# Blog

• ## Factor 4b^2-15b+9

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .Tap for more steps…Factor out of .Rewrite as plus Apply the distributive property.Factor out the greatest common factor from each group.Tap for more steps…Group the first two terms and the last […]

• ## Solve by Substitution y=4x+1 , 2y-4x=14

, Replace all occurrences of with in each equation.Tap for more steps…Replace all occurrences of in with .Simplify .Tap for more steps…Simplify each term.Tap for more steps…Apply the distributive property.Multiply by .Multiply by .Subtract from .Solve for in the first equation.Tap for more steps…Move all terms not containing to the right side of the equation.Tap […]

• ## Find Where Undefined/Discontinuous (3z)/(z^2-1)

Set the denominator in equal to to find where the expression is undefined.Solve for .Tap for more steps…Add to both sides of the equation.Take the square root of both sides of the equation to eliminate the exponent on the left side.The complete solution is the result of both the positive and negative portions of the […]

• ## Find the Inverse Function f(x)=5/2x-2

I am unable to solve this problem.

• ## Find the Vertex f(x)=4x^2-8x+2

Rewrite the equation in term of and .Rewrite the equation in vertex form.Tap for more steps…Complete the square for .Tap for more steps…Use the form , to find the values of , , and .Consider the vertex form of a parabola.Substitute the values of and into the formula .Simplify the right side.Tap for more steps…Cancel […]

• ## Rewrite in Standard Form (12i)/(1+i)

Multiply the numerator and denominator of by the conjugate of to make the denominator real.Multiply.Tap for more steps…Combine.Simplify the numerator.Tap for more steps…Apply the distributive property.Multiply by .Multiply .Tap for more steps…Multiply by .Raise to the power of .Raise to the power of .Use the power rule to combine exponents.Add and .Simplify each term.Tap for […]

• ## Solve for X X = log base 5 of 1

Logarithm base of is .

• ## Evaluate -12/-3

Divide by .Multiply by .

• ## Solve Using the Quadratic Formula -9=9x^2+2x

Move all the expressions to the left side of the equation.Tap for more steps…Subtract from both sides of the equation.Subtract from both sides of the equation.Use the quadratic formula to find the solutions.Substitute the values , , and into the quadratic formula and solve for .Simplify.Tap for more steps…Simplify the numerator.Tap for more steps…Raise to […]

• ## Evaluate Using Scientific Notation (2.4*10^11)/(5*10^6)

Divide using scientific notation.Tap for more steps…Group coefficients together and exponents together to divide numbers in scientific notation.Divide by .Subtract the exponent from the denominator from the exponent of the numerator for the same baseMultiply by .Subtract from .Write in proper scientific notation.

• ## Write in y=mx+b Form 1-(3y-4x)/2=7x+3

The slope-intercept form is , where is the slope and is the y-intercept.Rewrite in slope-intercept form.Tap for more steps…Simplify .Tap for more steps…Combine into one fraction.Tap for more steps…Write as a fraction with a common denominator.Combine the numerators over the common denominator.Simplify the numerator.Tap for more steps…Apply the distributive property.Multiply by .Multiply by .Multiply both […]

• ## Multiply ( square root of p+ square root of q)( square root of p- square root of q)

Expand using the FOIL Method.Tap for more steps…Apply the distributive property.Apply the distributive property.Apply the distributive property.Simplify terms.Tap for more steps…Combine the opposite terms in .Tap for more steps…Reorder the factors in the terms and .Add and .Add and .Simplify each term.Tap for more steps…Multiply .Tap for more steps…Raise to the power of .Raise to […]

• ## Simplify square root of 198

Rewrite as .Tap for more steps…Factor out of .Rewrite as .Pull terms out from under the radical.The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Solve by Factoring 3x^3+x^2-12x-4=0

Factor out the greatest common factor from each group.Tap for more steps…Group the first two terms and the last two terms.Factor out the greatest common factor (GCF) from each group.Factor the polynomial by factoring out the greatest common factor, .Rewrite as .Factor.Tap for more steps…Since both terms are perfect squares, factor using the difference of […]

• ## Convert to Radical Form (-81)^(1/4)

If is a positive integer that is greater than and is a real number or a factor, then .Use the rule to convert to a radical, where , , and .

• ## Simplify 3 square root of 32

Rewrite as .Tap for more steps…Factor out of .Rewrite as .Pull terms out from under the radical.Multiply by .The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Factor 5z^2+10z

Factor out of .Factor out of .Factor out of .

• ## Simplify (2b)^-5

Rewrite the expression using the negative exponent rule .Simplify the denominator.Tap for more steps…Apply the product rule to .Raise to the power of .

• ## Convert to Interval Notation 3(x^2-1)>-8x

Simplify .Tap for more steps…Apply the distributive property.Multiply by .Add to both sides of the inequality.Convert the inequality to an equation.Factor by grouping.Tap for more steps…Reorder terms.For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .Tap for more steps…Factor out […]

• ## Solve for x 2/(x-4)=16/(x^2-16)

Factor each term.Tap for more steps…Rewrite as .Since both terms are perfect squares, factor using the difference of squares formula, where and .Find the LCD of the terms in the equation.Tap for more steps…Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.The LCM […]

• ## Evaluate 2 square root of 28-5 square root of 63

Simplify each term.Tap for more steps…Rewrite as .Tap for more steps…Factor out of .Rewrite as .Pull terms out from under the radical.Multiply by .Rewrite as .Tap for more steps…Factor out of .Rewrite as .Pull terms out from under the radical.Multiply by .Subtract from .The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Find the Behavior (Leading Coefficient Test) -3x^4-6x^3

Write as a function.Identify the degree of the function.Tap for more steps…Identify the exponents on the variables in each term, and add them together to find the degree of each term.The largest exponent is the degree of the polynomial.Since the degree is even, the ends of the function will point in the same direction.EvenIdentify the […]

• ## Multiply (x+8)(x-6)

Expand using the FOIL Method.Tap for more steps…Apply the distributive property.Apply the distributive property.Apply the distributive property.Simplify and combine like terms.Tap for more steps…Simplify each term.Tap for more steps…Multiply by .Move to the left of .Multiply by .Add and .

• ## Evaluate 8/17

The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Find the Domain (x+5)^2+(y-6)^2=36

Subtract from both sides of the equation.Take the square root of each side of the equation to set up the solution for Remove the perfect root factor under the radical to solve for .Simplify the right side of the equation.Tap for more steps…Rewrite as .Since both terms are perfect squares, factor using the difference of […]

• ## Find the Domain square root of 4x-8

Set the radicand in greater than or equal to to find where the expression is defined.Solve for .Tap for more steps…Add to both sides of the inequality.Divide each term by and simplify.Tap for more steps…Divide each term in by .Cancel the common factor of .Tap for more steps…Cancel the common factor.Divide by .Divide by .The […]

• ## Factor x^2-3x+2.25

Rewrite as .Check that the middle term is two times the product of the numbers being squared in the first term and third term.Rewrite the polynomial.Factor using the perfect square trinomial rule , where and .

• ## Simplify (2y^3)^2

Apply the product rule to .Raise to the power of .Multiply the exponents in .Tap for more steps…Apply the power rule and multiply exponents, .Multiply by .

• ## Factor over the Complex Numbers 11x^4-x^3-33x^2+575x-52

Factor using the rational roots test.Tap for more steps…If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.Find every combination of . These are the possible roots of the polynomial function.Substitute and simplify the expression. […]

• ## Subtract the Expressions x^2-5x+6 , -x

, Subtract the second expression from the first expression .Multiply .Tap for more steps…Multiply by .Multiply by .Add and .

• ## Find the Equation Using Point-Slope Formula (-2,-6) , (0,-2)

, Find the slope of the line between and using , which is the change of over the change of .Tap for more steps…Slope is equal to the change in over the change in , or rise over run.The change in is equal to the difference in x-coordinates (also called run), and the change in […]

• ## Solve for x 2x-1=5

Move all terms not containing to the right side of the equation.Tap for more steps…Add to both sides of the equation.Add and .Divide each term by and simplify.Tap for more steps…Divide each term in by .Cancel the common factor of .Tap for more steps…Cancel the common factor.Divide by .Divide by .

• ## Plot 6y-2>=7

Move all terms not containing to the right side of the inequality.Tap for more steps…Add to both sides of the inequality.Add and .Divide each term by and simplify.Tap for more steps…Divide each term in by .Cancel the common factor of .Tap for more steps…Cancel the common factor.Divide by .Cancel the common factor of and .Tap […]

• ## Find the Range f(x) = square root of mx

The range of an even indexed radical starts at its starting point and extends to infinity.Interval Notation:Set-Builder Notation:

• ## Simplify (4x^2y^5)^-2

Rewrite the expression using the negative exponent rule .Simplify the denominator.Tap for more steps…Apply the product rule to .Apply the product rule to .Raise to the power of .Multiply the exponents in .Tap for more steps…Apply the power rule and multiply exponents, .Multiply by .Multiply the exponents in .Tap for more steps…Apply the power rule […]

• ## Factor 4x^2-36y^2

Factor out of .Tap for more steps…Factor out of .Factor out of .Factor out of .Rewrite as .Since both terms are perfect squares, factor using the difference of squares formula, where and .Factor.Tap for more steps…Multiply by .Remove unnecessary parentheses.

• ## Graph f(x)=1/2*(3)^x

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is .Horizontal Asymptote:

• ## Factor 2x^2+10x-48

Factor out of .Tap for more steps…Factor out of .Factor out of .Factor out of .Factor out of .Factor out of .Factor.Tap for more steps…Factor using the AC method.Tap for more steps…Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and […]

• ## Solve for x square root of 4-x = square root of 3x+4

To remove the radical on the left side of the equation, square both sides of the equation.Simplify each side of the equation.Tap for more steps…Multiply the exponents in .Tap for more steps…Apply the power rule and multiply exponents, .Cancel the common factor of .Tap for more steps…Cancel the common factor.Rewrite the expression.Simplify.Rewrite as .Tap for […]

• ## Factor 35x^2-39x-14

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .Tap for more steps…Factor out of .Rewrite as plus Apply the distributive property.Factor out the greatest common factor from each group.Tap for more steps…Group the first two terms and the last […]

• ## Find the Distance Between Two Points (1,-9) , (5,6)

, Use the distance formula to determine the distance between the two points.Substitute the actual values of the points into the distance formula.Simplify.Tap for more steps…Subtract from .Raise to the power of .Multiply by .Add and .Raise to the power of .Add and .The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Factor 8x^2-46xy+11y^2

Factor by grouping.Tap for more steps…For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .Tap for more steps…Reorder terms.Reorder and .Factor out of .Rewrite as plus Apply the distributive property.Remove unnecessary parentheses.Remove unnecessary parentheses.Factor out the greatest common factor from […]

• ## Find Three Ordered Pair Solutions f(x)=-3x-3

Rewrite the function as an equation.Choose any value for that is in the domain to plug into the equation.Choose to substitute in for to find the ordered pair.Tap for more steps…Remove parentheses.Simplify .Tap for more steps…Multiply by .Subtract from .Use the and values to form the ordered pair.Choose to substitute in for to find the […]

• ## Evaluate square root of 0.0036

The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Find Where Increasing/Decreasing f(x)=x^3-27x

Graph the polynomial in order to determine the intervals over which it is increasing or decreasing.Increasing on: Decreasing on:

• ## Convert to Regular Notation 2.2*10^5

Since the exponent of the scientific notation is positive, move the decimal point places to the right.

• ## Reduce the Fraction 31/60

The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Find the Function Rule table[[x,y],[1,5],[5,10],[9,15]]

Check if the function rule is linear.Tap for more steps…To find if the table follows a function rule, check to see if the values follow the linear form .Build a set of equations from the table such that .Calculate the values of and .Tap for more steps…Simplify each equation.Tap for more steps…Multiply by .Move to […]

• ## Find the GCF 24 , 14 , 21

, , Find the common factors for the numerical part:The factors for are .Tap for more steps…The factors for are all numbers between and , which divide evenly.Check numbers between and Find the factor pairs of where .List the factors for .The factors for are .Tap for more steps…The factors for are all numbers between […]

• ## Factor n^2+10n+24

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .Write the factored form using these integers.

• ## Find Three Ordered Pair Solutions x=9/2

Since is a vertical line, the x-values are for any value of y. Choose any three y-values to obtain three solutions.

• ## Evaluate log of 3*9

Multiply .Tap for more steps…Reorder and .Simplify by moving inside the logarithm.Raise to the power of .The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Convert to a Simplified Fraction 158%

Convert the percentage to a fraction by placing the expression over . Percentage means ‘out of ‘.Cancel the common factor of and .Tap for more steps…Factor out of .Cancel the common factors.Tap for more steps…Factor out of .Cancel the common factor.Rewrite the expression.

• ## Simplify cube root of -375x^6y^5

Rewrite as .Tap for more steps…Factor out of .Rewrite as .Rewrite as .Factor out .Move .Rewrite as .Add parentheses.Pull terms out from under the radical.

• ## Find the Degree -7x^4

The largest exponent is the degree of the polynomial.

• ## Find the Vertex -3x^2+12x-1

Set the polynomial equal to to find the properties of the parabola.Rewrite the equation in vertex form.Tap for more steps…Complete the square for .Tap for more steps…Use the form , to find the values of , , and .Consider the vertex form of a parabola.Substitute the values of and into the formula .Simplify the right […]

• ## Factor y^2-15y-54

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .Write the factored form using these integers.

• ## Factor 25b^2-35

Factor out of .Factor out of .Factor out of .

• ## Simplify square root of 15* square root of 6

Combine using the product rule for radicals.Multiply by .Rewrite as .Tap for more steps…Factor out of .Rewrite as .Pull terms out from under the radical.The result can be shown in multiple forms.Exact Form:Decimal Form:

• ## Factor x^2-ax-bx+ab

Factor out the greatest common factor from each group.Tap for more steps…Group the first two terms and the last two terms.Factor out the greatest common factor (GCF) from each group.Factor the polynomial by factoring out the greatest common factor, .

• ## Find the Range f(x)=(x-2)^2-1

Locate the vertex of the parabola.Tap for more steps…Use the vertex form, , to determine the values of , , and .Since the value of is positive, the parabola opens up.Opens UpFind the vertex .The range of a parabola that opens up starts at its vertex and extends to infinity.Interval Notation:Set-Builder Notation:

• ## Convert to a Fraction -0.4

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is number to the right of the decimal point, place the decimal number over . Next, add the whole number to the left of the decimal.Cancel the common factor of and .Tap for more steps…Factor out […]

• ## Find Any Equation Perpendicular to the Line y-1=1/3(x+2)

Choose a point that the perpendicular line will pass through.Solve .Tap for more steps…Simplify .Tap for more steps…Apply the distributive property.Combine and .Combine and .Move all terms not containing to the right side of the equation.Tap for more steps…Add to both sides of the equation.Write as a fraction with a common denominator.Combine the numerators over […]

• ## Factor y^3-11y^2+28y

Factor out of .Tap for more steps…Factor out of .Factor out of .Factor out of .Factor out of .Factor out of .Factor.Tap for more steps…Factor using the AC method.Tap for more steps…Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and […]

• ## Find the Median 55 , 70 , 80 , 90 , 105

, , , , Arrange the terms in ascending order.The median is the middle term in the arranged data set.

• ## Solve by Substitution Y=9+3Z , Y=58-4Z

, Eliminate the equal sides of each equation and combine.Solve for .Tap for more steps…Move all terms containing to the left side of the equation.Tap for more steps…Add to both sides of the equation.Add and .Move all terms not containing to the right side of the equation.Tap for more steps…Subtract from both sides of the […]

• ## Solve by Factoring 3x^2-5x=0

Factor out of .Tap for more steps…Factor out of .Factor out of .Factor out of .If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .Set the first factor equal to .Set the next factor equal to and solve.Tap for more steps…Set the […]

• ## Expand Using the Binomial Theorem (2a+6b)^3

Use the binomial expansion theorem to find each term. The binomial theorem states .Expand the summation.Simplify the exponents for each term of the expansion.Simplify each term.Tap for more steps…Multiply by .Apply the product rule to .Raise to the power of .Apply the product rule to .Rewrite using the commutative property of multiplication.Anything raised to is […]

• ## Round to the Nearest Thousandth 0.66666666

Find the number in the thousandth place and look one place to the right for the rounding digit . Round up if this number is greater than or equal to and round down if it is less than .

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