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 Mixture_Word_Problems/624995: Cream costs \$10 per gallon. Milk costs \$3 per gallon. 9 gallons of milk was mixed with 2 gallons of cream. What is the cost of 1 gallon of this mixture?1 solutions Answer 393218 by Alan3354(30993)   on 2012-06-30 21:24:31 (Show Source): You can put this solution on YOUR website!Cream costs \$10 per gallon. Milk costs \$3 per gallon. 9 gallons of milk was mixed with 2 gallons of cream. What is the cost of 1 gallon of this mixture? ------------ 9 + 2 = 11 gallons ---- 9*3 + 2*10 = \$47 for 11 gallons --> \$47/11 per gallon =~ \$4.27/gallon
 Square-cubic-other-roots/624958: please help multiply (-x - 2)(-4x^2 + 3x +3)1 solutions Answer 393204 by Alan3354(30993)   on 2012-06-30 18:39:26 (Show Source): You can put this solution on YOUR website!(-x - 2)(-4x^2 + 3x +3) ---------------- = I helped. Your move.
Square-cubic-other-roots/624960: If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
1 solutions

Answer 393203 by Alan3354(30993)   on 2012-06-30 18:37:58 (Show Source):
You can put this solution on YOUR website!
h(t) = -9.8t2 – 10t + 270
It hits the ground then h = 0
------------
h(t) = -9.8t2 – 10t + 270 = 0
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=10684 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -5.78384879976431, 4.763440636499. Here's your graph:

==============
t = x
Ignore the negative solution.
-----------------
t = 4.76 seconds
=================
Gravitional acceleration on Earth =~ 9.8 meters/sec/sec
The equation for the vertical position should be:
h(t) = -4.9t^2 – 10t + 270
not -9.8t^2
==============
It might be -9.8t^2 on some other planet somewhere, but not here.

 Trigonometry-basics/624950: 18. If cos= 2 to the square root of 10/7 calculate the value of sin. a. 3/7 b. square root of 29/7 c. square root of 69/7 d. square root of 89/71 solutions Answer 393201 by Alan3354(30993)   on 2012-06-30 18:21:05 (Show Source): You can put this solution on YOUR website!If cos= 2 to the square root of 10/7 ------------- ??? ??
 Travel_Word_Problems/624944: How long does it take to go 10 miles at 5 miles per hour1 solutions Answer 393198 by Alan3354(30993)   on 2012-06-30 17:23:48 (Show Source): You can put this solution on YOUR website!How long does it take to go 10 miles at 5 miles per hour ------------ Hint: In the 1st hour, you go 5 miles, right?
 Expressions-with-variables/624946: SHORT ANSWER! Simplify the expression: and Express in terms of i sqrt of -641 solutions Answer 393197 by Alan3354(30993)   on 2012-06-30 17:23:06 (Show Source): You can put this solution on YOUR website! SHORT ANSWER! Simplify the expression: and Express in terms of i sqrt of -64 ---------- Short answer:
 Expressions-with-variables/624945: COMPLEX expressions, ADD and Simplify. (-5.2-5.3i) + (-8.5 + 6.9i) My solution Answer is: -13.7 + 1.6i ( am I correct? )1 solutions Answer 393196 by Alan3354(30993)   on 2012-06-30 17:13:17 (Show Source): You can put this solution on YOUR website!That's correct.
 Polynomials-and-rational-expressions/624936: Please someone help me with this problem: If a stone is tossed from the top of a 170 meter building, the height of the stone as a function of time is given by h(t) = -9.8ft^2 - 10t + 170. where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundreth place, include units in your answer.1 solutions Answer 393194 by Alan3354(30993)   on 2012-06-30 16:53:01 (Show Source): You can put this solution on YOUR website!Please someone help me with this problem: If a stone is tossed from the top of a 170 meter building, the height of the stone as a function of time is given by h(t) = -9.8ft^2 - 10t + 170. ------------ I think you mean h(t) = -4.9t^2 - 10t + 170 (on Earth) The -10t means it's tossed downward. check that, repost
 Linear-systems/624888: What would be the solution and answer for this equation? 4x+3y=26 y=3x y+5x=15 8y+5x=20 3y-9x=-18 y-3x=-3 x=4 22=y+2x1 solutions Answer 393193 by Alan3354(30993)   on 2012-06-30 16:41:35 (Show Source): You can put this solution on YOUR website!What would be the solution and answer for this equation? 4x+3y=26 y=3x y+5x=15 8y+5x=20 3y-9x=-18 y-3x=-3 x=4 22=y+2x ---------- Is that one problem?
 Polynomials-and-rational-expressions/624934: Please someone help me with this problem : In solving the equation (x+3)(x-3)- 8, Eric stated that the solution would be x + 3 - -8 - 7x = -11 or (x - 3) = -8 =7x = -5 However, at least one of these solutions fails to work when substituted bach into the original equation. Why is that? Please help Eric solve the problem 1 solutions Answer 393192 by Alan3354(30993)   on 2012-06-30 16:40:15 (Show Source): You can put this solution on YOUR website!Please someone help me with this problem : In solving the equation (x+3)(x-3)- 8, Eric stated that the solution would be x + 3 - -8 - 7x = -11 or (x - 3) = -8 =7x = -5 However, at least one of these solutions fails to work when substituted bach into the original equation. Why is that? ==================== In solving the equation (x+3)(x-3)- 8, That's not an equation, there's no equal sign. ----- I can't figure out what you mean. Try again.
 Metalworking/624821: An aluminum piston 4 in. in diameter that moves in the cylinder of a cast iron engine block must have a clearance diameter of 0.003 in. when hot. The temperature rises from 70 degrees to 160 degrees Farenheit. What should the clearance between the bore diameter and the piston be if the linear coefficient of expansion per unit length (inch) per degree Farenheit is 0.0000124 for aluminum and 0.00000655 for cast iron when the temperature is 70 degrees F? Thank you, in advance for your time and attention to this matter. Mary Miller1 solutions Answer 393188 by Alan3354(30993)   on 2012-06-30 16:18:31 (Show Source): You can put this solution on YOUR website!An aluminum piston 4 in. in diameter that moves in the cylinder of a cast iron engine block must have a clearance diameter of 0.003 in. when hot. The temperature rises from 70 degrees to 160 degrees Farenheit. What should the clearance between the bore diameter and the piston be if the linear coefficient of expansion per unit length (inch) per degree Farenheit is 0.0000124 for aluminum and 0.00000655 for cast iron when the temperature is 70 degrees F? ---------------- Al: alpha = 1.24E-5 FE: alpha = 6.55E-6 ------ If the Al piston is 4 in diameter at 70F: Its diameter at 160F = 4 + (160-70)*4*1.24E-5 = 4 + 446.4E-5 = 4 + 4.465E-3 = 4.004465 inches -------------- If the bore is 4.003 at 70F, it changes to: 4.003 + 4.003*90*6.55E-6 = 4.003 + 2359.8E-6 = 4.003 + 2.36E-3 = 4.00536 inches ---------------- 4.00536 - 4.004465 = 0.000895", less than 1/1000 of an inch. ------------------ In reality, the expansion of the bore hole in the solid block is more complex. The iron expands to make the bore larger, but the surrounding structure also contributes to "squeezing" the hole, so it's not a linear function.
 Linear-equations/624891: Find the slope-intercept form for the line satisfying the following conditions. x=3, y=2/51 solutions Answer 393186 by Alan3354(30993)   on 2012-06-30 16:07:22 (Show Source): You can put this solution on YOUR website!Find the slope-intercept form for the line satisfying the following conditions. x=3, y=2/5 ------------ That has to be 2 lines, or 1 point. Either way, your question has no answer.
 Average/624920: Find the largest of 2 consecutive integers whose sum is 2141 solutions Answer 393179 by Alan3354(30993)   on 2012-06-30 15:05:40 (Show Source): You can put this solution on YOUR website!Find the largest of 2 consecutive integers whose sum is 214 ============== 106 + 107 = 213 107 + 108 = 215 See a problem?
 test/624923: reduce de fraction to the lower form1 solutions Answer 393178 by Alan3354(30993)   on 2012-06-30 15:04:26 (Show Source): You can put this solution on YOUR website!reduce de fraction to the lower form ======== OK
 test/624922: i1 solutions Answer 393177 by Alan3354(30993)   on 2012-06-30 15:03:53 (Show Source):
 Average/624917: If I have completed y assignments with an average score of z what score x do I need on the y+1 assignment in order to achieve an average score of a? 1 solutions Answer 393172 by Alan3354(30993)   on 2012-06-30 14:49:38 (Show Source): You can put this solution on YOUR website!If I have completed y assignments with an average score of z what score x do I need on the y+1 assignment in order to achieve an average score of a? ------------- a*(y+1) = (y*z + Score)/(y+1)
 Polynomials-and-rational-expressions/624904: (x+2z)(2x+z)..?? How to solve the given above problem using (a+b)(a-b) identity and 4ab=(a+b)^2 - (a-b)^2 identity...?? 1 solutions Answer 393157 by Alan3354(30993)   on 2012-06-30 13:25:21 (Show Source): You can put this solution on YOUR website!(x+2z)(2x+z)..?? How to solve the given above problem using (a+b)(a-b) identity and 4ab=(a+b)^2 - (a-b)^2 identity...?? -------------- There's nothing to solve. Equations are solved. ---- (x+2z)(2x+z)..?? = x*(2x+z) + 2z*(2x+z) = = ------------- How to solve the given above problem using (a+b)(a-b) identity and 4ab=(a+b)^2 - (a-b)^2 identity...?? -------- (x+2z)(2x+z) is not a sum and difference, like (a+b)(a-b)
 Age_Word_Problems/624847: 200(2)/(7)g of gold is distributed equally amongst three surviving daughters of Mrs. rosemary. If the eldest daughter expected to bequeth 100g of gold, how much less gold does she recieve short of her expectations1 solutions Answer 393128 by Alan3354(30993)   on 2012-06-30 11:10:43 (Show Source): You can put this solution on YOUR website!200(2)/(7)g of gold ---------- How much is that? 400/7 ?
 Linear-equations/624818: simplify. If a quotient is undefined, state this. 0/-10 divided by -3/8 1 solutions Answer 393118 by Alan3354(30993)   on 2012-06-30 09:29:43 (Show Source): You can put this solution on YOUR website!0/-10 divided by -3/8 ----- = (0/-10)*(8/-3) = 0
 Unit_Conversion_Word_Problems/624829: If a plane was traveling the speed of light at 3×10 8 m/sec, how long (days) would the plane require to circumnavigate the Earth (diameter= 4.18×10 7 ft) ? How long would the plane require in microseconds? I need help setting up the problem1 solutions Answer 393116 by Alan3354(30993)   on 2012-06-30 09:22:51 (Show Source): You can put this solution on YOUR website!If a plane was traveling the speed of light at 3×10 8 m/sec, how long (days) would the plane require to circumnavigate the Earth (diameter= 4.18×10 7 ft) ? ------------- Change meters to feet 1 meter = 3.21 feet ---- c = 3E8*3.21 = 9.63E8 ft/sec d = r*t d = 4.18E7*pi feet d =~ 13.14E7 ft = 1.314E8 feet t = d/r = 1.314E8/9.63E8 =~ 0.136 sec = 1.36E-1 seconds 1 day = 86400 seconds --> 1.36E-1/86400 days =~ 1.5783E-6 days --------- How long would the plane require in microseconds? 1.36E-1 seconds = 1.36E5 usecs = 136,000 usecs
 Travel_Word_Problems/624827: 1.An object moves along a straight with an acceleration of 2m/s2.If its initial speed is 10m/s,what will be its speed 5s later? 2.An object dropped from a cliff falls with a constant acceleration of 10m/s2. Find its speed 2 s after it was dropped?1 solutions Answer 393113 by Alan3354(30993)   on 2012-06-30 09:17:32 (Show Source): You can put this solution on YOUR website!1.An object moves along a straight with an acceleration of 2m/s2.If its initial speed is 10m/s,what will be its speed 5s later? v = 10 + 2*5 = 20 m/sec ------------------- 2.An object dropped from a cliff falls with a constant acceleration of 10m/s2. Find its speed 2 s after it was dropped? = 10*2 = 20 m/sec
 Triangles/624837: What is the height of a triangle with a base of 100in and the legs are 6 and 8 inches?1 solutions Answer 393112 by Alan3354(30993)   on 2012-06-30 09:15:52 (Show Source): You can put this solution on YOUR website!What is the height of a triangle with a base of 100in and the legs are 6 and 8 inches? ---------------- It's not possible to have a triangle with sides of 6, 8 & 100
 Linear-systems/624855: how to use elimination method and substitution methods1 solutions Answer 393105 by Alan3354(30993)   on 2012-06-30 08:47:45 (Show Source): You can put this solution on YOUR website!how to use elimination method and substitution methods ================ Here's substitution: method of usbstitution 1:a=5-2b 5a+2b=1 Sub for a in the 2nd eqn 5(5-2b) + 2b = 1 25-10b + 2b = 1 -8b = -24 b = 3 ----- a = 5-2b a = -1 -------- 2: 2m+n=0 m+2n=3 Solve either eqn for either m or n: m+2n=3 --> m = 3-2n Then it's the same as #1 ======================== 3 to 7 are the same as #2 ----- 3: x+y=4 2x-y=5 4: y-2x=1 3x-4y=1 5: a-2b=9 2a+3b=4 6: x+2y=7 3x-2y=3 7: 2a+b=9 3a-2b=11
 Systems-of-equations/624841: method of usbstitution 1:a=5-2b 5a+2b=1 2: 2m+n=0 m+2n=3 3: x+y=4 2x-y=5 4: y-2x=1 3x-4y=1 5: a-2b=9 2a+3b=4 6: x+2y=7 3x-2y=3 7: 2a+b=9 3a-2b=111 solutions Answer 393104 by Alan3354(30993)   on 2012-06-30 08:46:32 (Show Source): You can put this solution on YOUR website!method of usbstitution 1:a=5-2b 5a+2b=1 Sub for a in the 2nd eqn 5(5-2b) + 2b = 1 25-10b + 2b = 1 -8b = -24 b = 3 ----- a = 5-2b a = -1 -------- 2: 2m+n=0 m+2n=3 Solve either eqn for either m or n: m+2n=3 --> m = 3-2n Then it's the same as #1 ======================== 3 to 7 are the same as #2 ----- 3: x+y=4 2x-y=5 4: y-2x=1 3x-4y=1 5: a-2b=9 2a+3b=4 6: x+2y=7 3x-2y=3 7: 2a+b=9 3a-2b=11
 Linear-equations/624853: Find the slope and y-intercept of the line that passes through(-4,-8) &(-3,-2) Please show work I would really appreciate any help I can get with this problem, Ijust dont understand this slope stuff at all. Please help me!!!!1 solutions Answer 393099 by Alan3354(30993)   on 2012-06-30 08:16:00 (Show Source): You can put this solution on YOUR website!Find the slope and y-intercept of the line that passes through(-4,-8) &(-3,-2) Please show work ----------- Find the slope first. Slope, m = diffy/diffx m = 6/1 = 6 ------------- Use y = mx + b and the point to find b, the y-intercept -8 = 6*(-4) + b b = 16 or (0,16) -------
 Matrices-and-determiminant/624836: Use the determinant to find the area of the triangle with the following vertices: (-3,1) (1,-3) (2,3) I know the area should be positive, but I'm still confused.1 solutions Answer 393098 by Alan3354(30993)   on 2012-06-30 07:53:20 (Show Source): You can put this solution on YOUR website!Use the determinant to find the area of the triangle with the following vertices: A (-3,1) B (1,-3) C (2,3) ------- A_B_C_A -3 +1 +2 -3 +1 -3 +3 +1 ---------- Add the diagonals starting at the upper left = 9 + 3 + 2 = 14 -------- Add the diagonals starting at the lower left = 1 - 6 - 9 = -16 ---------- The absolute value of the difference = 30 Area = 30/2 = 15 sq units
 Linear-equations/624852: Find the slope and y-intercept of the line in the equation y=3/4x-2 I would really appreciate any help I can get with this problem, Ijust dont understand this slope stuff at all. Please help me!!!!1 solutions Answer 393097 by Alan3354(30993)   on 2012-06-30 07:45:13 (Show Source): You can put this solution on YOUR website!Find the slope and y-intercept of the line in the equation y=3/4x-2 ----------- Slope is the coefficient of x. m = 3/4 ----- the y-int = -2
 Expressions-with-variables/624819: Solve D = ABC for A .1 solutions Answer 393073 by Alan3354(30993)   on 2012-06-29 21:26:38 (Show Source): You can put this solution on YOUR website!Solve D = ABC for A . --------- A = D/BC
 Signed-numbers/624791: I am teaching myself with a workbook and am stuck. Problem is 490 divided by negative 15. I don't understand the process of coming up with the answer. negative 32.7 I don't understand how to write out the problem and come up with a decimal point.1 solutions Answer 393065 by Alan3354(30993)   on 2012-06-29 19:35:39 (Show Source): You can put this solution on YOUR website!Problem is 490 divided by negative 15. I don't understand the process of coming up with the answer. negative 32.7 I don't understand how to write out the problem and come up with a decimal ------------ 490/(-15) The result will be negative, right? = - (490/15) = - (98/3) --------- 98/3 = 32.666.... repeating 6's --> 32.7 -------- Or 32.67, or 32.666667
 Rational-functions/624765: Choose from the following functions: g (x) -sqrt x How do I find the function and what is the description of transformation? Points on graph are (1,2), (2,3),(5,4), (10,5), and (17, 6).1 solutions Answer 393062 by Alan3354(30993)   on 2012-06-29 18:58:53 (Show Source): You can put this solution on YOUR website!Choose from the following functions: g (x) -sqrt x How do I find the function and what is the description of transformation? Points on graph are (1,2), (2,3),(5,4), (10,5), and (17, 6). ---------- Hint: the change in y values is 1. the change in x values increases by 2: 1, 3, 5, 7...
 Exponential-and-logarithmic-functions/624788: express log in terms of ln 5 and ln 7 ln (1/25) 1 solutions Answer 393061 by Alan3354(30993)   on 2012-06-29 18:48:55 (Show Source): You can put this solution on YOUR website!express log in terms of ln 5 and ln 7 ln (1/25) ------------- If you recognize that 25 = 5*5, then = -2*ln(5) ----------- ln(7) is not involved, just thrown in to cause confusion.