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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 number 1 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 form 1 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+216 1 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 work 1 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-3 1 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)^22 1 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 Number Second Number Sum 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 -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 =============================================================== Answer: 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 -8 1 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 = C 1 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^4-16 1 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 5ft 1 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+y 1 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 Start with the given equation. 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 Start with the given equation. 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

Quadratic_Equations/549807: x^2+x-110=0 1 solutions Answer 358082 by jim_thompson5910(28503)   on 2011-12-22 12:40:55 (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 Rewrite as Add to 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

Numeric_Fractions/549806: dentify the correct slope and y-intercept of the equation 5x - 3y = -6 1 solutions Answer 358081 by jim_thompson5910(28503)   on 2011-12-22 12:39:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point

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)

Linear-systems/549803: 10x+15y=20 -9x-15y=-21 1 solutions Answer 358079 by jim_thompson5910(28503)   on 2011-12-22 12:35:48 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: 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. ------------------------------------------------------------------ Now go back to the first equation. Plug in . 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. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)

Conjunction/549795: Given p is true, q is false, and r is false, find the truth value of the statement (q V r)<-->~p 1 solutions Answer 358077 by jim_thompson5910(28503)   on 2011-12-22 12:32:22 (Show Source): You can put this solution on YOUR website! (q V r)<-->~p (F V F)<-->~T (F V F)<-->F F <--> F T So (q V r)<-->~p is true when p is true, q is false, and r is false

Linear-systems/549793: 4. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -2x + 3y = -37.5 -4x + 0y = -24 1 solutions Answer 358076 by jim_thompson5910(28503)   on 2011-12-22 12:31:14 (Show Source): You can put this solution on YOUR website! Hint: If -4x + 0y = -24, then -4x + 0y = -24 -4x = -24 x = -24/(-4) x = 6 Now use this to find y (by plugging it into the first equation and solving for y)

Numeric_Fractions/549800: whrite 385/420 in simpleiest form 1 solutions Answer 358075 by jim_thompson5910(28503)   on 2011-12-22 12:27:57 (Show Source): You can put this solution on YOUR website! Divide each component by the GCF 35 to get 385/420 = 11/12

Distributive-associative-commutative-properties/549799: Which property is illustrated -3(x – 4) = -3x + 12 1 solutions Answer 358074 by jim_thompson5910(28503)   on 2011-12-22 12:25:58 (Show Source): You can put this solution on YOUR website! The distributive property is being illustrated here.

Equations/549798: Determine the slope between the points (0,-5) and (6,0) 1 solutions Answer 358072 by jim_thompson5910(28503)   on 2011-12-22 12:23:19 (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

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