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Find x-intercept and y- intercept and graph



Step 1. x-intercept occurs when y=0 and y-intercept occurs when x=0.

Step 2. So at x=0 then





So y-intercept is 4 at point (0,4)

Step 3. At y=0 then





So x-intercept is -8/3 at point (-8/3,0)

Step 4. Here's the graph and note the x-intercept and y-intercept points on the graph.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -8/3 = -2.66666666666667. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -8/-2 = 4. Slope is -3/-2 = 1.5. Equation in slope-intercept form: y=1.5*x+4.

I hope the above steps were helpful.

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Dr J

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

Step 1. Let P be the perimeter of a square which means adding up all four sides.

Step 2. Let s be the side of a square.

Step 3 Then 4s=36 or s=9 centimeters after dividing by 4 to both sides of equation.

Step 4. Use Pythagorean Theorem to find diagonal which says that the sum of the square of the legs (=s^2+s^2=2s^2) is equal to square of the hypotenuse (diagonal in this case and letting d be the diagonal).









Step 5. ANSWER: The length of diagonal is centimeters

I hope the above steps were helpful.

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Two angles of a triangle measure 15 degree and 85 degree what is the measure for the third angle

Step 1. The sum of the angles in a triangle is equal to 180 degrees.

Step 2. Let x by the unknown third angle. Then





Step 3. Subtract 100 from both sides of equation to get x



ANSWER

I hope the above steps were helpful.

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A rectangle is 10 inches long and 8 inches wide, what is the length of the diagonal?

Step 1. Use the Pythagorean Theorem where the sum of the squares of the legs (length and width) is equal to the square of the hypotenuse (diagonal).

Step 2. Let d be the diagonal, then



ANSWER

I hope the above steps were helpful.

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What is the answer to this equation: 5x+10-6x+3=6-2x-2 and can you tell me how you solved it please and thank you

The following steps will solve the following equation:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=-9. Graphical form: Equation was fully solved. Text form: 5x+10-6x+3=6-2x-2 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 5x+10-6x+3=6-2x-2 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . 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 . Removed extra sign in front of It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Remove extraneous '1' from product It becomes . Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . 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 . 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+9 =0 It becomes . Result: This is an equation! Solutions: x=-9. Universal Simplifier and Solver Done!

I hope the above steps were helpful.

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Dr J

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The sum of four consecutive even integers is 276. Find the four integers.

Step 1. Let n be one even integer, n+2 the next consecutive integer, n+4 and n+6 are the next two consecutive integers.

Step 2. So n+n+2+n+4+n+6=276 as given by the problem statement.

Step 3. Solve using 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: n=66. Graphical form: Equation was fully solved. Text form: n+n+2+n+4+n+6=276 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( n+n+2+n+4+n+6=276 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . 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 4*n-264 =0 It becomes . Result: This is an equation! Solutions: n=66. Universal Simplifier and Solver Done!

Step 4. So the even integers are 66, 68, 70, 72. These integers add up to 276.

I hope the above steps were helpful.

And good luck in your studies!

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Here I assume you want to plot the line.

Step 1. Let's put it in slope-intercept form y=mx+b where m is the slope and b is the y-intercepts



Step 2. Subtract -2x from both sides of equation.







Step 3. Divide 3 to both sides of equation




Step 4. So y=-2x/3+2 where slope m=-2/3 and y-intercept b=2.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/2 = 3. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/3 = 2. Slope is -2/3 = -0.666666666666667. Equation in slope-intercept form: y=-0.666666666666667*x+2.

I hope the above steps were helpful.

And good luck in your studies!

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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: x=6. Graphical form: Equation was fully solved. Text form: x/2=3+(x-30/5) simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x/2=3+(x-30/5) ) 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 . Factors 30 and 5 have greatest common factor (GCF) of 5. Reducing fraction. 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 . 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 . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to -0.5*x+3 =0 It becomes . Result: This is an equation! Solutions: x=6. Universal Simplifier and Solver Done!

I hope the above steps were helpful.

And good luck in your studies!

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.

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Let's solve and simplify the above equation.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: x=6. Graphical form: Equation was fully solved. Text form: x/2=3+(x-30/5) simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x/2=3+(x-30/5) ) 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 . Factors 30 and 5 have greatest common factor (GCF) of 5. Reducing fraction. 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 . 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 . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to -0.5*x+3 =0 It becomes . Result: This is an equation! Solutions: x=6. Universal Simplifier and Solver Done!

I hope the above steps were helpful.

And good luck in your studies!

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.

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Dr J

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A Building AB, is observed across a street from the window of a house 7 metres above the ground. If the angle of elevation of the top of the building is 23degrees and the angle of depression of the foot of the building is 26degrees, calculate the height of the building.

Step 1. Let d be the distance to the building from the window. Given depression angle is 26 degrees and the height of the window is 7 meters, then we have the opposite side is 7 and the adjacent side is x. In this case, we have



metres

Step 2. Let x = be the height above seven metre reference, then total height of building h=x+. Then from the window looking at the building we have an angle of elevation of 23 degrees. Then the opposite side is x and the adjacent side is d. We have







Step 3. Then h=6.07+7=13.07 or 13.07 metres

I hope the above steps were helpful.

And good luck in your studies!

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Dr J

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1. x^3+216=0

Subtracting 216 from both sides of equation



Answer

2. 5x^3+30x^2+45x=0





where we have x=0, 5x+15=0 and x+3=0. Solving yields

x=0, x=-3 and x=-3, or solve quadratic equation using following steps,

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=0 is zero! That means that there is only one solution: . Expression can be factored: Again, the answer is: -3, -3. Here's your graph:

3. 1/x^2+8/x+15=0 Multiply by x^2 to get rid of denominator







where we have 5x+1=0 and 3x+1=0. Solving yields

So x=(-1/5) and x=(-1/3)

We can also use the quadratic formula as follows:

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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.2, -0.333333333333333. Here's your graph:

I hope the above steps were helpful.

And good luck in your studies!

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Is a circle a 'function' - it does not pass the vertical line test. tks!

Yes. You are correct. But it is an equation like centered at (0,0) or radius 1. So at x=0 then y has two possible values at +1 and -1.

Hope that was helpful!.

I hope the above steps were helpful.

And good luck in your studies!

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Find an expression or equation that is equivalent to the one given:

log(3)-log(3)9

Factor out log(3) to get

(1-9)log(3)=-8log(3)= -3.187 ANSWER

I hope the above steps were helpful.

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Dr J

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What is the 20th term for this set of numbers? 12, 19,26, 33

Step 1. Look for a pattern. In this case the next number is 7 greater than the previous number.

Step 2. Here's a formula for this set of numbers:

so if n=1 then expression is 12 if n=2 then expression is 19.

Step 3. Let n=20, then



Step 4. ANSWER: The 20th term is 145

I hope the above steps were helpful.

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Two angles are complementary. The larger of the two is 9 degrees more than twice the smaller. Find the 2 angles.

Step 1. Complementary angles is when 2 angles add up to 90 degrees.

Step 2. x is one angle and 2x+9

Step 3. Then x+2x+9=90

Step 4. Solve the above equation using 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=27. Graphical form: Equation was fully solved. Text form: x+2x+9=90 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x+2x+9=90 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION 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 3*x-81 =0 It becomes . Result: This is an equation! Solutions: x=27. Universal Simplifier and Solver Done!

Step 5. ANSWER: The angles are x=27 degrees and 2x+9=2(27)+9=63 degrees

I hope the above steps were helpful.

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The following steps will solve the above problem

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: a=0.666666666666667. Graphical form: Equation was fully solved. Text form: -4*(a+1)-3a=7*(2a-3)+3 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( -4*(a+1)-3a=7*(2a-3)+3 ) 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 . 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 . 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 . Expanded term by using associative property on 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 . 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 -21*a+14 =0 It becomes . Result: This is an equation! Solutions: a=0.666666666666667. Universal Simplifier and Solver Done!

ANSWER is or 0.666667

I hope the above steps were helpful.

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Step 1. Multiply by 10 to both sides of equation to get rid of denominator.







Step 2. add 14-3x to both sides of equation to isolate x on left side and number on right side of equation



ANSWER

I hope the above steps were helpful.

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Step 1. Multiply by 40 to both sides to get rid of denominator





Step 2. Subtract 24 from both sides of equation.





Step 3. Divide by 25 to both sides of equation.





I hope the above steps were helpful.

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Gold has a density of 19.3g/cm^3. What is the mass in kilograms of one cubic meter of gold?

Step 1. 1 kg = 1000 g and 1 m = 100 cm

Step 2. 19.3 g/cm^3 * 1kg/1000g * ((100)^3 cm^3/(1 m^3))* 1 m^3 = 19.3*1000000/1000 = 19.3*1000 kg = 1.93 x 10^4 kg

Step 3. ANSWER is 19,300 kg

I hope the above steps were helpful.

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The following solves the system of equations by substitution.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve: We'll use substitution. After moving -1*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J

Linear-equations/213723: This question is from textbook algebra one interactions course 2 use x- and y intercepts to draw the graph for 3x - y = 6 1 solutions Answer 161454 by drj(1380)   on 2009-09-14 23:34:37 (Show Source): You can put this solution on YOUR website! Use x- and y intercepts to draw the graph for 3x - y = 6 Step 1. The y-intercept occurs when x=0. We have so we have (0,-6) as one point on the line Step 2. The x-intercept occurs when y=0. We have {{x=2}}} so we have (2,0) as another point on the line. Step 3. Using these points, we can graph as follows: Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/3 = 2. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-1 = -6. Slope is -3/-1 = 3. Equation in slope-intercept form: y=3*x+-6. Step 4. Observe the points (2,0) and (0,-6) that are on the line and how it intercepts the axis. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J

Radicals/213722: please simplify radical. square root of five sixths . the square root of five over 2. Thank you 1 solutions Answer 161452 by drj(1380)   on 2009-09-14 23:23:52 (Show Source): You can put this solution on YOUR website! Please simplify radical. Square root of five sixths times the square root of five over 2. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J

Equations/213688: The speed limit on a certain highway is 72 km/h. What is the speed in cm/s? 1 solutions Answer 161451 by drj(1380)   on 2009-09-14 23:14:14 (Show Source): You can put this solution on YOUR website! The speed limit on a certain highway is 72 km/h. What is the speed in cm/s? Step 1. 1000 m = 1 km and 100 cm= 1 m or 10000 cm = 1 km Step 2. 72 km/h * 1000 m/km * 100 cm/m = 7,200,000 cm/h (note the units cancel in km and m when multiplying the units together. Step 3. Answer is 7.2 million cm/h I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J

Linear-systems/213715: This question is from textbook MATHPOWER 11 Solve by elimination. Check each solution. 21. 6x-5y=-3 2y-9x=-1 Please help me out ive been stuck on this one for a while! 1 solutions Answer 161449 by drj(1380)   on 2009-09-14 23:08:01 (Show Source): You can put this solution on YOUR website! Step 1. Rearrange to align the x and y terms. multiply by 3 to both sides to get 18x multiply by 2 to both sides to get -18x Eq 1 Eq 2 Step 2. Adding above equations Eq 1 and Eq 2 yields or y=1 Step 3. Substitute y=1 into 6x-5y=-3 yields Step 4. The solution is and . Step 5. To verify, the following will solve the linear systems using substitution. Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving -5*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 Step 6. Same result...the solution is and . I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J Polynomials-and-rational-expressions/213564: Simplify the rational expression: 6y - -- 46 1 solutions Answer 161368 by drj(1380)   on 2009-09-14 18:43:58 (Show Source): You can put this solution on YOUR website! Simplify the rational expression: I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J Radicals/213584: please help me simplify radical. the square root of two thirds and the square root of three fourths. studying for a chapter test tomorrow. 1 solutions Answer 161367 by drj(1380)   on 2009-09-14 18:41:57 (Show Source): You can put this solution on YOUR website! Simplify the square root of two thirds and the square root of three fourths. Step 1. The idea is to get rid of the radical in the denominator by multiplying by the radical itself as follows where we multiplied by in the above equation. Step 2. Simplify the denominator for where I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J Sequences-and-series/213568: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these with a simple math trick or formula. (Algebra 1) Thanks 1 solutions Answer 161365 by drj(1380)   on 2009-09-14 18:34:48 (Show Source): You can put this solution on YOUR website! Find 2 consecutive even integers whose sum is 217. Step 1. Let n be one odd integer and n+2 be the next consecutive odd integer Step 2. Note: The sum of two even integers is always even. So in this example there is no solution since 217 is odd. Step 3. Solve anyway as n+n+2=217 or 2n+2=217 Step 4. Solving 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: n=107.5. Graphical form: Equation was fully solved. Text form: 2n+2=217 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 2n+2=217 ) 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 . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 2*n-215 =0 It becomes . Result: This is an equation! Solutions: n=107.5. Universal Simplifier and Solver Done! Step 5. ANSWER: NO SOLUTION I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. Good luck in your studies! Respectfully, Dr J