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 Triangles/673545: If there is an equilateral triangle with one side being 3x+1 and the other being 2x+5 what is the length of the missing side? Can you please explain how you got the answer because I have a quiz tomorrow and I am still very confused!1 solutions Answer 418719 by jim_thompson5910(28595)   on 2012-10-29 22:09:43 (Show Source): You can put this solution on YOUR website!This is an equilateral triangle, so ALL 3 SIDES ARE EQUAL (sorry if that sounds like I'm shouting, I'm just emphasizing the point) This means that 3x+1 = 2x+5 Solve that for x. Then plug this value of x back into either 3x+1 or 2x+5 to find the side length of the triangle.
 Systems-of-equations/673533: how do you solve 8=4(r+4)1 solutions Answer 418704 by jim_thompson5910(28595)   on 2012-10-29 20:42:28 (Show Source): You can put this solution on YOUR website!8=4(r+4) 4(r+4) = 8 4r+16 = 8 4r = 8-16 4r = -8 r = -8/4 r = -2
 Linear-equations/673507: Line p is parallel to line q. If line p has a slope of 3, what is the slope of line q1 solutions Answer 418703 by jim_thompson5910(28595)   on 2012-10-29 20:40:46 (Show Source): You can put this solution on YOUR website!If two lines are parallel, then they have the same slope. So if p and q are parallel, and the slope of p is 3, then the slope of q is also 3.
 Exponents/673525: solve 3+7-2st 1 solutions Answer 418702 by jim_thompson5910(28595)   on 2012-10-29 20:39:54 (Show Source): You can put this solution on YOUR website!You can't solve, but you can simplify 3+7-2st (3+7)-2st 10-2st So the answer is 10-2st
 Equations/673496: 4m/0.8=-7 need help 4 homework plz katie1 solutions Answer 418701 by jim_thompson5910(28595)   on 2012-10-29 20:38:35 (Show Source): You can put this solution on YOUR website!Multiply both sides by 0.8 to get 4m/0.8=-7 4m = -7*0.8 4m = -5.6 Then divide both sides by 4 to completely isolate m 4m = -5.6 m = -5.6/4 m = -1.4 So the solution is m = -1.4
 Polynomials-and-rational-expressions/673375: Please solve x^2-3x+6=0 Thanks1 solutions Answer 418628 by jim_thompson5910(28595)   on 2012-10-29 16:13:01 (Show Source): You can put this solution on YOUR website!Use the quadratic formula to solve for x or or The two solutions are or Note: these are exact solutions and they are complex/imaginary solutions (ie non-real solutions).
 Expressions-with-variables/673374: 2 +7b - 44= -3b +12+ 9b1 solutions Answer 418627 by jim_thompson5910(28595)   on 2012-10-29 16:11:40 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
 Functions/673311: I am very confused about this question: Let h(x) = 2x + 7. Find the value of h(x) + 14. I have done many other questions like this but they have been with only one value. Could you please show the steps to this problem? Thanks in advance! :)1 solutions Answer 418585 by jim_thompson5910(28595)   on 2012-10-29 13:59:50 (Show Source): You can put this solution on YOUR website!h(x) + 14 (2x+7) + 14 ... Replace 'h(x)' with '2x+7' (since h(x) = 2x+7) 2x + 7 + 14 2x + (7 + 14) 2x + 21 So h(x) + 14 = 2x + 21
 test/673111: (7p)^-2 Simplify1 solutions Answer 418489 by jim_thompson5910(28595)   on 2012-10-28 23:27:49 (Show Source):
 Quadratic-relations-and-conic-sections/673124: solve the equation (11r+8) (3r-5)=01 solutions Answer 418488 by jim_thompson5910(28595)   on 2012-10-28 23:23:11 (Show Source): You can put this solution on YOUR website! or or or So the solutions are or
 Trigonometry-basics/672918: if your distance from the foot of the tower is 20m and the angle of elevation is 40 degrees, find the height of the tower?1 solutions Answer 418393 by jim_thompson5910(28595)   on 2012-10-28 15:14:14 (Show Source): You can put this solution on YOUR website!tan(angle) = opp/adj tan(40) = x/20 20*tan(40) = x x = 20*tan(40) x = 16.7819926 So the tower is roughly 16.7819926 meters tall.
 Complex_Numbers/672826: list the non real solutions of the equstion 2x^2-4x+4 1 solutions Answer 418381 by jim_thompson5910(28595)   on 2012-10-28 14:18:03 (Show Source): You can put this solution on YOUR website!In the case of , it is in the form , so , , Use the quadratic formula to solve for x Plug in , , or or or or So the two nonreal (or complex) solutions are or
 test/672793: If p=2c prove that b=c1 solutions Answer 418380 by jim_thompson5910(28595)   on 2012-10-28 14:14:14 (Show Source): You can put this solution on YOUR website!Something is missing as there is no relationship established between b and p.
 Square-cubic-other-roots/672891: what is g(x)=6|x-3|+4 in a graph1 solutions Answer 418379 by jim_thompson5910(28595)   on 2012-10-28 14:13:38 (Show Source): You can put this solution on YOUR website!Use a graphing calculator to get the following (graph in green)
 Problems-with-consecutive-odd-even-integers/672884: Prove that for every positive integer n, n3 + n is even1 solutions Answer 418378 by jim_thompson5910(28595)   on 2012-10-28 14:12:42 (Show Source): You can put this solution on YOUR website!Case 1: n is an even integer Let n be an even integer. So n = 2k for some integer k. So if n = 2k, then n^3 = (2k)^3 = 8k^3 and n^3 + n becomes 8k^3 + 2k which partially factors to 2(4k^3 + k) which is in the form 2q where q = 4k^3 + k (which can be proven that it is also an integer). Since 2q is even for any integer q, this proves that if n is an even integer, then n^3+n is even. ------------------------------------------------------------------------- Case 2: n is an odd integer Let n be an odd integer. So n = 2k+1 for some integer k. So if n = 2k+1, then n^3 = (2k+1)^3 = 8k^3 + 12k^2 + 6k + 1 So n^3 + n becomes (8k^3 + 12k^2 + 6k + 1) + (2k + 1) 8k^3 + 12k^2 + 6k + 1 + 2k + 1 8k^3 + 12k^2 + 8k + 2 which partially factors to 2(4k^3+6k^2+4k+1) which is in the form 2q where q = 4k^3+6k^2+4k+1 (which can be proven that it is also an integer). Since 2q is even for any integer q, this proves that if n is an odd integer, then n^3+n is even. =========================================================================================================== We've exhausted all possibilities and scenarios because any integer is either even or odd (cannot be something else or both). So these two cases prove that n^3 + n is an even integer for every integer n.
 Linear-equations/672879: (X+3)(x+3)=6x + 12?1 solutions Answer 418369 by jim_thompson5910(28595)   on 2012-10-28 13:45:42 (Show Source): You can put this solution on YOUR website! or So the two exact solutions are or
Polynomials-and-rational-expressions/672866: 8a^2+14a-49
1 solutions

Answer 418360 by jim_thompson5910(28595)   on 2012-10-28 13:27:42 (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 :
1,2,4,7,8,14,28,49,56,98,196,392
-1,-2,-4,-7,-8,-14,-28,-49,-56,-98,-196,-392

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

These factors pair up and multiply to .
1*(-392) = -392
2*(-196) = -392
4*(-98) = -392
7*(-56) = -392
8*(-49) = -392
14*(-28) = -392
(-1)*(392) = -392
(-2)*(196) = -392
(-4)*(98) = -392
(-7)*(56) = -392
(-8)*(49) = -392
(-14)*(28) = -392

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

First NumberSecond NumberSum
1-3921+(-392)=-391
2-1962+(-196)=-194
4-984+(-98)=-94
7-567+(-56)=-49
8-498+(-49)=-41
14-2814+(-28)=-14
-1392-1+392=391
-2196-2+196=194
-498-4+98=94
-756-7+56=49
-849-8+49=41
-1428-14+28=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).

 Word_Problems_With_Coins/672875: how many ways can 1.00 dollar be made using 19 coins? i am not aloud to use 50 cent pieces.1 solutions Answer 418359 by jim_thompson5910(28595)   on 2012-10-28 13:26:40 (Show Source): You can put this solution on YOUR website!There are 7 ways to do this (where you use exactly 19 coins to get \$1.00): ================================================================================================= 18 nickels + 1 dime = \$1.00 ----------------------------------------- 5 pennies + 9 nickels + 5 dimes = \$1.00 ----------------------------------------- 5 pennies + 12 nickels + 1 dime + 1 quarter = \$1.00 ----------------------------------------- 10 pennies + 9 dimes = \$1.00 ----------------------------------------- 10 pennies + 3 nickels + 5 dimes + 1 quarter = \$1.00 ----------------------------------------- 10 pennies + 6 nickels + 1 dime + 2 quarters = \$1.00 ----------------------------------------- 15 pennies + 1 dime + 3 quarters = \$1.00 ================================================================================================= Again, there are 7 ways to do this
 Linear-systems/672870: -1x + 2 = -4/5x + 8/51 solutions Answer 418354 by jim_thompson5910(28595)   on 2012-10-28 13:15:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. 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
Polynomials-and-rational-expressions/672867: 9y^2+17y-2
1 solutions

Answer 418353 by jim_thompson5910(28595)   on 2012-10-28 13:14:28 (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 :
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18

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

These factors pair up and multiply to .
1*(-18) = -18
2*(-9) = -18
3*(-6) = -18
(-1)*(18) = -18
(-2)*(9) = -18
(-3)*(6) = -18

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

First NumberSecond NumberSum
1-181+(-18)=-17
2-92+(-9)=-7
3-63+(-6)=-3
-118-1+18=17
-29-2+9=7
-36-3+6=3

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).

 Numeric_Fractions/672673: i need to put this problem into 2 equal parts 5 7/8 into two equal pieces1 solutions Answer 418273 by jim_thompson5910(28595)   on 2012-10-27 22:06:26 (Show Source): You can put this solution on YOUR website!5 7/8 = 5+7/8 5 7/8 = 5(8/8)+7/8 5 7/8 = 40/8+7/8 5 7/8 = 47/8 ----------------------------- Now cut 47/8 in half by multiplying it by 1/2 47/8 * 1/2 = (47*1)/8*2) = 47/16 Then convert back to a mixed number 47/16 = 2 remainder 15 47/16 = 2 + 15/16 47/16 = 2 15/16 So 5 7/8 cut in half is 2 15/16
 Functions/672712: simplify 84/144 to the lowest terms.1 solutions Answer 418272 by jim_thompson5910(28595)   on 2012-10-27 22:03:28 (Show Source): You can put this solution on YOUR website!Divide each by the LCM 12 to get 84/12 = 7 144/12 = 12 So 84/144 reduces to 7/12
 Functions/672710: Evaluate the function at the indicated values f(x)=2|x-1| ; f(-2) How far did I do f(-2)=2|-2-1| =2|-3| 1 solutions Answer 418270 by jim_thompson5910(28595)   on 2012-10-27 22:02:51 (Show Source): You can put this solution on YOUR website!f(x) = 2|x-1| f(-2) = 2|-2-1| f(-2) = 2|-3| f(-2) = 2(3) f(-2) = 6
 Expressions-with-variables/672662: 4a+5b-6c=2 -3a-2b+7c=-15 -a+4b+2c=-13 I know the answer is (-3, -2 -4) but can't figure out how to get it1 solutions Answer 418268 by jim_thompson5910(28595)   on 2012-10-27 21:50:23 (Show Source): You can put this solution on YOUR website!There are many ways to do this, but here is one of them. Convert 4a+5b-6c=2 -3a-2b+7c=-15 -a+4b+2c=-13 to matrix form to get ```4 5 -6 2 -3 -2 7 -15 -1 4 2 -13 ``` Then use row reduction ```4 5 -6 2 -3 -2 7 -15 -1 4 2 -13 1 1.25 -1.5 0.5 0.25*R1 -3 -2 7 -15 -1 4 2 -13 1 1.25 -1.5 0.5 0 1.75 2.5 -13.5 R2 + (3)*R1 -1 4 2 -13 1 1.25 -1.5 0.5 0 1.75 2.5 -13.5 0 5.25 0.5 -12.5 R3 + (1)*R1 1 1.25 -1.5 0.5 0 1 1.4286 -7.7143 0.571429*R2 0 5.25 0.5 -12.5 1 0 -3.2857 10.1429 R1 + (-1.25)*R2 0 1 1.4286 -7.7143 0 5.25 0.5 -12.5 1 0 -3.2857 10.1429 0 1 1.4286 -7.7143 0 0 -7 28 R3 + (-5.25)*R2 1 0 -3.2857 10.1429 0 1 1.4286 -7.7143 0 0 1 -4 -0.142857*R3 1 0 0 -3 R1 + (3.28571)*R3 0 1 1.4286 -7.7143 0 0 1 -4 1 0 0 -3 0 1 0 -2 R2 + (-1.42857)*R3 0 0 1 -4 ``` The right hand column is -3, -2, -4 These 3 values correspond to a, b, and c respectively. So the solutions are... a = -3 b = -2 c = -4 They form the ordered triple (-3, -2, -4)
 Exponents-negative-and-fractional/672713: simplify 7x^-2 using positive exponents 1 solutions Answer 418265 by jim_thompson5910(28595)   on 2012-10-27 21:44:01 (Show Source):
 Graphs/672643: find the slope if x = -31 solutions Answer 418236 by jim_thompson5910(28595)   on 2012-10-27 17:45:02 (Show Source): You can put this solution on YOUR website!x = -3 is a vertical line. So the slope is undefined.
 Distributive-associative-commutative-properties/672639: -144/41 solutions Answer 418233 by jim_thompson5910(28595)   on 2012-10-27 17:29:24 (Show Source): You can put this solution on YOUR website!-144/4 = (-36*4)/4 = -36
 Complex_Numbers/672609: Please help me solve this equation: x^2-20x=125 We have to solve the equation to see what its roots/complex numbers are. 1 solutions Answer 418229 by jim_thompson5910(28595)   on 2012-10-27 17:22:53 (Show Source): You can put this solution on YOUR website! Use the quadratic formula to solve for x Plug in , , or or or or So the two roots/solutions are or
 Radicals/672638: Find the distance between (–4, 0) and (–5, –3). Express your answer in simplified radical form.1 solutions Answer 418228 by jim_thompson5910(28595)   on 2012-10-27 17:18:41 (Show Source): You can put this solution on YOUR website!d = sqrt((x2-x1)^2+(y2-y1)^2) d = sqrt((-5-(-4))^2+( -3- 0)^2) d = sqrt((-5+4)^2+( -3- 0)^2) d = sqrt((-1)^2+(-3)^2) d = sqrt(1+9) d = sqrt(10) So exact distance between the two points is sqrt(10) units. Using a calculator, the approximate distance is roughly 3.16228 units.
 Equations/672635: what does t equal in 7t-3=101 solutions Answer 418224 by jim_thompson5910(28595)   on 2012-10-27 17:11:40 (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
 Quadratic_Equations/672615: A bicyclist is riding at a speed of 18mi/h when she starts down a long hill. The distance d she travels in feet can be modeled by d(t) = 4t^2 + 18t, where t is the time in seconds. How long will it take her to reach the bottom of a 400-foot-long hill? We have to use the quadratic formula to find t. I attempted the problem and i got 12.5 seconds.. but im not sure if im right Heres my work: d(t)=4t^2+18t=400 d(t)=4t^2+18t=400/4 t^2+4.5t=100 t^2+4.5t-100=0 (x-12.5)(x+8) 12.5 & -8 seconds. is this correct? Thanks(:1 solutions Answer 418216 by jim_thompson5910(28595)   on 2012-10-27 15:51:24 (Show Source): You can put this solution on YOUR website!You should have 8 or -12.5 seconds. Because a negative amount of time doesn't make sense, you toss out the negative solution to get t = 8 seconds.