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List the set of integers such that -3 < x < 5.

ANSWER: The set of integers is {-2, -1, 0, 1, 2, 3, 4}

I hope the above steps and explanation were helpful.

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Step 1. Multiply 4 to both sides of the equation to get rid of denominator





Step 2. Add 28 to both sides to get x-terms on left side and numbers on right side of equation.





Step 3. Divide 18 to both sides of the equation to get x.





Step 4. So answer is x=20.

I hope the above steps and explanation were helpful.

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Factor the polynomial



Step 1. Factor out 3s in the three terms. That is,

Step 2. Need to find two integers m and n such that their product is mn=5*6=30 and their sum is m+n=-7.

Step 3. After several tries, the numbers are no numbers that satisfy step 2. Note if equation was then the numbers would be -10 and 3 for the quadratic expression. We can factor with grouping where and

.

Then the factor for this changed problem yields:


Step 4. We can use the quadratic formula given as



where a=5, b=-7 and c=6.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -71 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -71 is + or - . The solution is Here's your graph:

Step 5. We have imaginary results for this example and there are no real solutons.

I hope the above steps and explanation were helpful.

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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: k=19. Graphical form: Equation was fully solved. Text form: 10k-9=9k+10 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 10k-9=9k+10 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved these terms to the left , It becomes . Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to k-19 =0 It becomes . Result: This is an equation! Solutions: k=19. Universal Simplifier and Solver Done!

I hope the above steps and explanation were helpful.

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True or False:
All integers are irrational numbers? False. Integers can be expressed as a fraction. Example 5=5/1.

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Explain the difference between a rational and an irrational number.

A rational number can be express as a fraction or ratio of real numbers. An irrational number cannot be expressed as a fraction or its decimal equivalent goes on forever like or

I hope the above explanation was helpful.

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A man has 25 coins, all dimes and quarters. If he has $4.60 total, how many of each type of coin does he have? (Solve using a linear equation. No credit for guessing).

Step 1. Let x be the number of dimes and let 25-x be the number of quarters.

Step 2. Let 0.10x be the total cost for x number of dimes

Step 3. Let 0.25(25-x) be the total cost for 25-x number of quarters.

Step 4. Since the man has $4.60, then 4.60=0.10x+0.25(25-x). Solving for x yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

With x=11 , then 25-x=14. Check total: 11*0.10+14*0.25=4.60 which is a true statement.

Step 5. ANSWER: The number of dimes is 11 and the number of quarters is 14.

I hope the above steps and explanation were helpful.

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The length of a diagonal of a rectangle is 34 feet. If the length of one of its sides is 16 feet, what is the length of the other side?

Step 1. Let a be the unknown side and 16 is the other side.

Step 2. Use the Pythagorean Theorem for this example which states that the sum of the squares of the legs is the square of the hypotenuse. The hypotenuse c is the diagonal of 34 feet and the legs are a and 16 feet for this example or where a and b are the legs of a right triangle.

Step 3. Then solve for a.













Step 4. ANSWER: The length of the other side is 30 feet.

I hope the above steps and explanation were helpful.

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Two cards are drawn in succession without replacement from a standard deck of 52 playing cards. What is the probability that the first card drawn was a diamond given that the second card drawn was not a diamond? (Round your answer to four decimal places.)

Step 1. Let P(A) be the probability of a diamond and P(B) is not a diamond or 1-P(A) for the first card. For the first card P(A)=13/52=0.25 and P(B)=1-P(A)=0.75

Step 2. Let Probability of a diamond occurring in the second card given that probaility of diamond occurring in the first card be given as P(A|B)= P(A and B)/P(B).

Step 3. The probability of a diamond in the second card is P(A and B)=13/51.

Step 4. P(A|B)=P(A and B)/P(B)= (13/51)/((39/52)=0.3399

Step 5. Answer is P(is a diamond on second card |not a diamond on first card)=P(A|B)=0.3399

I hope the above steps were helpful.

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Thank you for your time. We are looking for the circumference length for a 60ft. circle. I've forgotten the formula. Thank's again, Scott

I assume 60 ft is the diameter. Then the circumference C is or where , d is the diameter and r is the radius.

For your example, or ft

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-7 and 8 means -7+8=15

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The perimeter of an equilateral triangle is 21 inches. find the length of the altitude.

Step 1. An equilateral triangle has three equal sides. Let c be the side.

Step 2. Perimeter P means adding up the three sides of the triangle or P=c+c+c=3c

Step 3. Then

Step 4. The altitude a is one of the sides of a right triangle inside the equilateral triangle while the other leg is b= inches.

Step 5. The Pythagorean theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse or









inches

Step 5. ANSWER: Altitude is 6.06 inches.

I hope the above steps were helpful.

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Step 1. Add three to both sides of the equation





Step 2.Divide by five to both sides of the equation





Step 3. Take the square root to both sides of the equation

and ANSWER

I hope the above steps were helpful.

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The perimeter of a square is 20 cm. Find the length of the diagonal.

Step 1. We'll use the Pythagorean Theorem which states that the sum of the square of the sides or legs of a right triangle is equal to the square of the hypotenuse or and for this example, c is the diagonal and a=b is the side since it's a square.

Step 2. So with a=b then or c=a*sqrt(2) and

Step 3. Perimeter P means that we add up all the form sides or or . If P=20, then or cm

Step 4. The diagonal is 7.07 cm.

I hope the above steps were helpful.

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The perimeter of a square is 36 cm. Find the length of the diagonal.

Step 1. We'll use the Pythagorean Theorem which states that the sum of the square of the sides or legs of a right triangle is equal to the square of the hypotenuse or and for this example, c is the diagonal and a=b is the side since it's a square.

Step 2. So with a=b then or c=a*sqrt(2) and

Step 3. Perimeter P means that we add up all the form sides or or . If P=36, then or cm

Step 4. The diagonal is 12.73 cm.

I hope the above steps were helpful.

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The diagonal of a square is 26 inches. Find the length of a side and the perimeter.

Step 1. We'll use the Pythagorean Theorem which states that the sum of the square of the sides or legs of a right triangle is equal to the square of the hypotenuse or and for this example, c is the diagonal and a=b is the side since it's a square.

Step 2. So with a=b then or c=a*sqrt(2).

Step 3. Since c=26 inches then or inches.

Step 4. Perimeter P means that we add up all the form sides or or P=73.39 inches.

Step 5. The side is 18.38 inches and the perimeter is 93.39 inches.

I hope the above steps were helpful.

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In Triangle ABC, Angle B is 8 less then one-half of angle A and angle C is 28 larger than angle A. Find the measure of the three angles of the triangle.

Step 1. The three angles of triangle add up to 180 degrees.

Step 2. Given angle , then let be angle B, and let be angle C

Step 3. Then, add up all the angle to get 180 degrees or . Multiply by 2 to both sides of equation to get rid of denominator.









With , then and

Then A+B+C=180 as a check. So 64+24+92=180 or 180=180 which is a true statement.

Step 4. The angles are A=64 degrees, B=24 degrees, and C=92 degrees.

I hope the above steps were helpful.

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The measure of an angle is 12 degrees less than the measure of its supplement. Find the measure of the angle and the measure of its supplement.

Step 1. Supplementary angles means that two angles add up to 180 degrees.

Step 2. Let x be one angle and 180-x be its supplementary angle.

Step 3. Since the measure of an angle is 12 degrees less than the measure of its supplement, then x=180-x-12 or 2x=168 or x=84 and 180-x=96.

Step 4. ANSWER: The angle is 84 degrees and its supplementary angle is 96 degrees.

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Determine which angle is such that its supplement is five times the angle itself.

Step 1. Supplementary angles means that two angles add up to 180 degrees.

Step 2. Let x be one angle and 180-x be it supplementary angle.

Step 3. Let 5x be five time the angle itself.

Step 4. Since its supplement is five times the angle itself, then 180-x=5x or 180=6x or x=30 degrees and 5x=150 degrees.

Step 5. Answer is 30 degrees and its supplement is 150 degrees.

I hope the above steps were helpful.

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One number is 8 less than another number. Find the numbers if three times the smaller number is six less than two times the larger number

Step 1. Let x be the smaller number and x+8 be the larger number

Step 2. Let 3x be three times the smaller number.

Step 3. Let 2(x+8) be two times the larger number.

Step 4. Since three times the smaller number is six less than two times the larger number, then

Step 5. Solving the equation in Step 4 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=10. Graphical form: Equation was fully solved. Text form: 3x=2*(x+8)-6 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 3x=2*(x+8)-6 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved these terms to the left , It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to x-10 =0 It becomes . Result: This is an equation! Solutions: x=10. Universal Simplifier and Solver Done!

With x=10 , then x+8=18

Step 6. ANSWER: The numbers are 10 and 18.

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Find the measure of an angle if its measure is 3 degrees less than twice the measure of its complement.

Step 1. Complementary angles means that two angles add up to 90 degrees.

Step 2. Let x be the angle and 90-x be its complementary angle

Step 3. Let 2(90-x) be twice the complementary angle

Step 4. Since the angle x is 3 degrees less than twice the measure of its complement, then .

Step 5. Solving the equation in Step 4 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=59. Graphical form: Equation was fully solved. Text form: x=2*(90-x)-3 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x=2*(90-x)-3 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left , It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Solved linear equation equivalent to 3*x-177 =0 It becomes . Result: This is an equation! Solutions: x=59. Universal Simplifier and Solver Done!

Step 6. ANSWER: The angle is 59 degrees

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If one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110. Find the measure of the angle.

Step 1. Let x be the angle.

Step 2. Complementary angles means two angles add up to 90 degrees and supplementary angles means two angles add up to 180 degrees.

Step 3. Let 90-x be the complementary angle of x and 180-x be the supplementary angle of x.

Step 4. Let be one half of the complementary angle.

Step 5. Let be 3/4 of the supplementary angle.

Step 6. Adding Steps 4 and 5 will be 110 degrees as given by the problem statement or in equation form we have



Multiply by 4 to both sides of the equation toget rid of denominators






Step 7. Solving for x yields the following steps:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=56. Graphical form: Equation was fully solved. Text form: 2*(90-x)+3*(180-x)=440 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 2*(90-x)+3*(180-x)=440 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved to the right of expression It becomes . Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Removed extra sign in front of It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Solved linear equation equivalent to -5*x+280 =0 It becomes . Result: This is an equation! Solutions: x=56. Universal Simplifier and Solver Done!

Step 8. ANSWER: The angle is 56 degrees.

I hope the above steps were helpful.

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The sum of three numbers is 40. One number is 5 more than the second number. It is twice the third number. What are the numbers.

Step 1. Let x be one number, 5+x be the second number, and x/2 is the third number (since the number is twice the third number)

Step 2. The the sum is x+5+x+x/2=40 or

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=14. Graphical form: Equation was fully solved. Text form: x+5+x+x/2=40 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x+5+x+x/2=40 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved to the right of expression It becomes . Look at . Eliminated similar terms ,, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor , It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 2.5*x-35 =0 It becomes . Result: This is an equation! Solutions: x=14. Universal Simplifier and Solver Done!

With x=14, then 5+x=19 and x/2=14/2=7.

Step 3. ANSWER: The numbers are 14, 19, and 7.

I hope the above steps were helpful.

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Determine which angle is such that its supplement is fourteen times the angle itself.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Let x be one angle and 14x be the supplementary angle.

Step 3. Then x+14x=180 degrees or 15x=180 or x=12 degrees. Also 14x=168.

Step 4. The supplementary angles are 14 degrees and 168 degrees.

I hope the above steps were helpful.

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Suppose that the width of a rectangle is 3 centimeters less than two-thirds of its length. The perimeter of the rectangle is 114 centimeters. Find the length and width of the rectangle.

Step 1. Let be the length and let be the width

Step 2. Perimeter P means adding up all four sides of a rectangle.

Step 3. Then,

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=36. Graphical form: Equation was fully solved. Text form: x+x+(2x/3-3)+(2x/3-3)=114 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x+x+(2x/3-3)+(2x/3-3)=114 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Remove unneeded parentheses around terms , It becomes . Look at . Remove unneeded parentheses around terms , It becomes . Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms ,,, replacing them with It becomes . Look at . Multiplied numerator integers It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor , It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 3.33333333333333*x-120 =0 It becomes . Result: This is an equation! Solutions: x=36. Universal Simplifier and Solver Done!

With , then is

Step 4. The length is 36 cm and width is 21 cm

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Step 1. Square both sides













Step 2. Square both sides of equation







Step 3. Use quadratic formula given as



where a=1, b=-46 and c=205

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=1296 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 41, 5. Here's your graph:

I hope the above steps were helpful.

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SOLVE AND CHECK











Check: 8*(9/8)+4=9+4=13=13 which is a true statement.











Check: 7*(16/7)-16=0=0 which is a true statement.

5A2/3=3 Don't understand this one. Is it ? Please clarify and resubmit this one problem.

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Please enter your one problem and resubmit.

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Vivian is 5 years older than Carmen. When Vivian's age is doubled and then subtracted from four times Carmen's age, the result is Carmen's present age, increased by 10. How old is each?

Step 1. Let x be Carmen's age and let x+5 be Vivian's age.

Step 2. Let 2(x+5) be doubled Vivian's age and let 4x be 4 times Carmen's age.

Step 3. Now translate "When Vivian's age is doubled and then subtracted from four times Carmen's age, the result is Carmen's present age, increased by 10." into an algebraic expression, given as:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=20. Graphical form: Equation was fully solved. Text form: 4x-2*(x+5)=x+10 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 4x-2*(x+5)=x+10 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved these terms to the left , It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Eliminated similar terms , replacing them with It becomes . Look at . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to x-20 =0 It becomes . Result: This is an equation! Solutions: x=20. Universal Simplifier and Solver Done!

With x=20 , then x+5=25

Step 4. ANSWER: Carmen is 20 and Vivian is 25

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

You can put this solution on YOUR website!
One of two complementary angles added to one-half the other yields 72. Find half the measure of the larger angle.

Step 1. Two angles are complementary when they add up to 90 degrees.

Step 2. Let x be one angle and 90-x be its complementary angle.

Step 3. Let x/2 be one-half of one complementary angle

Step 4. One of two complementary angles added to one-half the other yields 72. Translating this problem into an equation and solving yields



Multiply by 2 to both sides of equation to get rid of denominator.







Add x-144 to both sides to solve for x.





Step 5. The complementary angle of 36 is 90-36=54. One-half of 54 is 27.

Step 6. ANSWER: Half the measure of the larger angle is 27 degrees.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

You can put this solution on YOUR website!
Charles is 8 years older than three times Tom's age. When Charles's age is subtracted from Tom's age, the number obtained is Tom's age 14 years ago. How old is each?

Step 1. Let x be Tom's age and let 3x+8 be Charles' age.

Step 2. When Charles's age is subtracted from Tom's age, the number obtained is Tom's age 14 years ago. We have Charles' age - Tom's Age = 14 or













With x=3, then 3x+8=9+8=17. Note the difference is 17-3=14 which is a true statement based on the problem statement.

Step 3. ANSWER. Tom is 3 years old and Charles is 17 years old.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J