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 Equations/698475: -20m - 6 = 541 solutions Answer 430710 by jim_thompson5910(28715)   on 2013-01-04 19:08:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 test/698373: If the intreset value of saving $24000 is$ 6000 for a period of 5 years, then find the rate of interest per year. 1 solutions Answer 430709 by jim_thompson5910(28715)   on 2013-01-04 19:07:35 (Show Source): You can put this solution on YOUR website!I = Prt 6000 = 24000*r*5 6000 = 120000r 6000/120000 = r r = 6000/120000 r = 6/120 r = 1/20 r = 0.05 So the interest rate is 5%
 Quadratic_Equations/698472: 2x-8x+14=01 solutions Answer 430702 by jim_thompson5910(28715)   on 2013-01-04 18:36:39 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Angles/698467: find measurement of angle A(6x+7) and m of angle B(3x+20) if angle A and angle B are complementary 1 solutions Answer 430691 by jim_thompson5910(28715)   on 2013-01-04 18:06:19 (Show Source): You can put this solution on YOUR website!angle A and angle B are complementary m angle A + m angle B = 90 6x+7 + 3x+20 = 90 9x+27=90 9x=90-27 9x=63 x=(63)/(9) x=7 Angle A: 6x+7 = 6(7)+7 = 49 degrees Angle B: 3x+20 = 3(7)+20 = 41 degrees
 Angles/698464: Find measurement of angle A (6x+7) and measurement of angle B (3x+20) if angle A and angle B are supplementary. 1 solutions Answer 430689 by jim_thompson5910(28715)   on 2013-01-04 17:49:25 (Show Source): You can put this solution on YOUR website!angle A and angle B are supplementary m angle A + m angle B = 180 6x+7 + 3x+20 = 180 9x+27=180 9x=180-27 9x=153 x=(153)/(9) x=17 Angle A: 6x+7 = 6(17)+7 = 109 degrees Angle B: 3x+20 = 3(17)+20 = 71 degrees
 Money_Word_Problems/698457: Jerome paid $85 for a calculator. He had no one-dollar bills or coins. How many ways could he have paid if he had no bills more than$20?1 solutions Answer 430678 by jim_thompson5910(28715)   on 2013-01-04 17:02:10 (Show Source): You can put this solution on YOUR website!There are 25 ways to do this 1 five + 4 twenties = 5 bills total 1 five + 2 tens + 3 twenties = 6 bills total 1 five + 4 tens + 2 twenties = 7 bills total 3 fives + 1 ten + 3 twenties = 7 bills total 1 five + 6 tens + 1 twenty = 8 bills total 3 fives + 3 tens + 2 twenties = 8 bills total 5 fives + 3 twenties = 8 bills total 1 five + 8 tens = 9 bills total 3 fives + 5 tens + 1 twenty = 9 bills total 5 fives + 2 tens + 2 twenties = 9 bills total 3 fives + 7 tens = 10 bills total 5 fives + 4 tens + 1 twenty = 10 bills total 7 fives + 1 ten + 2 twenties = 10 bills total 5 fives + 6 tens = 11 bills total 7 fives + 3 tens + 1 twenty = 11 bills total 9 fives + 2 twenties = 11 bills total 7 fives + 5 tens = 12 bills total 9 fives + 2 tens + 1 twenty = 12 bills total 9 fives + 4 tens = 13 bills total 11 fives + 1 ten + 1 twenty = 13 bills total 11 fives + 3 tens = 14 bills total 13 fives + 1 twenty = 14 bills total 13 fives + 2 tens = 15 bills total 15 fives + 1 ten = 16 bills total 17 fives = 17 bills total Again, there are 25 ways. Each case has the bills' value adding up to $85.  Money_Word_Problems/698447: 6% of$340 is what amount?1 solutions Answer 430661 by jim_thompson5910(28715)   on 2013-01-04 15:57:39 (Show Source): You can put this solution on YOUR website!6% of 340 = (6/100)*340 6% of 340 = (0.06)*340 6% of 340 = 20.40 So 6% of $240 is$20.40
 Vectors/698444: how would find the 17th term of the arithmetic sequence. if a16= 18, and d= 1/21 solutions Answer 430658 by jim_thompson5910(28715)   on 2013-01-04 15:43:50 (Show Source): You can put this solution on YOUR website!a17 = a16 + d a17 = 18 + 1/2 a17 = 36/2 + 1/2 a17 = 37/2
 Coordinate-system/698439: Name two points on the x-axis that are 10 units from (1, 8)1 solutions Answer 430651 by jim_thompson5910(28715)   on 2013-01-04 15:12:16 (Show Source): You can put this solution on YOUR website!Equation of the circle centered at (1,8) that has a radius of 10: (x-1)^2 + (y-8)^2 = 100 You plug in y = 0 and solve for x (x-1)^2 + (y-8)^2 = 100 (x-1)^2 + (0-8)^2 = 100 (x-1)^2 + (-8)^2 = 100 (x-1)^2 + 64 = 100 (x-1)^2 = 100-64 (x-1)^2 = 36 x-1 = sqrt(36) or x-1 = -sqrt(36) x-1 = 6 or x-1 = -6 x = 6+1 or x = -6+1 x = 7 or x = -5 So the two points are (7, 0) and (-5, 0)
 Circles/698438: If the segment connecting (−6, −5) and (4, −3) is the diameter of the circle, what are the coordinates for the center? 1 solutions Answer 430650 by jim_thompson5910(28715)   on 2013-01-04 15:06:50 (Show Source): You can put this solution on YOUR website!Average the corresponding endpoints X: (-6+4)/2 = -2/2 = -1 Y: (-5 + (-3) )/2 = -8/2 = -4 So the center is the point (-1, -4)
 Expressions-with-variables/698436: (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1) The answer the book has is (2u + 1) / (u -4) It am a parent and I can't figure this out to explain to my homeschooled child. The chapter is multiplying and dividing rational expressions.1 solutions Answer 430648 by jim_thompson5910(28715)   on 2013-01-04 15:03:34 (Show Source): You can put this solution on YOUR website!4u^2 - 1 factors to (2u + 1)(2u - 1) using the difference of squares rule The second term "(2u - 1)" cancels with the last term "(2u - 1)" on the very right. -------------------------------------------------------------------------- u^3 - 16u factors to u(u^2 - 16) which further factors to u(u-4)(u+4) using the difference of squares rule -------------------------------------------------------------------------- u^2 + 4u factors to u(u + 4) Notice the last two final factorizations have a 'u' and a 'u+4' in common. They cancel =========================================================================== =========================================================================== =========================================================================== So after all of the factorizations and cancellations, we go from (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1) to ((2u - 1)(2u + 1))/(u(u-4)(u+4)) * (u(u+4))/(2u - 1) which simplifies to (2u + 1) / (u-4)
 Linear-equations/698432: Determine the type of boundary line and shading for the graph of the inequality -3x + y > 6. Dashed line with shading on the side that includes the origin. Solid line with shading on the side that does not include the origin. Dashed line with shading on the side that does not include the origin. Solid line with shading on the side that includes the origin.1 solutions Answer 430645 by jim_thompson5910(28715)   on 2013-01-04 14:46:24 (Show Source): You can put this solution on YOUR website!The inequality sign does NOT have a line under it. So the line isn't solid, so it must be dashed. The origin is not in the solution set because if you plug in (0,0) you get -3x + y > 6 -3(0) + 0 > 6 0 + 0 > 6 0 > 6 Which is false. So that shows why (0,0) is not in the solution set. So the origin is not in the shaded region. That points us to the answer of choice C
 Linear-systems/698424: y = 3x-2 1 solutions Answer 430644 by jim_thompson5910(28715)   on 2013-01-04 14:39:01 (Show Source): You can put this solution on YOUR website!If you want to graph, then... Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 test/698425: If a trainis traveling at 65 miles per hour, what is the train traveling in feet per minute1 solutions Answer 430643 by jim_thompson5910(28715)   on 2013-01-04 14:38:07 (Show Source): You can put this solution on YOUR website!65 miles/hr * (1 hr/60 min) * (5280 ft/1 mile) 65*5280/60 ft/min 5,720 ft/min So 65 mph = 5,720 ft/min
 Linear-systems/698428: y = 3x-2 1 solutions Answer 430642 by jim_thompson5910(28715)   on 2013-01-04 14:36:14 (Show Source): You can put this solution on YOUR website!Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1 So starting at , go up 3 units and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Functions/698327: Find f(-3) if f(x)=2x²-5 A. -23 B. 13 C. 1 D. -111 solutions Answer 430595 by jim_thompson5910(28715)   on 2013-01-04 04:12:07 (Show Source): You can put this solution on YOUR website!f(x) = 2x^2 - 5 f(-3) = 2(-3)^2 - 5 f(-3) = 2(9) - 5 f(-3) = 18 - 5 f(-3) = 13
 sets-and-operations/698310: List the elements of the given set in roster notation {x|7-x=9;x,an integer} thank you1 solutions Answer 430584 by jim_thompson5910(28715)   on 2013-01-03 23:17:19 (Show Source): You can put this solution on YOUR website!7-x = 9 7 = 9 + x 7 - 9 = x -2 = x x = -2 So the set {x|7-x=9;x,an integer} is the same as the set { -2 } Since only the number -2 satisfies the equation 7 - x = 9
 Geometry_Word_Problems/698259: The area and length of a rectangle are 30 square feet and 6 feet, respectively.What is the width of the rectange?1 solutions Answer 430557 by jim_thompson5910(28715)   on 2013-01-03 19:58:30 (Show Source): You can put this solution on YOUR website!A = LW 30 = 6W 30/6 = W 5 = W W = 5 Width is 5 feet.
 Equations/698253: This is on my son's homework and I keep getting an answer that doesn't make sense. 21(2-x)+12x = 44 When I distribute, I get 42-21x +12x = 44 Then, -21x+12x=2 -9x=2 x=-.2222 What are we doing wrong?1 solutions Answer 430549 by jim_thompson5910(28715)   on 2013-01-03 19:08:46 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is Since -0.22222... is equivalent to , you have the correct answer.
 Rectangles/698073: Find the area of a rectangle with base of 9 inches and height of 2 ft 1 solutions Answer 430426 by jim_thompson5910(28715)   on 2013-01-03 00:19:53 (Show Source): You can put this solution on YOUR website!2 ft = 24 inches Area = Base*Height A = bh A = 9*24 A = 216 square inches
 Inequalities/698068: solve -5<2d-1<31 solutions Answer 430425 by jim_thompson5910(28715)   on 2013-01-02 23:58:50 (Show Source): You can put this solution on YOUR website!-5 < 2d-1 < 3 -5+1 < 2d-1+1 < 3+1 -4 < 2d < 4 -4/2 < 2d/2 < 4/2 -2 < d < 2 Answer: -2 < d < 2
 test/698069: What's the slope for (-2,-4) and (2,4) 1 solutions Answer 430424 by jim_thompson5910(28715)   on 2013-01-02 23:57:41 (Show Source): You can put this solution on YOUR website! 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 Reduce So the slope of the line that goes through the points and is
 Length-and-distance/698023: Find the midpoint between points (-5,11) and (-4,8)1 solutions Answer 430395 by jim_thompson5910(28715)   on 2013-01-02 20:27:39 (Show Source): You can put this solution on YOUR website!Average the x coordinates: (-5+(-4))/2 = -9/2 = -4.5 Average the y coordinates: (11+8)/2 = 19/2 = 9.5 So the midpoint is (-4.5, 9.5)
 Proportions/697943: Solve the Proportion for x: x/8 = 5/3 1 solutions Answer 430365 by jim_thompson5910(28715)   on 2013-01-02 16:27:38 (Show Source): You can put this solution on YOUR website!x/8 = 5/3 x = 8(5/3) x = 40/3
 Word_Problems_With_Coins/697933: Bjon has 5 coins with a total value of 50 cents. Not all of the coins are dimes. What are the coins?1 solutions Answer 430359 by jim_thompson5910(28715)   on 2013-01-02 15:34:09 (Show Source): You can put this solution on YOUR website!You simply do this by trial and error. 3 nickels + 1 dime + 1 quarter = 5 coins total Value of 3 nickels: 3*5 = 15 cents Value of 1 dime: 1*10 = 10 cents Value of 1 quarter: 1*25 = 25 cents Total value = 3 nickels + 1 dime + 1 quarter Total value = 15 cents + 10 cents + 25 cents Total value = 50 cents So Bjon has 3 nickels, 1 dime, and 1 quarter.
1 solutions

Answer 430346 by jim_thompson5910(28715)   on 2013-01-02 15:13:44 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,4,7,14,28
-1,-2,-4,-7,-14,-28

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*28 = 28
2*14 = 28
4*7 = 28
(-1)*(-28) = 28
(-2)*(-14) = 28
(-4)*(-7) = 28

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1281+28=29
2142+14=16
474+7=11
-1-28-1+(-28)=-29
-2-14-2+(-14)=-16
-4-7-4+(-7)=-11

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

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