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 Equations/551124: please solve 4(2h+3-5h)= -2281 solutions Answer 359419 by jim_thompson5910(28595)   on 2011-12-30 15:51:33 (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
 Quadratic_Equations/551109: How many real and imaginary roots does 4x^2+8x+4 have?1 solutions Answer 359418 by jim_thompson5910(28595)   on 2011-12-30 15:37:51 (Show Source): You can put this solution on YOUR website!From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Subtract from to get So the discriminant is Since the discriminant is equal to zero, this means that there is one real root. So there are no imaginary roots.
 Travel_Word_Problems/551122: How long does it take to walk 45 miles?1 solutions Answer 359417 by jim_thompson5910(28595)   on 2011-12-30 15:36:23 (Show Source): You can put this solution on YOUR website!It all depends on the speed. For instance, if you walk 5 mph, then it will take t = 45/5 = 9 hours.
 Quadratic_Equations/551123: x^2+5x+6=01 solutions Answer 359416 by jim_thompson5910(28595)   on 2011-12-30 15:35:41 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or
 Equations/551121: find the eqaution (2,11) (7,26)1 solutions Answer 359415 by jim_thompson5910(28595)   on 2011-12-30 15:32:42 (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 Reduce 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 11 to both sides. Combine like terms. So the equation that goes through the points and is
 Pythagorean-theorem/551114: In a 3-D setting: Given 1 leg and the Hypotenuse, calculate the missing leg. HOW TO DO!?! I was out sick from school right before winter break and I missed an exam! I completely forgot! Then on the Thursday that I returned on, I did not have Math class that day and Friday was a short day with no academics. Now, I had all week to study for this test but I'm buckling down right now! If i don't get a good grade on this exam I will look foolish and be disappointed! After all, A week to study for a test?!? Along with extra time before this week!?! I have to get a good grade other wise that is just not acceptable! 1 solutions Answer 359402 by jim_thompson5910(28595)   on 2011-12-30 14:49:19 (Show Source): You can put this solution on YOUR website!Let a and b be the legs of a triangle and c be the hypotenuse. The pythagorean theorem then says that Now say that b is the missing leg, this would then mean that solving for b would give us
Polynomials-and-rational-expressions/551105: Factor x^2+18x+81
1 solutions

Answer 359388 by jim_thompson5910(28595)   on 2011-12-30 13:59:41 (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 :
1,3,9,27,81
-1,-3,-9,-27,-81

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

These factors pair up and multiply to .
1*81 = 81
3*27 = 81
9*9 = 81
(-1)*(-81) = 81
(-3)*(-27) = 81
(-9)*(-9) = 81

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

First NumberSecond NumberSum
1811+81=82
3273+27=30
999+9=18
-1-81-1+(-81)=-82
-3-27-3+(-27)=-30
-9-9-9+(-9)=-18

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).

 Linear-systems/551102: 7x-8y=11 8x-7y=71 solutions Answer 359377 by jim_thompson5910(28595)   on 2011-12-30 13:45:37 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 7. Distribute and multiply. Multiply the both sides of the second equation by -8. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent.
 Inequalities/551104: -1.6>b-(-4.4)1 solutions Answer 359375 by jim_thompson5910(28595)   on 2011-12-30 13:43:52 (Show Source): You can put this solution on YOUR website!-1.6 > b-(-4.4) -1.6 > b+4.4 -1.6-4.4 > b -6 > b b < -6
Polynomials-and-rational-expressions/551103: Factor 3x^2+14x+16
1 solutions

Answer 359374 by jim_thompson5910(28595)   on 2011-12-30 13:37:16 (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 :
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48

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

These factors pair up and multiply to .
1*48 = 48
2*24 = 48
3*16 = 48
4*12 = 48
6*8 = 48
(-1)*(-48) = 48
(-2)*(-24) = 48
(-3)*(-16) = 48
(-4)*(-12) = 48
(-6)*(-8) = 48

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

First NumberSecond NumberSum
1481+48=49
2242+24=26
3163+16=19
4124+12=16
686+8=14
-1-48-1+(-48)=-49
-2-24-2+(-24)=-26
-3-16-3+(-16)=-19
-4-12-4+(-12)=-16
-6-8-6+(-8)=-14

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).

 expressions/551094: Insert parentheses to make each statement true. 1. 8+12/4*5=1 2. 6*3+1+1=251 solutions Answer 359372 by jim_thompson5910(28595)   on 2011-12-30 13:30:13 (Show Source): You can put this solution on YOUR website!1. (8+12)/(4*5)=1 2. 6*(3+1)+1=25
 Numbers_Word_Problems/551100: What is the average number of these numbers 48,23,371 solutions Answer 359371 by jim_thompson5910(28595)   on 2011-12-30 13:29:20 (Show Source): You can put this solution on YOUR website!The average is (48+23+37)/3 = 108/3 = 36
 Rate-of-work-word-problems/551099: working alone, ryan can dig a 10 ft by 10 ft hole in five hours. castel can dig the hole in six hours. how long would it take them if they worked together?1 solutions Answer 359369 by jim_thompson5910(28595)   on 2011-12-30 13:28:14 (Show Source): You can put this solution on YOUR website!1/5 + 1/6 = 1/t 6t + 5t = 30 11t = 30 t = 30/11 t = 2 8/11 So it will take 2 8/11 hours or roughly 2.545 hours if they worked together.
 test/551091: A circle passes through (3,5) and(1,2) ,find its equation1 solutions Answer 359362 by jim_thompson5910(28595)   on 2011-12-30 12:51:58 (Show Source): You can put this solution on YOUR website!I'm assuming that these are the endpoints of the diameter. Recall that the general equation of a circle is . So we need the center (h,k) and the radius squared . First, let's find the center (h,k). Since the center is the midpoint of the line segment with endpoints (3,5) and (1,2), we need to find the midpoint. X-Coordinate of Midpoint = Since the x coordinate of midpoint is , this means that Y-Coordinate of Midpoint = Since the y coordinate of midpoint is , this means that So the center is the point (2, 7/2) --------------------------------------------------- Now let's find the radius squared Use the formula , where (h,k) is the center and (x,y) is an arbitrary point on the circle. In this case, and . Also, and . Plug these values into the equation above and simplify to get: So because , , and , this means that the equation of the circle that passes through the points (3,5) and (1,2) (which are the endpoints of the diameter) is .
 Linear-equations/551090: 1. Write the equation of the line passing through the points (0, -4) and (-2, 2. Write the equation of the line with a slope of -5 and a y-intercept of (0,3). 3. Write the equation of the line passing through the points (0, -4) and (-2, 4. Write the equation of the line passing through the points (-6,1) and (-4,2). 1 solutions Answer 359361 by jim_thompson5910(28595)   on 2011-12-30 12:42:55 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. # 1 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 Reduce 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 Subtract 4 from both sides. Combine like terms. 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
 Equations/551025: solve 3(4x-7)=2(7x+13)1 solutions Answer 359303 by jim_thompson5910(28595)   on 2011-12-30 02:57:17 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Add to 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
 Equations/551016: solve 2x+5x-6 = 14x-321 solutions Answer 359300 by jim_thompson5910(28595)   on 2011-12-30 02:41:57 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Add to 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
 Equations/551011: solve 5x-12+2x=22x-31 solutions Answer 359299 by jim_thompson5910(28595)   on 2011-12-30 02:33:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Add to 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
 Equations/551008: solve 9x-7 = 241 solutions Answer 359296 by jim_thompson5910(28595)   on 2011-12-30 02:23:43 (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 . ---------------------------------------------------------------------- Answer: So the solution is
 Equations/551006: solve 3x+4 = 121 solutions Answer 359294 by jim_thompson5910(28595)   on 2011-12-30 02:21:24 (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 . ---------------------------------------------------------------------- Answer: So the solution is
 Quadratic-relations-and-conic-sections/550955: identify the vertex of the graph of the function y=(x+3) square root-2.1 solutions Answer 359248 by jim_thompson5910(28595)   on 2011-12-29 20:21:26 (Show Source): You can put this solution on YOUR website!The vertex of y = a(x-h)^2+k is (h,k). In the case of y = (x+3)^2-2, we see that h = -3 and k = -2 So the vertex is (-3, -2)
 Linear-equations/550944: Given the linear equation y= -5/6+2, find the y-coordinates of the points (-6), (0), and (6). Plot those points and graph the linear equation.1 solutions Answer 359242 by jim_thompson5910(28595)   on 2011-12-29 18:54:46 (Show Source): You can put this solution on YOUR website!y= -5/6x+2 y= -5/6(-6)+2 y= 30/6+2 y= 5+2 y= 7 So we have one point (-6,7) --------------- y= -5/6x+2 y= -5/6(0)+2 y= 0/6+2 y= 0+2 y= 2 So we have one point (0,1) --------------- y= -5/6x+2 y= -5/6(6)+2 y= -30/6+2 y= -5+2 y= -3 So we have one point (6,-3) Now plot these points and draw a straight line through them to graph the line (I'll let you do this).
 Linear-equations/550943: Determine if (-5/2,1) is a solution to -2x+3y=21 solutions Answer 359241 by jim_thompson5910(28595)   on 2011-12-29 18:51:54 (Show Source): You can put this solution on YOUR website!-2x+3y=2 -2(-5/2)+3(1)=2 10/2+3=2 5+3=2 8=2 Since the equation is false, (-5/2,1) is NOT a solution
Polynomials-and-rational-expressions/550941: Factor the following expression completely:
70w^3 – 125w^2 + 30w
1 solutions

Answer 359240 by jim_thompson5910(28595)   on 2011-12-29 18:49:19 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF .

Now let's try to factor the inner expression

---------------------------------------------------------------

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 :
1,2,3,4,6,7,12,14,21,28,42,84
-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84

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

These factors pair up and multiply to .
1*84 = 84
2*42 = 84
3*28 = 84
4*21 = 84
6*14 = 84
7*12 = 84
(-1)*(-84) = 84
(-2)*(-42) = 84
(-3)*(-28) = 84
(-4)*(-21) = 84
(-6)*(-14) = 84
(-7)*(-12) = 84

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

First NumberSecond NumberSum
1841+84=85
2422+42=44
3283+28=31
4214+21=25
6146+14=20
7127+12=19
-1-84-1+(-84)=-85
-2-42-2+(-42)=-44
-3-28-3+(-28)=-31
-4-21-4+(-21)=-25
-6-14-6+(-14)=-20
-7-12-7+(-12)=-19

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 then factors further to

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

So completely 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/550942: Use the “difference of squares” rule to factor the following expression: 36x^2 - 9y^21 solutions Answer 359239 by jim_thompson5910(28595)   on 2011-12-29 18:48:18 (Show Source): You can put this solution on YOUR website!36x^2 - 9y^2 9(4x^2 - y^2) 9((2x)^2 - y^2) 9(2x-y)(2x+y)
 Exponents-negative-and-fractional/550919: Evaluate the following expression. 2^ -31 solutions Answer 359222 by jim_thompson5910(28595)   on 2011-12-29 17:03:02 (Show Source): You can put this solution on YOUR website!2^(-3) = 1/(2^3) = 1/8 So 2^(-3)= 1/8
 Equations/550902: a+b=s+r for s1 solutions Answer 359196 by jim_thompson5910(28595)   on 2011-12-29 16:17:57 (Show Source): You can put this solution on YOUR website!a+b=s+r a+b-r=s+r -r a+b-r = s s = a+b-r
 Inequalities/550898: 7-10z>5 please show work.1 solutions Answer 359192 by jim_thompson5910(28595)   on 2011-12-29 16:10:15 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is Which in decimal form is
 Inequalities/550900: 9+6y>69 please show work.1 solutions Answer 359191 by jim_thompson5910(28595)   on 2011-12-29 16:09:23 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/550861: Perform the indicated operations: -42÷6+(-7)1 solutions Answer 359152 by jim_thompson5910(28595)   on 2011-12-29 13:00:20 (Show Source): You can put this solution on YOUR website!-42÷6+(-7) -7+(-7) -7 - 7 -14 So -42÷6+(-7) = -14
 Travel_Word_Problems/550869: if traveling 60 miles,and going 40 miles an hour ,how long will it take to get there 1 solutions Answer 359151 by jim_thompson5910(28595)   on 2011-12-29 12:57:49 (Show Source): You can put this solution on YOUR website!d = rt 60 = 40t 60/40 = t 3/2 = t t = 3/2 t = 1 1/2 So it will take 1 1/2 (one and a half) hours