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test/742354: Solve the equation by completing the square: 4x^2 - 17x + 24 = 0
1 solutions

Answer 452462 by Alan3354(30993)   on 2013-04-27 11:29:06 (Show Source):
You can put this solution on YOUR website!
Solve the equation by completing the square: 4x^2 - 17x + 24 = 0
----------
4x^2 - 17x + 24 = 0
4x^2 - 17x = -24
x^2 - (17/4)x = -6
c to added = (b/2a)^2 = (17/8)^2
c = 289/64
------
x^2 - (17/4)x + 289/64 = -6 + 289/64 = -95/64
(x - 17/8)^2 = -95/64

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 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 : . The discriminant -95 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -95 is + or - . The solution is , or Here's your graph:

 Probability-and-statistics/742431: A man and his wife are each the weight of a full cart. They have two children, each weighing half of a cart. They need to cross a river, but the boat can only carry the weight of one cart. Devise a plan to get everyone across the river so that the boat does not sink. There must always be someone rowing the boat. 1 solutions Answer 452461 by Alan3354(30993)   on 2013-04-27 11:22:24 (Show Source): You can put this solution on YOUR website!A man and his wife are each the weight of a full cart. They have two children, each weighing half of a cart. They need to cross a river, but the boat can only carry the weight of one cart. Devise a plan to get everyone across the river so that the boat does not sink. There must always be someone rowing the boat. ---------------- The 2 kids row over, 1 rows back. The man rows over, the kid rows back. The 2 kids row over again, 1 rows back. The woman rows over, the kid rows back. The 2 kids row over.
 Travel_Word_Problems/742210: how long would it take for me to get to....Sandy Glade Holiday Park Coast Road Berrow Burnham-on-Sea Somerset TA8 2QX from wv14 8hn1 solutions Answer 452327 by Alan3354(30993)   on 2013-04-26 13:49:36 (Show Source): You can put this solution on YOUR website!how long would it take for me to get to....Sandy Glade Holiday Park Coast Road Berrow Burnham-on-Sea Somerset TA8 2QX from wv14 8hn ============= d = distance r = rate or speed --- d = r*t t = d/r
 Volume/742203: If the smaller cone has a volume of 343 cubic feet, what is the volume of the larger cone? 1 solutions Answer 452325 by Alan3354(30993)   on 2013-04-26 13:48:06 (Show Source): You can put this solution on YOUR website!If the smaller cone has a volume of 343 cubic feet, what is the volume of the larger cone? -------------- More than 343 cu ft
 logarithm/742182: Solve a) 3^x =2 b) 4^x-5 c) 7^(-x)=3 d) 3^(1-x) = 5 e) (1/8)^x = 25 f) 5^(3x) =41 Can you please help me out? thanks so much in advance:) Can you show the work too because I will understand better thankyou:)1 solutions Answer 452306 by Alan3354(30993)   on 2013-04-26 11:43:18 (Show Source): You can put this solution on YOUR website!Solve a) 3^x =2 b) 4^x-5 c) 7^(-x)=3 d) 3^(1-x) = 5 e) (1/8)^x = 25 f) 5^(3x) =41 ------ These are all similar. I'll do the "hardest" ones. Solve a) 3^x =2 b) 4^x-5 No equal sign c) 7^(-x)=3 d) 3^(1-x) = 5 (1-x)*log(3) = log(5) 1-x = log(5)/log(3) ----------------- e) (1/8)^x = 25 x*log(1/8) = log(25) x = log(25)/log(1/8) x =~ -1.54795 ----------------- f) 5^(3x) =41
 Radicals/742194: 512m to the third power1 solutions Answer 452305 by Alan3354(30993)   on 2013-04-26 11:38:27 (Show Source): You can put this solution on YOUR website!512m to the third power ----------- What about it?
 Volume/742192: what is p 8p − 12 = 4(2p − 12)1 solutions Answer 452304 by Alan3354(30993)   on 2013-04-26 11:37:49 (Show Source): You can put this solution on YOUR website!8p - 12 = 4(2p - 12) 8p - 12 = 8p - 48 -12 = -48 ---------- No solution.
 logarithm/742181: Solve to the nearest thousand a) 2^x=11 b) 3^x=11 c) 5^(x-1)=9 d) 5^(1+x) = 2^(1-x) Can you please help me out? thanks so much in advance:)1 solutions Answer 452303 by Alan3354(30993)   on 2013-04-26 11:32:14 (Show Source): You can put this solution on YOUR website!Solve to the nearest thousand a) 2^x=~ 11 ------------------- x*log(2) = log(11) x = log(11)/log(2) x =~ 3.45943 To the nearest 1000, x = 0 ------------ b) 3^x=11 Do it like the 1st one. --------------------- c) 5^(x-1)=9 (x-1)*log(5) = log(9) ------------------ d) 5^(1+x) = 2^(1-x) Same as above.
 Rational-functions/742105: The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream?1 solutions Answer 452297 by Alan3354(30993)   on 2013-04-26 10:46:06 (Show Source): You can put this solution on YOUR website!The speed of a boat in still water is 8 km/h. It travels 60 km upstream and 60 km downstream in a total time of 16 hours. What is the speed of the stream? ------------- Avg speed of a round trip = 2*r1*r2/(r1+r2) = 120/16 = 7.5 2*(8-c)*(8+c)/16 = 7.5 c = 2 km/hr
 test/742152: 6-9i ------- 3i1 solutions Answer 452295 by Alan3354(30993)   on 2013-04-26 10:35:32 (Show Source): You can put this solution on YOUR website!6-9i ------- 3i ============== = (2 - 3i)/i = i*(2 - 3i)/i^2 = (2i - 3i^2)/-1 = 3i^2 - 2i = -3 - 2i
 Angles/742175: Can anyone help me? I've been stuck on this problem for days now: "Find the measure of an angle if its measure is four times the measure of its complement." 1 solutions Answer 452294 by Alan3354(30993)   on 2013-04-26 10:32:48 (Show Source): You can put this solution on YOUR website!"Find the measure of an angle if its measure is four times the measure of its complement." ----------- Angle + complement = 90 degs A + C = 90 A = 4C 4C + C = 90 5C = 90 C = 18 A = 90 - 18 Angle = 72 degs
 Trigonometry-basics/742168: tanx sinx+sinX=o1 solutions Answer 452292 by Alan3354(30993)   on 2013-04-26 10:13:45 (Show Source): You can put this solution on YOUR website!duplicate
 Trigonometry-basics/742169: tanx sinx+sinX=o1 solutions Answer 452291 by Alan3354(30993)   on 2013-04-26 10:11:55 (Show Source): You can put this solution on YOUR website!tanx sinx+sinX=o --------- tan(x)*sin(x) + sin(x) = 0 Are you too busy to try to make sense? sin(x)*(tan(x) + 1) = 0 sin(x) = 0 x = 0 + n*pi, n = 0,1,2,3... ------ tan(x) + 1 = 0 tan(x) = -1 x = 3pi/4 + n*pi, n = 0,1,2,3...
 logarithm/742138: Write the given equation in logarithmic form. 7^2=24011 solutions Answer 452290 by Alan3354(30993)   on 2013-04-26 10:04:24 (Show Source): You can put this solution on YOUR website!Write the given equation in logarithmic form. 7^2=2401 ------------ It's not an equation since the 2 sides are not equal. 7^4 = 2401
 test/742172: X^2.5=321 solutions Answer 452289 by Alan3354(30993)   on 2013-04-26 10:01:59 (Show Source): You can put this solution on YOUR website!duplicate
 test/742171: X^2.5=321 solutions Answer 452288 by Alan3354(30993)   on 2013-04-26 09:58:44 (Show Source): You can put this solution on YOUR website!X^2.5=32 ----------- Square both sides x^5 = 1024 x = 4
 logarithm/742163: How do you solve 49^log(base 7)(9)?1 solutions Answer 452287 by Alan3354(30993)   on 2013-04-26 09:56:10 (Show Source): You can put this solution on YOUR website!How do you solve 49^log(base 7)(9)? ---------- Solve for what? There's no variable.
 Triangles/742167: the graphs of y - 2x = 1, 4x + y = 7, and 2y - x = -4 contain the sides of the triangle. Find the coordinates and vertices of the triangle1 solutions Answer 452286 by Alan3354(30993)   on 2013-04-26 09:51:47 (Show Source): You can put this solution on YOUR website!the graphs of y - 2x = 1, 4x + y = 7, and 2y - x = -4 contain the sides of the triangle. Find the coordinates and vertices of the triangle ----------------- Coordinates of the vertices? They're the intersections of the 3 lines. Solve the pairs of eqns 2 at a time. ---- y - 2x = 1 --> y = 2x + 1 4x + y = 7 Sub for y in the 2nd eqn 4x + (2x+1) = 7 x = 1 y = 3 --> (1,3) ================= 2y - x = -4 4x + 7 = 7 Solve for the intersection. -------- 2y - x = -4 y - 2x = 1 Solve for the 3rd vertex.
 Pythagorean-theorem/742165: if b:11 in.; and c: 20 in. whats a? 1 solutions Answer 452285 by Alan3354(30993)   on 2013-04-26 09:46:50 (Show Source): You can put this solution on YOUR website!if b:11 in.; and c: 20 in. whats a? ----------------- How is a related to b & c ?
 Trigonometry-basics/742157: How do you find the solutions for: sin^2(x)=sin(x)+21 solutions Answer 452284 by Alan3354(30993)   on 2013-04-26 09:37:08 (Show Source): You can put this solution on YOUR website!How do you find the solutions for: sin^2(x)=sin(x)+2 --------------- sin^2(x) - sin(x) - 2 = 0 sub for sin(x) u^2 - u - 2 = 0 (u - 2)*(u + 1) = 0 u = 2 --> sin(x) = 2 (no real number solution) u = -1 --> sin(x) = -1 x = pi + 2n*pi, n = 0, 1, 2, 3...
 Surface-area/742125: The percentage change in the surface area of a cube when each side is tripled is1 solutions Answer 452283 by Alan3354(30993)   on 2013-04-26 09:28:48 (Show Source): You can put this solution on YOUR website!The percentage change in the surface area of a cube when each side is tripled ------------------ Surface area is a function of the square of side length --- 3x length --> 9x SA An increase of 800% ======================= Notice that 8 times more = 9 times as much
 Trigonometry-basics/741958: Find the radius of the circle when the central angle is π/2 and the arc length is 3π.1 solutions Answer 452232 by Alan3354(30993)   on 2013-04-25 20:38:32 (Show Source): You can put this solution on YOUR website!Find the radius of the circle when the central angle is π/2 and the arc length is 3π. ----------- arc = angle*r r = arc/angle = 3pi/(pi/2) r = 6
 Travel_Word_Problems/741972: WHAT is the unit rate of an airplane flying 1,200 miles in 6 hours?1 solutions Answer 452230 by Alan3354(30993)   on 2013-04-25 20:36:58 (Show Source): You can put this solution on YOUR website!WHAT is the unit rate of an airplane flying 1,200 miles in 6 hours? ------------ d = r*t r = d/t
 test/741980: Help please ?: find the measure of each angle to the nearest tenth of a degree. ; cos W = 0.01751 solutions Answer 452229 by Alan3354(30993)   on 2013-04-25 20:35:25 (Show Source): You can put this solution on YOUR website!find the measure of each angle to the nearest tenth of a degree. ; cos W = 0.0175 ------------- You need to get a calculator.
 Numbers_Word_Problems/741882: I am the only one in class who does not understand these: Twice the tens digit of a positive, two-digit integer is 1 less than the ones digit. Reversing the digits increases the number by 45. What is the number? Can you please help me get started.1 solutions Answer 452208 by Alan3354(30993)   on 2013-04-25 18:58:03 (Show Source): You can put this solution on YOUR website!Twice the tens digit of a positive, two-digit integer is 1 less than the ones digit. Reversing the digits increases the number by 45. What is the number? ------------------ t = 10's digit u = units ---- 2t + 1 = u 10t + u + 45 = 10u + t --- 2 eqns in 2 variables 2t + 1 = u --> u = 2t + 1 10t + u + 45 = 10u + t --> 9t + 45 = 9u --> t + 5 = u ------------- u = 2t + 1 t + 5 = u --- t + 5 = 2t + 1 t = 4 ---- u = 9 --> 49
 Average/741910: simplify 10^2-6^21 solutions Answer 452207 by Alan3354(30993)   on 2013-04-25 18:52:28 (Show Source): You can put this solution on YOUR website!duplicate
 �t�e�s�t/741903: If a/10 = 0.57, a is equal to what?1 solutions Answer 452205 by Alan3354(30993)   on 2013-04-25 18:51:34 (Show Source): You can put this solution on YOUR website!If a/10 = 0.57, a is equal to what? ----------- Multiply both sides by 10
 Average/741933: 10^3/10^-2= (a) 10 (b) 10 (c) 10 (d) 10 (e) None of these how do you solve this1 solutions Answer 452203 by Alan3354(30993)   on 2013-04-25 18:50:33 (Show Source): You can put this solution on YOUR website!10^3/10^-2= (a) 10 (b) 10 (c) 10 (d) 10 (e) None of these ---------------- Equations are solved. There's nothing on the right side, so it's not an equation. -------- PS a, b, c & d are the same. It's not 10.
 Average/741911: simplify 10^2-6^2 with basic calculator1 solutions Answer 452202 by Alan3354(30993)   on 2013-04-25 18:48:26 (Show Source): You can put this solution on YOUR website!simplify 10^2-6^2 with basic calculator --------------------- Is there some reason you can't do that?
 Polynomials-and-rational-expressions/741921: Please help! What is (2x-5)^2 as a perfect square trinomial?1 solutions Answer 452199 by Alan3354(30993)   on 2013-04-25 18:40:27 (Show Source): You can put this solution on YOUR website!What is (2x-5)^2 -------------- Multiply it. = (2x-5)*(2x-5) = 2x*(2x-5) - 5*(2x-5)
 Angles/741922: can the angles in a triangle have the measures given? 67 degrees,108 degrees,15 degrees 163 deg,10.7 deg,6.3 deg 22 2/3 deg,57 1/3 deg, 100 deg1 solutions Answer 452195 by Alan3354(30993)   on 2013-04-25 18:31:37 (Show Source): You can put this solution on YOUR website!can the angles in a triangle have the measures given? 67 degrees,108 degrees,15 degrees 163 deg,10.7 deg,6.3 deg 22 2/3 deg,57 1/3 deg, 100 deg --------------- The sum of the 3 angles has to be 180 degs. Add them.