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Linear-systems/552815: how do system of equations using substitution x+y=4 2x+3y=9 1 solutions Answer 360518 by jim_thompson5910(28536)   on 2012-01-04 20:22:05 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 12 from both sides Combine like terms on the right side Divide both sides by -1 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and which form the point Now let's graph the two equations (if you need help with graphing, check out this solver) From the graph, we can see that the two equations intersect at . This visually verifies our answer. graph of (red) and (green) and the intersection of the lines (blue circle). If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

Linear-equations/552785: How do you write the equation of a line in slope-intercept form passing through (4,5) and (6,8)? 1 solutions Answer 360513 by jim_thompson5910(28536)   on 2012-01-04 20:00:47 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 5 to both sides. Combine like terms. Simplify So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

percentage/552797: What percent of 8 is 20.7? 1 solutions Answer 360512 by jim_thompson5910(28536)   on 2012-01-04 19:59:23 (Show Source): You can put this solution on YOUR website! 8x = 20.7 x = 20.7/8 x = 2.5875 Now multiply by 100 to get 258.75%

test/552795: 1 solutions Answer 360511 by jim_thompson5910(28536)   on 2012-01-04 19:58:29 (Show Source): You can put this solution on YOUR website! Please post the full problem along with the full instructions.

Polynomials-and-rational-expressions/552792: write a polynomial function with rational coefficients so that P(x)= 0. 1.5 and 9 2.-4 and 2i thanks 1 solutions Answer 360509 by jim_thompson5910(28536)   on 2012-01-04 19:57:42 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started. # 1 or Start with the given solutions. or Get everything to one side so that only 0 remains on the right side (for both equations). Use the zero product property to combine the equations. FOIL out the left side. So the answer is To check your work, simply solve for x. Doing so will show you that the solutions are or , which confirm the answer.

Complex_Numbers/552761: Simplify: (-7i)-(4i)-(5-6i) 1 solutions Answer 360504 by jim_thompson5910(28536)   on 2012-01-04 19:19:10 (Show Source): You can put this solution on YOUR website! (-7i)-(4i)-(5-6i) -7i-4i-5+6i -5-5i So (-7i)-(4i)-(5-6i) = -5-5i

Complex_Numbers/552710: g(x)=2x^2-5 g(3) Do you square the 3 and then multiply by 2? 1 solutions Answer 360503 by jim_thompson5910(28536)   on 2012-01-04 19:15:28 (Show Source): You can put this solution on YOUR website! Yes, you are correct. g(x)=2x^2-5 g(3)=2(3)^2-5 g(3)=2(9)-5 g(3)=18-5 g(3)=13

Complex_Numbers/552758: Simplify: -4(-6+3i)-7(-7+5i) 1 solutions Answer 360501 by jim_thompson5910(28536)   on 2012-01-04 19:14:36 (Show Source): You can put this solution on YOUR website! -4(-6+3i)-7(-7+5i) 24-12i+49-35i 73-47i So -4(-6+3i)-7(-7+5i) = 73-47i

Complex_Numbers/552755: Simplify: (5i)(-4i)-8(-1+8i) 1 solutions Answer 360500 by jim_thompson5910(28536)   on 2012-01-04 19:12:30 (Show Source): You can put this solution on YOUR website! (5i)(-4i)-8(-1+8i) -20i^2+8-64i -20(-1)+8-64i 20+8-64i 28-64i So (5i)(-4i)-8(-1+8i) = 28-64i If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

Exponents/552269: what is 3^-2 1 solutions Answer 360499 by jim_thompson5910(28536)   on 2012-01-04 19:10:33 (Show Source): You can put this solution on YOUR website! 3^-2 = 1/(3^2) = 1/9 So 3^-2 = 1/9

Expressions-with-variables/552615: Please help me solve this equation: -27-(-4)-(-7) 1 solutions Answer 360498 by jim_thompson5910(28536)   on 2012-01-04 19:09:46 (Show Source): You can put this solution on YOUR website! -27-(-4)-(-7) -27+4+7 -23+7 -16 So -27-(-4)-(-7) = -16

Exponents/552726: simplify the expression x^-3y/xy^-2 1 solutions Answer 360497 by jim_thompson5910(28536)   on 2012-01-04 19:08:35 (Show Source): You can put this solution on YOUR website! x^-3y/xy^-2 x^(-3-1)*y^(1-(-2)) x^(-4)*y^(3) (y^3)/(x^4) So x^-3y/xy^-2 = (y^3)/(x^4) for all nonzero values of x and y

Linear-equations/552751: i need help solving this ASAP. Please help me convert this to the slope-intercept form! y+10=-4/5(x-5) 1 solutions Answer 360496 by jim_thompson5910(28536)   on 2012-01-04 19:06:33 (Show Source): You can put this solution on YOUR website! y+10=-4/5(x-5) y+10=-4/5x+(-4/5)(-5) y+10=-4/5x+4 y=-4/5x+4-10 y=-4/5x-6 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

expressions/551720: Evaluate -10/5x-x^2+5 for x= -2 1 solutions Answer 360495 by jim_thompson5910(28536)   on 2012-01-04 19:04:40 (Show Source): You can put this solution on YOUR website! -10/(5x-x^2+5) -10/(5(-2)-(-2)^2+5) -10/(5(-2)-4+5) -10/(-10-4+5) -10/(-9) 10/9 So -10/(5x-x^2+5) = 10/9 when x = -2

expressions/552511: Evaluate the two given expressions. 1. ^6C^3 2. ^7P^2 1 solutions Answer 360494 by jim_thompson5910(28536)   on 2012-01-04 19:03:26 (Show Source): You can put this solution on YOUR website! # 1 C(n,r) = (n!)/(r!(n-r)!) C(6,3) = (6!)/(3!*(6-3)!) C(6,3) = (6!)/(3!*3!) C(6,3) = (6*5*4*3!)/(3!*3!) C(6,3) = (6*5*4)/(3!) C(6,3) = (6*5*4)/(3*2*1) C(6,3) = (120)/(6) C(6,3) = 20 ======================================================= # 2 P(n,r) = (n!)/((n-r)!) P(7,2) = (7!)/((7-2)!) P(7,2) = (7!)/(5!) P(7,2) = (7*6*5!)/(5!) P(7,2) = 7*6 P(7,2) = 42 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

expressions/551948: Rewrite expression without parentheses. Simplify. 22-(60x-41) Evaluate expression. 1.7-(1.6-20.2) 1 solutions Answer 360493 by jim_thompson5910(28536)   on 2012-01-04 19:02:02 (Show Source): You can put this solution on YOUR website! 22-(60x-41) 22-60x+41 63-60x ------------------------------------------------------- 1.7-(1.6-20.2) 1.7-1.6+20.2 20.3

Equations/552739: 8f+11=-7f-19 1 solutions Answer 360491 by jim_thompson5910(28536)   on 2012-01-04 19:01:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Numeric_Fractions/552744: Add these two fractions and reduce the answer to lowest terms: 13/27 + 8/27 I really don't understand how to reduce to lowest term. Please help. 1 solutions Answer 360490 by jim_thompson5910(28536)   on 2012-01-04 19:00:31 (Show Source): You can put this solution on YOUR website! 13/27 + 8/27 (13+8)/27 21/27 7/9 ... Note: to reduce, divide each component by the GCF 3 So 13/27 + 8/27 = 7/9 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

expressions/552746: Please help:::WHICH EXPRESSION SHOWS 3(X PLUS Y)IN ITS SIMPLIFIED FORM? 1 solutions Answer 360489 by jim_thompson5910(28536)   on 2012-01-04 18:59:11 (Show Source): You can put this solution on YOUR website! Using the distributive property, 3(x+y) = 3x + 3y

Linear-equations/552747: Find an equation of the line containing the given pair of points.(-7,-6) and (-1,-5)The equation of the line in slope-intercept form is y= 1 solutions Answer 360488 by jim_thompson5910(28536)   on 2012-01-04 18:58:30 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Rewrite as Distribute Multiply Subtract 6 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

Equations/552734: Good Afternoon, i just wanted to know how do you get 2/9 of -36 ? 1 solutions Answer 360485 by jim_thompson5910(28536)   on 2012-01-04 18:40:07 (Show Source): You can put this solution on YOUR website! 2/9 of -36 = (2/9)*(-36) = (2*(-36))/9 = -72/9 = -8 So 2/9 of -36 is -8

Equations/552728: Please help! How would I solve two step equations like these? 10x + 17 = 4x - 1 1 solutions Answer 360483 by jim_thompson5910(28536)   on 2012-01-04 18:33:24 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

Number-Line/552729: how do you graph 2/3 on a number line 1 solutions Answer 360482 by jim_thompson5910(28536)   on 2012-01-04 18:33:00 (Show Source): You can put this solution on YOUR website! 2/3 = 0.667, so plot 2/3 between 0.6 and 0.7 Optionally, you can plot 2/3 between 0.5 and 1

Inequalities/552693: im trying to graph m<7 on a number line and i cannot figure out if i need to put a closed circle on the 7 or a open circle. 1 solutions Answer 360467 by jim_thompson5910(28536)   on 2012-01-04 17:49:51 (Show Source): You can put this solution on YOUR website! If you have , then you draw an open circle at 7 and you shade to the left on the number line. The open circle tells you to exclude the endpoint 7.

Inequalities/552690: -24<1/2b 1 solutions Answer 360463 by jim_thompson5910(28536)   on 2012-01-04 17:32:07 (Show Source): You can put this solution on YOUR website! -24<1/2b -24*2< (1/2b)*2 -48 < b b > -48 If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim

Exponents-negative-and-fractional/552685: I'm not sure how to simplify this fraction: (8t)^3 ------ 8t^3 1 solutions Answer 360461 by jim_thompson5910(28536)   on 2012-01-04 17:27:27 (Show Source): You can put this solution on YOUR website! (8t)^3 ------ 8t^3 512t^3 ------ 8t^3 64 So (8t)^3 ------ = 64 8t^3

Triangles/552683: The legs of an isosceles right triangle are 5 inches long. what is the length of the hypotenuse of the triangle to the nearest inch? 1 solutions Answer 360460 by jim_thompson5910(28536)   on 2012-01-04 17:25:52 (Show Source): You can put this solution on YOUR website! If the leg of an isosceles right triangle is x inches, then the hypotenuse is inches long. So in this case, the hypotenuse is , which is approximately 7.0710678 and that rounds to 7 inches.

Length-and-distance/552682: You are fencing in a backyard that measures 30 ft by 20 ft. How much fencing should you buy? 1 solutions Answer 360458 by jim_thompson5910(28536)   on 2012-01-04 17:23:56 (Show Source): You can put this solution on YOUR website! Assuming the backyard is a rectangle, the perimeter of the yard is then P = 2*30 + 2*20 = 60+40 = 100 ft So you need 100 ft of fencing.

Linear-systems/552680: 2x=-4y+10 6y=-3x+12 Is it no solution? 1 solutions Answer 360457 by jim_thompson5910(28536)   on 2012-01-04 17:22:33 (Show Source): You can put this solution on YOUR website! You are correct. There are no solutions. Good job.

Geometry_Word_Problems/552681: The width of a rectangle is 9x and the length is 3X + 11 solve for x then find the peremeter. I have to give the equation, the value of x, and the peremeter. I don't think I'm on the right track, but here is what I have tried. P= 2(3x+11) + 2(9x) P= 6x + 22 + 18x P= 24x + 22 1 solutions Answer 360456 by jim_thompson5910(28536)   on 2012-01-04 17:21:52 (Show Source): You can put this solution on YOUR website! You are correct. The perimeter is P = 24x + 22

Probability-and-statistics/552659: A box is filled with 4 brown cards, 4 yellow cards, and 6 blue cards. A card is chosen at random from the box. What is the probability that it is a brown or a blue card? Would the answer be 5/7? 1 solutions Answer 360443 by jim_thompson5910(28536)   on 2012-01-04 16:23:13 (Show Source): You can put this solution on YOUR website! P(Brown or Blue) = P(Brown) + P(Blue) P(Brown or Blue) = 4/14 + 6/14 P(Brown or Blue) = 10/14 P(Brown or Blue) = 5/7 So you have the correct answer. Congrats.