Solved problems

Percentages

Percentages solver →

What is 15% of 240?What is 20% of 50?45 is what percent of 180?What is the percentage change from 80 to 92?A jacket costs $64 and is 20% off. What is the sale price?What is 30% of 150?What number is 12 25% of?If a $75 item is discounted by 15%, what is the final price?A price rose from 200 to 250. What is the percentage increase?What is 7.5% of 1200?How many liters of 20% acid solution must be added to 10 liters of 50% acid solution to get a 30% solution?You invest $2000 at 5% interest compounded annually. What is it worth after 3 years?A car depreciates 15% a year. What is a $24,000 car worth after 2 years?

Fractions

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Convert 3/8 to a percentageAdd 2/3 + 1/4 and simplifyDivide 3/4 by 2/5 and simplifySimplify the fraction 84/126Multiply the mixed numbers 2 1/2 and 1 3/5Subtract 5/6 - 1/3What is 1/2 + 1/3 + 1/6?Convert 7/8 to a decimalSimplify 45/60Multiply 3/5 by 10/9Which is bigger, 5/8 or 7/12?

Factoring

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Factor x^2 - 5x + 6Factor x^2 + 7x + 12Factor 4x^2 - 9Factor 6x^2 + 11x - 10Factor x^3 - 8Factor x^2 - 16Factor x^3 + 27Factor completely 3x^3 - 12xFactor x^2 - 4x - 21Factor 9x^2 - 24x + 16Factor by grouping x^3 + 2x^2 - 4x - 8Factor 2x^2 + 7x + 3

Algebra

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Solve the inequality -3x + 7 <= 1Solve log base 2 of x plus log base 2 of (x - 2) = 3Solve 2^x = 32Solve sqrt(2x + 3) = xSolve the inequality 2x - 5 > 9Expand (2x + 3)^2Solve e^x = 7Solve 5^(x+1) = 125Simplify sqrt(50) + sqrt(18)Find the slope of the line through (2, 3) and (6, 11)Write the equation of the line through (1, 4) with slope -2Simplify (2x^3)(5x^4)

Equations

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Solve 3x - 7 = 11Solve 2(x - 4) = 3x + 1Solve 4x + 9 = 25Solve 5x - 3 = 2x + 12Solve x/3 + (x - 2)/4 = 3Solve 7 - 2(x - 3) = 15Solve 0.5x + 1.2 = 3.7Solve |2x - 5| = 7Solve 6x - 4 = 2x + 16Solve for x: 3x + 5 = 20Solve A = P(1 + rt) for rSolve 9 - x = 4x + 24Solve 2/x + 1 = 5Solve 5(2x - 1) = 3(x + 4)Solve (x + 1)/2 = (2x - 3)/5Solve by substitution y = x + 3 and 2x + y = 12Solve by elimination 3x + 4y = 10 and 2x - 4y = 5Solve 3(x + 2) - 4 = 2(x - 1) + 9A 10 ft ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?Two cars leave the same point travelling in opposite directions at 50 and 70 mph. How long until they are 360 miles apart?

Quadratics

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Solve x^2 + 4x - 5 = 0Solve x^2 - 5x + 6 = 0Solve x^2 = 16Solve x^2 - 6x + 13 = 0Solve 2x^2 - 4x - 3 = 0Solve x^2 - 6x + 2 = 0 by completing the squareSolve 3x^2 + 7x - 6 = 0Solve x^2 + 2x - 8 = 0Solve x^2 - 9 = 0Use the quadratic formula to solve 5x^2 - 3x - 2 = 0Find the vertex of y = x^2 - 6x + 5Find the roots of 2x^2 + 5x - 12 = 0Simplify (3x^2 y)^3Simplify (x^2 - 9)/(x^2 - x - 6)Find dy/dx by implicit differentiation for x^2 + y^2 = 25

Systems

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Solve the system 2x + y = 7 and x - y = 2Solve the system y = 2x - 1 and 3x + 2y = 12Solve the system x + y = 10 and x - y = 4Solve the system 3x + 2y = 16 and 5x - 2y = 0Solve the system x + y + z = 6, 2x - y + z = 3, x + 2y - z = 2Solve the system 4x - 3y = 11 and 2x + y = 3

Calculus

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Find the maximum value of f(x) = -x^2 + 4x + 1Find the critical points of f(x) = x^3 - 3x^2Find the average value of f(x) = x^2 on [0, 3]Determine whether the series sum of 1/n^2 convergesFind the Taylor series of e^x about x = 0 up to the x^3 termProve that the sum of the first n odd numbers equals n squared, using induction

Derivatives

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Find the derivative of x^3 * sin(x)Find the derivative of (2x + 1)^5Find the derivative of (x^2 + 1)/(x - 3)Find the derivative of e^(2x)Find the derivative of ln(x^2 + 1)Find the second derivative of x^3 - 4xFind the derivative of x^4 - 3x^2 + 7Find the derivative of sqrt(x)Find the derivative of x * ln(x)Find the derivative of tan(x)Find the equation of the tangent line to y = x^2 at x = 3

Integrals

Integrals solver →

Evaluate the integral of (2x + 1) dx from 0 to 3Integrate x * e^x dxIntegrate 2x(x^2 + 1)^4 dxIntegrate 1/(x^2 - 1) dx using partial fractionsIntegrate sin(x) dx from 0 to piIntegrate x^2 dxIntegrate 1/x dxFind the area under y = x^2 from 0 to 2Integrate cos(3x) dxIntegrate sec^2(x) dxIntegrate ln(x) dxEvaluate the integral of e^(-x) dx from 0 to infinity

Limits

Limits solver →

Find the limit as x approaches 0 of sin(x)/xFind the limit as x approaches 3 of (x^2 - 9)/(x - 3)Find the limit as x approaches infinity of (3x^2 + 2x)/(5x^2 - 1)Find the limit as x approaches 2 of (x^2 - 4)/(x - 2)Find the limit as x approaches infinity of 1/xFind the limit as x approaches 0 of (e^x - 1 - x)/x^2Find the limit as x approaches 0 of (1 - cos x)/xFind the limit as x approaches 4 of (sqrt(x) - 2)/(x - 4)

Statistics

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Find the mean, median and mode of 4, 8, 15, 16, 23, 42Find the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9What is the probability that two dice sum to 7?Find the median of 3, 7, 9, 12, 15How many ways are there to choose 3 items from 10?Find the variance of 10, 12, 23, 23, 16, 23, 21, 16What is the probability of getting exactly 2 heads in 3 coin flips?A test has a mean of 75 and a standard deviation of 8. What is the z-score for 91?How many permutations of 5 items taken 2 at a time?A bag has 3 red and 5 blue balls. Two are drawn without replacement. What is the probability both are red?

Word problems

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A train travels 180 miles in 2.5 hours. What is its average speed in miles per hour?One painter can paint a room in 6 hours and another in 4 hours. How long do they take together?The sum of three consecutive integers is 72. What are they?A rectangle has a perimeter of 36 cm and is twice as long as it is wide. Find its area.A recipe for 4 people needs 300 g of flour. How much is needed for 10 people?Sarah is 4 years older than twice her brother. Together they are 34. How old is each?