Algebra

Problem 22001

Given cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

See Solution

Problem 22002

Next week, you charged \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find the revenue function $R(p)=$ . (c) Given costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Find break-even entrance fees, rounding to two decimal places.

See Solution

Problem 22003

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

See Solution

Problem 22004

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

See Solution

Problem 22005

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

See Solution

Problem 22006

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

See Solution

Problem 22007

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

See Solution

Problem 22008

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

See Solution

Problem 22009

List the four steps to solve a linear equation from these options: isolate variable, check solution, collect terms, simplify.

See Solution

Problem 22010

Next week, you charge \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees $p=$ .

See Solution

Problem 22011

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

See Solution

Problem 22012

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

See Solution

Problem 22013

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

See Solution

Problem 22014

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

See Solution

Problem 22015

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

See Solution

Problem 22016

RideEm Bicycles produces 170 bikes for \ $10,300 and 190 bikes for \$10,900. Find the cost function$ C(x)$ and fixed/variable costs.

See Solution

Problem 22017

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

See Solution

Problem 22018

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

See Solution

Problem 22019

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

See Solution

Problem 22020

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

See Solution

Problem 22021

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

See Solution

Problem 22022

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

See Solution

Problem 22023

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

See Solution

Problem 22024

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

See Solution

Problem 22025

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

See Solution

Problem 22026

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

See Solution

Problem 22027

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

See Solution

Problem 22028

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

See Solution

Problem 22029

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

See Solution

Problem 22030

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

See Solution

Problem 22031

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

See Solution

Problem 22032

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

See Solution

Problem 22033

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

See Solution

Problem 22034

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

See Solution

Problem 22035

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

See Solution

Problem 22036

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

See Solution

Problem 22037

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

See Solution

Problem 22038

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

See Solution

Problem 22039

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

See Solution

Problem 22040

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

See Solution

Problem 22041

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

See Solution

Problem 22042

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

See Solution

Problem 22043

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

See Solution

Problem 22044

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

See Solution

Problem 22045

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

See Solution

Problem 22046

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

See Solution

Problem 22047

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

See Solution

Problem 22048

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

See Solution

Problem 22049

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

See Solution

Problem 22050

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

See Solution

Problem 22051

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

See Solution

Problem 22052

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

See Solution

Problem 22053

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

See Solution

Problem 22054

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

See Solution

Problem 22055

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

See Solution

Problem 22056

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

See Solution

Problem 22057

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

See Solution

Problem 22058

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

See Solution

Problem 22059

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

See Solution

Problem 22060

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

See Solution

Problem 22061

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

See Solution

Problem 22062

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

See Solution

Problem 22063

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

See Solution

Problem 22064

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

See Solution

Problem 22065

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

See Solution

Problem 22066

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

See Solution

Problem 22067

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

See Solution

Problem 22068

Mark earns \$1,650/month. New job pays \$9.80/hour + overtime. Find overtime hours to match weekly earnings.

See Solution

Problem 22069

Solve the equation $2x = 2$ .

See Solution

Problem 22070

Find the number of digits in the product of $2^{101}$ and $5^{99}$ .

See Solution

Problem 22071

Find the sum of squares of even numbers: $2^{2}+4^{2}+6^{2}+\cdots+100^{2}$ . Use $1^{2}+2^{2}+\cdots+n^{2}=\frac{1}{6} n(n+1)(2 n+1)$ .

See Solution

Problem 22072

Find the value of $abc$ given $2^{a}=3$ , $3^{b}=7$ , and $7^{c}=64$ .

See Solution

Problem 22073

Tina, Dawn, and Harry have a total of \$ 175. If Tina has 3 times Dawn's amount and Dawn has 2 times Harry's, find their amounts.

See Solution

Problem 22074

For the function $f(x)=x^{2}+4 x$ , find its vertex, axis of symmetry, and intercepts. Does it open up or down?

See Solution

Problem 22075

A 10-foot board is cut into 3 pieces. One piece is 1 foot longer than the shortest and 2 feet shorter than the longest. Find the lengths.

See Solution

Problem 22076

Analyze the function $f(x)=x^{2}+8x$ : find if it opens up/down, vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts.

See Solution

Problem 22077

Find x-intercepts, y-intercept, domain, range of $f(x) = x^2 + 4x$ , and graph the function.

See Solution

Problem 22078

Graph the quadratic function $f(x)=x^{2}+8x$ : find vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts. Does it open up or down?

See Solution

Problem 22079

Find the value of $c$ where $c=\sqrt{105+24 \sqrt{6}}-\sqrt{105-24 \sqrt{6}}$ is rational.

See Solution

Problem 22080

For the function $f(x)=x^{2}-8x$ , find the x-intercepts and y-intercept. What are they?

See Solution

Problem 22081

For the function $f(x)=x^{2}-8 x$ , determine if it opens up or down, and find its vertex and intercepts.

See Solution

Problem 22082

Miss Ma's income rises by 6% from \$420000. Calculate the percentage change in her salaries tax payable with fixed allowances.

See Solution

Problem 22083

Find the 2014 annual rates for a flat with a 2.5% yearly increase, starting from \$5200 per quarter in 2008.

See Solution

Problem 22084

Terri has $\frac{1}{4}$ of her father's and $\frac{1}{7}$ of her grandfather's Canadian stamps. Together they have 120 stamps. How many does each have?

See Solution

Problem 22085

Miss Lee's tax is \$4500. Find her net chargeable income using the tax rates: 2\% for \$40000, 7\% for next \$40000, 12\% for next \$40000, and 17\% for the rest. Round to the nearest dollar.

See Solution

Problem 22086

For the function $f(x)=-x^{2}+8x$ , find its vertex, axis of symmetry, and intercepts. Does it open up or down?

See Solution

Problem 22087

Dimitri's car gets 21 miles/gallon with a 12-gallon tank. Can he drive 202.4 miles? Show calculations and use dimensional analysis.

See Solution

Problem 22088

For the function $f(x)=-x^{2}+8x$ , find the $y$ -intercept and state the domain and range in interval notation.

See Solution

Problem 22089

Solve for the number in the equation: 9 - $\frac{x}{7} = -5$ .

See Solution

Problem 22090

Graph the function $f(x)=-x^{2}+6x$ : determine if it opens up or down, and find the vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts.

See Solution

Problem 22091

Demuestra que el producto de cuatro enteros consecutivos más uno es un cuadrado. Escribe 3 ejemplos. $n(n+1)(n+2)(n+3)+1$

See Solution

Problem 22092

For the function $f(x)=-x^{2}+8x$ , find the $x$ -intercepts, $y$ -intercept, domain, and range.

See Solution

Problem 22093

A car worth \ $22,500 decreases by \$3200 per year for 6 years. Define$ V(x) $for$ 0 \leq x \leq 6 $and find$ V(3)$.

See Solution

Problem 22094

Compare the sums $O = 3 + 5 + 7 + \ldots + 103$ and $E = 4 + 6 + 8 + \ldots + 104$ . Which is greater and by how much?

See Solution

Problem 22095

Find $a$ , $b$ , $c$ , and $d$ in a 3x3 magic square where each row, column, and diagonal sums to 45.

See Solution

Problem 22096

Graph the pool emptying rate function to find the time to empty it. Transform $f(x) = |x - 1| + 3$ with a horizontal shrink by $\frac{1}{3}$ .

See Solution

Problem 22097

The pool drains at 3 inches/hour. After 5 hours, the depth is 32 inches. Find the point-slope equation.

See Solution

Problem 22098

Solve the equation $|5x - 2| = |5x + 4|$ .

See Solution

Problem 22099

Graph the equation $y-32=-3(x-5)$ to find how long it takes to empty the pool.

See Solution

Problem 22100

Find the total distance driven after 3.5 more hours if $y=65x+80$ and $x$ is the driving time in hours.

See Solution

1 ...218 219 220 221 222 223 224 ...313

Algebra

Problem 22001

Given cell phone sales and prices for Q1 2009 and 2010, find the demand function q(p)q(p)q(p). Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

Problem 22002

Problem 22003

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

Problem 22004

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 22005

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

Problem 22006

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 22007

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 22008

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 22009

List the four steps to solve a linear equation from these options: isolate variable, check solution, collect terms, simplify.

Problem 22010

Next week, you charge \$9 per guest with 39 guests on average. (a) Find the demand equation q(p)=q(p)=q(p)=. (b) Find revenue R(p)=R(p)=R(p)=. (c) Costs C(p)=−25.5p+488C(p)=-25.5p+488C(p)=−25.5p+488, find profit P(p)=P(p)=P(p)=. (d) Determine break-even entrance fees p=p=p=.

Problem 22011

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

Problem 22012

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 22013

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

Problem 22014

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

Problem 22015

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 22016

RideEm Bicycles produces 170 bikes for \10,300and190bikesfor$10,900.Findthecostfunction10,300 and 190 bikes for \$10,900. Find the cost function 10,300and190bikesfor$10,900.FindthecostfunctionC(x)$ and fixed/variable costs.

Problem 22017

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

Problem 22018

Solve for xxx in the equation: 2+log⁡3(2x+5)−log⁡3x=42+\log _{3}(2x+5)-\log _{3}x=42+log3​(2x+5)−log3​x=4.

Problem 22019

Find the exact value of ln⁡e6\ln \mathrm{e}^{\sqrt{6}}lne6​ using logarithm properties without a calculator.

Problem 22020

Rewrite the expression as a sum/difference of logarithms: log⁡6(x−1x4)\log_{6}\left(\frac{x-1}{x^{4}}\right)log6​(x4x−1​).

Problem 22021

Find the domain of the function f(x)=log⁡3(x−9)2f(x)=\log _{3}(x-9)^{2}f(x)=log3​(x−9)2.

Problem 22022

Find the exact value of log⁡211⋅log⁡118\log _{2} 11 \cdot \log _{11} 8log2​11⋅log11​8 using logarithm properties without a calculator.

Problem 22023

Convert the logarithm log⁡214\log _{2} \frac{1}{4}log2​41​ to its equivalent exponential form.

Problem 22024

Find log⁡bB2\log_{b} B^{2}logb​B2 if log⁡bA=5\log_{b} A = 5logb​A=5 and log⁡bB=−4\log_{b} B = -4logb​B=−4.

Problem 22025

Solve for xxx in the equation: log⁡3(x+4)=−2\log _{3}(x+4)=-2log3​(x+4)=−2.

Problem 22026

Convert the exponential equation 53=1255^{3}=12553=125 to a logarithmic form.

Problem 22027

Find log⁡bAB\log_{b} ABlogb​AB given that log⁡bA=5\log_{b} A=5logb​A=5 and log⁡bB=−2\log_{b} B=-2logb​B=−2.

Problem 22028

Rewrite the exponential equation 43=x4^{3}=x43=x using logarithms.

Problem 22029

Find the value of log⁡91729\log _{9} \frac{1}{729}log9​7291​.

Problem 22030

Find the exact value of 7log⁡70.4997^{\log_{7} 0.499}7log7​0.499 using logarithm properties without a calculator.

Problem 22031

Rewrite the exponential equation 45/2=324^{5 / 2}=3245/2=32 using a logarithm.

Problem 22032

Rewrite the expression 3−33^{-3}3−3 using a logarithm.

Problem 22033

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

Problem 22034

Solve the equation: e3x=5e^{3 x} = 5e3x=5

Problem 22035

Convert the logarithmic expression to an exponent: ln⁡1e4=−4\ln \frac{1}{e^{4}}=-4lne41​=−4.

Problem 22036

Find the value of ln⁡e4\ln e^{4}lne4.

Problem 22037

Solve the equation 3x+8=73^{x+8}=73x+8=7 and express the solution using natural logarithms.

Problem 22038

Calculate the value of log⁡8164\log _{8} \frac{1}{64}log8​641​.

Problem 22039

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

Problem 22040

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

Given cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

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?

Next week, you charge \$9 per guest with 39 guests on average.
(a) Find the demand equation $q(p)=$ . (b) Find revenue $R(p)=$ . (c) Costs $C(p)=-25.5p+488$ , find profit $P(p)=$ . (d) Determine break-even entrance fees $p=$ .

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

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

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

RideEm Bicycles produces 170 bikes for \ $10,300 and 190 bikes for \$10,900. Find the cost function$ C(x)$ and fixed/variable costs.

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 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: $\log_{3} 6 - \log_{3} 2$ .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solve the equation $2x = 2$ .

Find the number of digits in the product of $2^{101}$ and $5^{99}$ .

Find the sum of squares of even numbers: $2^{2}+4^{2}+6^{2}+\cdots+100^{2}$ . Use $1^{2}+2^{2}+\cdots+n^{2}=\frac{1}{6} n(n+1)(2 n+1)$ .

Find the value of $abc$ given $2^{a}=3$ , $3^{b}=7$ , and $7^{c}=64$ .

For the function $f(x)=x^{2}+4 x$ , find its vertex, axis of symmetry, and intercepts. Does it open up or down?