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 Linear-equations/718936: Find the equation of the line passing though (-1,3) and (2,-5) Thanks!1 solutions Answer 441122 by jim_thompson5910(28595)   on 2013-02-25 20:19:56 (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 Distribute Multiply Add 3 to 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
 Inequalities/718929: solve the inequality for -3(4-2v)-v<41 solutions Answer 441120 by jim_thompson5910(28595)   on 2013-02-25 20:19:07 (Show Source): You can put this solution on YOUR website! Answer:
 test/718839: If 4/5 x _=2/5 what is _?1 solutions Answer 441085 by jim_thompson5910(28595)   on 2013-02-25 18:12:13 (Show Source): You can put this solution on YOUR website!the 5s in the denominator effectively cancel when you multiply both sides by 5 so you're left with 4x__ = 2 that means the number 1/2 goes in the blank since 4 times 1/2 = 2 therefore 4/5 x 1/2 = 2/5
 Length-and-distance/718829: find the center and radius of the circle whose equation is 1 solutions Answer 441081 by jim_thompson5910(28595)   on 2013-02-25 17:50:59 (Show Source): You can put this solution on YOUR website! Compare the last equation to We see that h = 0, k = -2 and r = 5 So the center is (0, -2) and the radius is 5 units.
 Rectangles/718821: if you have a parking lot that is 90 yds long and has an area of 7200 sq. yds what is the width?1 solutions Answer 441075 by jim_thompson5910(28595)   on 2013-02-25 17:31:11 (Show Source): You can put this solution on YOUR website!Assuming this is a rectangle, the width would be W = 7200/90 = 80 yards
 Complex_Numbers/718812: find the values of x and y that makes each equation true 2x+5i=-14-(20y)i1 solutions Answer 441069 by jim_thompson5910(28595)   on 2013-02-25 17:19:39 (Show Source): You can put this solution on YOUR website!Hint: equate the real and imaginary parts 2x = -14 and 5 = -20y
 Equations/718807: what is the answer to 2y-3=5-2y1 solutions Answer 441064 by jim_thompson5910(28595)   on 2013-02-25 17:07:45 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to 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
 Travel_Word_Problems/718766: How long would it take a ball dropped from a 196 foot building to hit the ground. Round two decimal places.1 solutions Answer 441046 by jim_thompson5910(28595)   on 2013-02-25 16:12:09 (Show Source): You can put this solution on YOUR website!16t^2 = 196 t^2 = 196/16 t^2 = 12.25 t = sqrt(12.25) t = 3.5 So roughly 3.5 seconds
 Angles/718701: Two angles are complementary and their sizes are in the ratio 5 : 7 What is the size of the smaller of the two angles? 1 solutions Answer 441040 by jim_thompson5910(28595)   on 2013-02-25 15:59:20 (Show Source): You can put this solution on YOUR website!5x + 7x = 90 12x = 90 x = 90/12 x = 15/2 x = 7.5 5x = 5*7.5 = 37.5 7x = 7*7.5 = 52.5 So the two angles are 37.5 degrees and 52.5 degrees Therefore, the smaller angle is 37.5 degrees
 Functions/718729: x - 5 > -10. Choose the solution set. 1 solutions Answer 441037 by jim_thompson5910(28595)   on 2013-02-25 15:49:42 (Show Source): You can put this solution on YOUR website!x - 5 > -10 x - 5 + 5 > -10 + 5 x + 0 > -5 x > -5 Answer: x > -5
test/718715: 18x^2+11x-24
1 solutions

Answer 441035 by jim_thompson5910(28595)   on 2013-02-25 15:48:51 (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 :
1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-27,-36,-48,-54,-72,-108,-144,-216,-432

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

These factors pair up and multiply to .
1*(-432) = -432
2*(-216) = -432
3*(-144) = -432
4*(-108) = -432
6*(-72) = -432
8*(-54) = -432
9*(-48) = -432
12*(-36) = -432
16*(-27) = -432
18*(-24) = -432
(-1)*(432) = -432
(-2)*(216) = -432
(-3)*(144) = -432
(-4)*(108) = -432
(-6)*(72) = -432
(-8)*(54) = -432
(-9)*(48) = -432
(-12)*(36) = -432
(-16)*(27) = -432
(-18)*(24) = -432

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

First NumberSecond NumberSum
1-4321+(-432)=-431
2-2162+(-216)=-214
3-1443+(-144)=-141
4-1084+(-108)=-104
6-726+(-72)=-66
8-548+(-54)=-46
9-489+(-48)=-39
12-3612+(-36)=-24
16-2716+(-27)=-11
18-2418+(-24)=-6
-1432-1+432=431
-2216-2+216=214
-3144-3+144=141
-4108-4+108=104
-672-6+72=66
-854-8+54=46
-948-9+48=39
-1236-12+36=24
-1627-16+27=11
-1824-18+24=6

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 Polynomials-and-rational-expressions/718760: How would this look like in a descending order? I am having trouble with it. 11a6– 8a – 3 +12a31 solutions Answer 441034 by jim_thompson5910(28595)   on 2013-02-25 15:48:11 (Show Source): You can put this solution on YOUR website!When they say decreasing order, they just want the exponents to be sorted from largest to smallest. So 6 is the largest exponent here and it goes first. 3 is the next largest exponent, so it goes next. One is the next largest (the exponent for ), so that goes next. Finally, the last term is -3 since it has an exponent of 0 (-3 = -3a^0) So the answer is
 Triangles/718758: can triangle can be formed by three segments with the lengths of 27 inches, 31 inches, and 48 inches?1 solutions Answer 441032 by jim_thompson5910(28595)   on 2013-02-25 15:46:01 (Show Source): You can put this solution on YOUR website!Notice how adding any two sides always results in a sum that's larger than the third side (that you didn't add). So this shows you that a triangle is possible here. -------------------------------------------------------------------------- Here's where a triangle isn't possible: side lengths of 1, 2, 18 Notice how 1+2 = 3 but that's not larger than 18, so the side lengths come up short making this triangle not possible
 Miscellaneous_Word_Problems/718695: 500 balls and 250 balls what would be the ratio 1 solutions Answer 441031 by jim_thompson5910(28595)   on 2013-02-25 15:44:17 (Show Source): You can put this solution on YOUR website!If it's 500 red balls to 250 green balls (for instance), then the ratio of red to green is 500:250 which reduces to 2:1 So the ratio of red balls to green balls is 2:1
 Permutations/718747: There are 36 dogs entered in a show where there will be a first, second, and third place award. How many possiblites are there or these awards?1 solutions Answer 441029 by jim_thompson5910(28595)   on 2013-02-25 15:43:20 (Show Source): You can put this solution on YOUR website!There are 36*35*34 = 42,840 different ways to award these awards. Alternatively, you can compute 36 P 3 to get the same answer.
 Linear-equations/718510: y=x+51 solutions Answer 440946 by jim_thompson5910(28595)   on 2013-02-25 01:47:28 (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 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1 So starting at , go up 1 unit 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/718551: 2x^2+13x+15
1 solutions

Answer 440945 by jim_thompson5910(28595)   on 2013-02-25 01:45:54 (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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

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

These factors pair up and multiply to .
1*30 = 30
2*15 = 30
3*10 = 30
5*6 = 30
(-1)*(-30) = 30
(-2)*(-15) = 30
(-3)*(-10) = 30
(-5)*(-6) = 30

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

First NumberSecond NumberSum
1301+30=31
2152+15=17
3103+10=13
565+6=11
-1-30-1+(-30)=-31
-2-15-2+(-15)=-17
-3-10-3+(-10)=-13
-5-6-5+(-6)=-11

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 Number-Line/717898: x|x is a natural number less than 121 solutions Answer 440641 by jim_thompson5910(28595)   on 2013-02-23 19:25:31 (Show Source): You can put this solution on YOUR website!x|x is a natural number less than 12 translates to this set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
 Linear-equations/717775: Can you help show me how to solve the following equation? 16x-1= -4x+141 solutions Answer 440529 by jim_thompson5910(28595)   on 2013-02-23 02:15:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to 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
 Equations/717782: 12 - 8d = -81 solutions Answer 440528 by jim_thompson5910(28595)   on 2013-02-23 02:14:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Permutations/717769: Please how do i recognise if a question is permutative or Combinative1 solutions Answer 440522 by jim_thompson5910(28595)   on 2013-02-23 00:05:19 (Show Source): You can put this solution on YOUR website!If order matters, you use a permutation. If order does not matter, then you use a combination.
 Miscellaneous_Word_Problems/717743: IF I WANTED TO PAYOFF DEBT AND IT AMOUNTED TO 8596. HOW MUCH WILL MY MONTHLY PAYMENT BE IF I WANTED TO PAYOFF IN A YEAR1 solutions Answer 440477 by jim_thompson5910(28595)   on 2013-02-22 20:48:49 (Show Source): You can put this solution on YOUR website!If you want to pay off $8596 in 12 months, then you would need to make a monthly payment of 8596/12 = 716.333333... = 716.34 dollars (round up) per month.  Graphs/717733: What is the slope of the line that contains the points (-1, 8) and (5, -4)?1 solutions Answer 440471 by jim_thompson5910(28595) on 2013-02-22 20:20:58 (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  Equations/717737: If f(x)=x/(x-3) and g(x)=2x-1, find (f-g)(x). My choices are: A. (-2x^2+8x-3)/(x-3) B. (-2x^2+6x+1)/(x-3) C. (-2x^2+5x-3)/(x-3) D. (2x^2+6x+3)/(x-3) If I had to guess I would say either A or C, but I have no idea. Thank you for your help!1 solutions Answer 440469 by jim_thompson5910(28595) on 2013-02-22 20:15:45 (Show Source): You can put this solution on YOUR website!(f-g)(x) = f(x) - g(x) (f-g)(x) = x/(x-3) - (2x - 1) (f-g)(x) = x/(x-3) - (2x - 1)(x-3)/(x-3) (f-g)(x) = (x- (2x - 1)(x-3))/(x-3) (f-g)(x) = (x- (2x^2 - 6x - x + 3))/(x-3) (f-g)(x) = (x- (2x^2 - 7x + 3))/(x-3) (f-g)(x) = (x- 2x^2 + 7x - 3)/(x-3) (f-g)(x) = (-2x^2 + 8x - 3)/(x-3) So the answer is choice A  Coordinate-system/717712: Determine the missing coordinate for the point (x,(1/4))on the unit circle that in in quadrant II.1 solutions Answer 440424 by jim_thompson5910(28595) on 2013-02-22 16:10:31 (Show Source): You can put this solution on YOUR website!We're in quadrant II, so x < 0 x^2 + y^2 = 1 x^2 + (1/4)^2 = 1 x^2 + 1/16 = 1 x^2 = 1 - 1/16 x^2 = 16/16 - 1/16 x^2 = 15/16 x = -sqrt(15/16)... remember, x < 0 x = -sqrt(15)/sqrt(16) x = -sqrt(15)/4 So  Travel_Word_Problems/717711: It coats John$13.50 to take Mary out for the evening 60 percent of this total was for theater tickets. What was the coat of each ticket?1 solutions Answer 440420 by jim_thompson5910(28595)   on 2013-02-22 16:00:06 (Show Source): You can put this solution on YOUR website!60% of $13.50 is 0.6*13.50 = 8.10 Cut this figure in half to get 8.10/2 = 4.05 So the cost of each ticket was$4.05
 Triangles/716974: 1 angle is 60 another 20 whats the missing angle 1 solutions Answer 440039 by jim_thompson5910(28595)   on 2013-02-20 21:13:41 (Show Source): You can put this solution on YOUR website!If this is a triangle, then the missing angle is 180 - 60 - 20 = 100 degrees
Graphs/716968: x^2+2x+1
1 solutions

Answer 440035 by jim_thompson5910(28595)   on 2013-02-20 21:09:19 (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
-1

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

These factors pair up and multiply to .
1*1 = 1
(-1)*(-1) = 1

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

First NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

Condense the terms.

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 Numeric_Fractions/716926: 8(6x-5)+7(7x-6)-5=7-31 solutions Answer 440029 by jim_thompson5910(28595)   on 2013-02-20 20:35:20 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Money_Word_Problems/716567: An advertisement says that 4 out of 5 doctors prefer a certain product. What percent of the doctors do not prefer the product1 solutions Answer 439890 by jim_thompson5910(28595)   on 2013-02-20 00:53:13 (Show Source): You can put this solution on YOUR website!1 out of 5 do not prefer it, so 1/5 = 0.2 = 20% do not prefer the product.
 Human-and-algebraic-language/716561: 10x-2(2x1)=8+2(x-1) 1 solutions Answer 439889 by jim_thompson5910(28595)   on 2013-02-20 00:32:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is