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 Exponential-and-logarithmic-functions/549847: You invest $800 in an account with an annual interest rate of 3.2%, compounded annually. How much in in the account after 15 years? Round your answer to the nearest whole number1 solutions Answer 358126 by jim_thompson5910(28503) on 2011-12-22 14:39:20 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula Plug in , (the decimal equivalent of 3.2%), and . Evaluate to get Add to to get Multiply and to get . Evaluate to get . Multiply and to get . Round to the nearest hundredth (ie to the nearest penny). So there will be$1283.17 in the account.
 Polynomials-and-rational-expressions/549845: Write the equation y - 2 = 4(x + 5) in standard form1 solutions Answer 358123 by jim_thompson5910(28503)   on 2011-12-22 14:29:27 (Show Source): You can put this solution on YOUR website!y - 2 = 4(x + 5) y - 2 = 4x + 20 -22 = 4x - y 4x - y = -22
 test/549844: Factor 27x^3+2161 solutions Answer 358121 by jim_thompson5910(28503)   on 2011-12-22 14:22:18 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply ----------------------------------- Answer: So factors to . In other words,
 test/549843: Point B is the midpoint of AC . A (2, -1) B (k, t) C (2, 5) What is the value of t? 1 solutions Answer 358120 by jim_thompson5910(28503)   on 2011-12-22 14:21:49 (Show Source): You can put this solution on YOUR website!t is equal to the average of the y coordinates of points A and B So t = (-1+5)/2 = 4/2 = 2 which means that t = 2
 test/549842: Factor 8y^3-125 1 solutions Answer 358119 by jim_thompson5910(28503)   on 2011-12-22 14:20:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the difference of cubes formula. Remember the difference of cubes formula is Multiply ----------------------------------- Answer: So factors to . In other words,
 test/549841: Fond 15c7by hand show work1 solutions Answer 358118 by jim_thompson5910(28503)   on 2011-12-22 14:19:41 (Show Source): You can put this solution on YOUR website!(n!)/(r!(n-r)!) (15!)/(7!*(15-7)!) (15!)/(7!*8!) (15*14*13*12*11*10*9*8!)/(7!*8!) (15*14*13*12*11*10*9)/(7!) (15*14*13*12*11*10*9)/(7*6*5*4*3*2*1) (32432400)/(5040) 6435 So 15 C 7 = 6435
 Polynomials-and-rational-expressions/549840: If y varies directly with x and y = -7 when x = -1, find x when y = -84.1 solutions Answer 358117 by jim_thompson5910(28503)   on 2011-12-22 14:17:55 (Show Source): You can put this solution on YOUR website!y = kx -7 = k(-1) -7/(-1) = k 7 = k k = 7 So the equation is y = 7x So when y = -84, then y = 7x -84 = 7x -84/7 = x -12 = x x = - 12
 Linear-equations/549838: Write the point-slope form of the equation passing through (5, -1) with a slope of 6.1 solutions Answer 358114 by jim_thompson5910(28503)   on 2011-12-22 14:13:27 (Show Source): You can put this solution on YOUR website!y - y1 = m(x-x1) y - (-1) = 6(x-5) y + 1 = 6(x-5)
 Radicals/549833: I did look at question 549764 but I still can not figure out what needs to be done to get the choices that I have to choose from find a polynomial of degree 3 with roots 5, 3+4i x^3-11x^2-6x+5 x^3-22x^2+34x-45 x^3-11x^2+55x-125 x^3-81x^2+50x-31 solutions Answer 358112 by jim_thompson5910(28503)   on 2011-12-22 14:01:03 (Show Source): You can put this solution on YOUR website!, , or , , or , , or or or So the polynomial of degree 3 with roots 5, 3+4i is
 Money_Word_Problems/549828: What is the simple interest rate if a loan of £9000 gains interest of £2520 in 4 years? 1 solutions Answer 358105 by jim_thompson5910(28503)   on 2011-12-22 13:38:22 (Show Source): You can put this solution on YOUR website!I = Prt 2520 = 9000r(4) 2520 = 9000*4r 2520 = 36000r 2520/36000 = r 0.07 = r r = 0.07 So the interest rate is 7%
 Travel_Word_Problems/549826: How far would a car travel in 6.0 s if it started from rest, and accelerated at 2.0m/s2?1 solutions Answer 358103 by jim_thompson5910(28503)   on 2011-12-22 13:28:49 (Show Source): You can put this solution on YOUR website!d = v[i]*t + (1/2)*a*t^2 d = (0)(6) + (1/2)*(2)*(6)^2 d = (0)(6) + (1/2)*(2)*(36) d = 0 + (1/2)*(72) d = 0 + 36 d = 36 So the car would travel 36 meters
 Rational-functions/549825: (11^sqrt(3x^2)^221 solutions Answer 358100 by jim_thompson5910(28503)   on 2011-12-22 13:19:18 (Show Source): You can put this solution on YOUR website! So
Polynomials-and-rational-expressions/549824: factor x^2+36x+308
1 solutions

Answer 358097 by jim_thompson5910(28503)   on 2011-12-22 13:08:44 (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 :
1,2,4,7,11,14,22,28,44,77,154,308
-1,-2,-4,-7,-11,-14,-22,-28,-44,-77,-154,-308

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

These factors pair up and multiply to .
1*308 = 308
2*154 = 308
4*77 = 308
7*44 = 308
11*28 = 308
14*22 = 308
(-1)*(-308) = 308
(-2)*(-154) = 308
(-4)*(-77) = 308
(-7)*(-44) = 308
(-11)*(-28) = 308
(-14)*(-22) = 308

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

First NumberSecond NumberSum
13081+308=309
21542+154=156
4774+77=81
7447+44=51
112811+28=39
142214+22=36
-1-308-1+(-308)=-309
-2-154-2+(-154)=-156
-4-77-4+(-77)=-81
-7-44-7+(-44)=-51
-11-28-11+(-28)=-39
-14-22-14+(-22)=-36

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).

 Geometry_Word_Problems/549822: Use either < or >for box to write a true sentence 0 box -81 solutions Answer 358095 by jim_thompson5910(28503)   on 2011-12-22 13:05:34 (Show Source): You can put this solution on YOUR website!0 > -8
 Geometry_Word_Problems/549819: In a right triangle, find the length of the side not given. Given an exact answer and an approximate to three decimal places. Assume C represent the length of the hypotenuse 6 & 8 = C1 solutions Answer 358094 by jim_thompson5910(28503)   on 2011-12-22 13:05:08 (Show Source): You can put this solution on YOUR website!I'm assuming you have a triangle with legs of length 6 and 8. We basically have this triangle set up: To find the unknown length, we need to use the Pythagorean Theorem. Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Combine like terms. Rearrange the equation. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Simplify the square root. ================================================================ Answer: So the solution is . So the missing side is 10 units long.
 logarithm/549818: Find the real roots of f(x)=x^4-161 solutions Answer 358092 by jim_thompson5910(28503)   on 2011-12-22 13:00:42 (Show Source): You can put this solution on YOUR website!f(x) = x^4-16 0 = x^4-16 x^4-16 = 0 (x^2-4)(x^2+4) = 0 (x-2)(x+2)(x^2+4) = 0 x-2=0, x+2=0, or x^2+4=0 x=2, x=-2, x=2i, or x=-2i So the real roots are 2 and -2
 test/549817: -11(3/2)(.12(-12))1 solutions Answer 358091 by jim_thompson5910(28503)   on 2011-12-22 12:59:11 (Show Source): You can put this solution on YOUR website!-11(3/2)(.12(-12)) -11(3/2)(-1.44) (-33/2)(-1.44) (-16.5)(-1.44) 23.76 So -11(3/2)(.12(-12)) = 23.76
 Geometry_Word_Problems/549812: Find the perimeter and the area of the figure: use 3.14 (pi) of 2ft and 5ft1 solutions Answer 358089 by jim_thompson5910(28503)   on 2011-12-22 12:56:06 (Show Source): You can put this solution on YOUR website!We would need to see the figure to be able to help you out.
 Numeric_Fractions/549815: Reduce: 4x^2-y^2 / 2x+y1 solutions Answer 358088 by jim_thompson5910(28503)   on 2011-12-22 12:55:06 (Show Source): You can put this solution on YOUR website!(4x^2-y^2)/(2x+y) ((2x+y)(2x-y))/(2x+y) 2x-y So (4x^2-y^2)/(2x+y) = 2x-y
Numeric_Fractions/549811: Identify the correct x-intercept and y-intercept of the equation 15x - 5y = 30.
1 solutions

Answer 358085 by jim_thompson5910(28503)   on 2011-12-22 12:49:24 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Multiply and 0 to get 0.

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

 Numeric_Fractions/549809: the slope between the two points (1, 5) and (6, 4)?1 solutions Answer 358083 by jim_thompson5910(28503)   on 2011-12-22 12:43:20 (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 So the slope of the line that goes through the points and is
 Numeric_Fractions/549804: Angela currently has an account balance of $4,298.55. She opened the account 15 years ago with a deposit of$1,987.22. If the interest compounds monthly, what is the interest rate on the account?1 solutions Answer 358080 by jim_thompson5910(28503)   on 2011-12-22 12:37:57 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula Plug in , , and . Multiply and to get . Divide both sides by . Evaluate to get . Take the 180th root of both sides. Take the 180th root of to get . Subtract 1 from both sides. Combine like terms. Multiply boths sides by to isolate "r". Multiply and to get . Rearrange the equation. Round to the nearest ten-thousandth. So the interest rate is 5.15% (multiply by 100 to convert to a percentage)
 Equations/549797: Adair has deposited $361 in a savings account that earns interest at a rate of 1.3% compounded daily. What will the account balance be in 16 years?1 solutions Answer 358071 by jim_thompson5910(28503) on 2011-12-22 12:20:10 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula Plug in , (the decimal equivalent of 1.3%), and . Evaluate to get Add to to get Multiply and to get . Evaluate to get . Multiply and to get . Round to the nearest hundredth (ie to the nearest penny). So the account balance will be$444.47