$ .

Solve the equation: $\log _{3} x + \log _{3}(x-24) = 4$

Find the derivative of $f(x) = 5x^2$ .

Rewrite the equation $e^{x}=10$ using logarithms.

Evaluate $\log _{3} 25$ using the Change-of-Base Formula and round to two decimal places.

Solve the equation: $\log _{3}(x-5)+\log _{3}(x-11)=3$ .

Solve the equation: $\ln \sqrt{x+3} = 7$ .

Solve for $x$ in the equation: $2+\log _{3}(2x+5)-\log _{3}x=4$ .

Find the exact value of $\ln \mathrm{e}^{\sqrt{6}}$ using logarithm properties without a calculator.

Rewrite the expression as a sum/difference of logarithms: $\log_{6}\left(\frac{x-1}{x^{4}}\right)$ .

Find the domain of the function $f(x)=\log _{3}(x-9)^{2}$ .

Find the exact value of $\log _{2} 11 \cdot \log _{11} 8$ using logarithm properties without a calculator.

Convert the logarithm $\log _{2} \frac{1}{4}$ to its equivalent exponential form.

Find $\log_{b} B^{2}$ if $\log_{b} A = 5$ and $\log_{b} B = -4$ .

Solve for $x$ in the equation: $\log _{3}(x+4)=-2$ .

Convert the exponential equation $5^{3}=125$ to a logarithmic form.

Find $\log_{b} AB$ given that $\log_{b} A=5$ and $\log_{b} B=-2$ .

Rewrite the exponential equation $4^{3}=x$ using logarithms.

Find the value of $\log _{9} \frac{1}{729}$ .

Find the exact value of $7^{\log_{7} 0.499}$ using logarithm properties without a calculator.

Rewrite the exponential equation $4^{5 / 2}=32$ using a logarithm.

Rewrite the expression $3^{-3}$ using a logarithm.

Solve for $x$ in the equation: $e^{x+8}=2$ .

Solve the equation: $e^{3 x} = 5$

Convert the logarithmic expression to an exponent: $\ln \frac{1}{e^{4}}=-4$ .

Find the value of $\ln e^{4}$ .

Solve the equation $3^{x+8}=7$ and express the solution using natural logarithms.

Calculate the value of $\log _{8} \frac{1}{64}$ .

Find the exact value of $\ln \mathrm{e}$ .

Determine the domain of the function $f(x)=\log (x+6)$ .

Solve for $x$ in the equation: $\log_{2} x = 3$ .

Combine the logarithms: $\log_{c} q + \log_{c} r$ as a single logarithm.

Find the exact value of $2 \ln e^{4.2}$ using logarithm properties without a calculator.

Combine the expression into one logarithm: $2 \log_{c} m - \frac{4}{3} \log_{c} n + \frac{1}{6} \log_{c} j - 6 \log_{c} k$ .

Solve the equation $e^{x+7}=5$ and express the solution using natural logarithms.

Rewrite the logarithmic expression as an exponent: $\log_{4} x = 3$ .

Solve for $x$ in the equation $\log _{4} 64=x$ . Choose from: {16, 3, 256, 68}.

Find the integral of $\frac{1-x^{2}}{x(1-2 x)}$ and simplify to get the final expression.

Find the value of $x$ in the equation $\log _{4} 64=x$ .

Solve the equation $e^{5x} = 3$ and express the solution using natural logarithms.

Find the exact value of the expression using logarithm properties: $\log_{3} 6 - \log_{3} 2$ .