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 Points-lines-and-rays/437927: Find the supplementary angle of 79°1 solutions Answer 302931 by nerdybill(6959)   on 2011-04-19 15:26:30 (Show Source): You can put this solution on YOUR website!Find the supplementary angle of 79° . Supplementary angles add up to 180 . Let x = supplemenatry angle then x + 79 = 180 x = 180 - 79 x = 101 degrees
 Points-lines-and-rays/437926: Find the complementary angle of 63°1 solutions Answer 302929 by nerdybill(6959)   on 2011-04-19 15:24:59 (Show Source): You can put this solution on YOUR website!Find the complementary angle of 63° . Complementary angles add up to 90 degrees. . Let x = complementary angle then x + 63 = 90 x = 90-36 x = 54 degrees
 Square-cubic-other-roots/437838: what is the √2+√3/√3-√2?1 solutions Answer 302863 by nerdybill(6959)   on 2011-04-19 12:07:55 (Show Source):
 Inequalities/437741: what is the answer to x/5 < 1/31 solutions Answer 302811 by nerdybill(6959)   on 2011-04-19 08:59:14 (Show Source): You can put this solution on YOUR website!x/5 < 1/3 multiplying both sides by 5: x < 5/3
 Graphs/437751: Simplify (3+4)^2+7(1+8)1 solutions Answer 302810 by nerdybill(6959)   on 2011-04-19 08:58:32 (Show Source): You can put this solution on YOUR website!(3+4)^2+7(1+8) (12)^2+7(9) 144+7(9) 144+63 207
 logarithm/437727: Solve for x. logx(x+6) = 2 Check the validity of each solution in the original equation. 1 solutions Answer 302808 by nerdybill(6959)   on 2011-04-19 08:53:39 (Show Source): You can put this solution on YOUR website!I presume you mean log base x... if not, please write back. . x = {-2, 3} you can toss out the negative solution (extraneous) leaving x = 3
 Linear-equations/437744: how do i find the slope to f(x)=-4x-51 solutions Answer 302807 by nerdybill(6959)   on 2011-04-19 08:49:14 (Show Source): You can put this solution on YOUR website!how do i find the slope to f(x)=-4x-5 . The slope is -4 we can tell immediately because it is already in "slope-intercept" form of: y = mx + b where m is slope b is the y-intercept
 Quadratic_Equations/437603: The height of an acorn falling out of a tree is given by h=-16t squared+b. If an acorn takes 1 second to fall to the ground. What is the value of b?1 solutions Answer 302729 by nerdybill(6959)   on 2011-04-18 21:02:38 (Show Source): You can put this solution on YOUR website!The height of an acorn falling out of a tree is given by h=-16t squared+b. If an acorn takes 1 second to fall to the ground. What is the value of b? . If it hits the ground h = 0 and they give you that t = 1 . plug it all into: h = -16t^2+b 0 = -16(1)^2+b 0 = -16(1)+b 0 = -16+b 16 = b
 Linear-equations/437388: Find the equation of the line having given slope and containing the given point m=7/8, (7,-9)1 solutions Answer 302574 by nerdybill(6959)   on 2011-04-18 14:37:37 (Show Source): You can put this solution on YOUR website!m=7/8, (7,-9) plug into "point-slope" form: y - y1 = m(x - x1) y - (-9) = (7/8)(x - 7) y + 9 = (7/8)x - 49/8 y = (7/8)x - 49/8 - 9 y = (7/8)x - 49/8 - 72/8 y = (7/8)x - 121/8 (this is what they're looking for)
 Volume/437394: how many gallons of water will a tank that's 36" long, 12 1/2" wide and 16 3/4 high hold?1 solutions Answer 302571 by nerdybill(6959)   on 2011-04-18 14:34:30 (Show Source): You can put this solution on YOUR website!since 1 cubic inch holds 0.0043 gallons of water . volume of tank = 36*12.5*16.75 volume of tank = 7537.5 cubic inches . gallons = 7537.5*0.0043 = 32.4 gallons
 Money_Word_Problems/437274: you owe a friend of 420. she decide to cancel 120 from you debt how much do you owe her now?1 solutions Answer 302478 by nerdybill(6959)   on 2011-04-18 10:21:27 (Show Source): You can put this solution on YOUR website!you owe a friend of 420. she decide to cancel 120 from you debt how much do you owe her now? 420 - 120 = \$300
 Percentage-and-ratio-word-problems/437255: Ann and Sean, paid \$208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost \$15 each and floor cost \$22 each. How many of each type of ticket did they purchase ? I have actually figured out the problem to be 8 balcony and 4 floor. The problem is that work has to be shown in algebraic form and I can't figure out how to set the problem up in algebraic form. 1 solutions Answer 302477 by nerdybill(6959)   on 2011-04-18 10:20:38 (Show Source): You can put this solution on YOUR website!Ann and Sean, paid \$208 for concert tickets. They bought twice as many balcony tickets as floor tickets. Balcony tickets cost \$15 each and floor cost \$22 each. How many of each type of ticket did they purchase ? . Let x = number of floor tickets then from "They bought twice as many balcony tickets as floor tickets." 2x = number of balcony tickets . Our equation comes from: "Balcony tickets cost \$15 each and floor cost \$22 each." and the fact that they paied \$208: 15(2x) + 22x = 208 30x + 22x = 208 52x = 208 x = 4 (floor tickets) . balcony tickets: 2x = 2(4) = 8
 Triangles/437287: A TRIANGLE HAS ONE ANGLE THAT MEASURES 16 DEGREES, ONE ANGLE THAT MEASURES 90 DEGREES, AND ANOTHER ANGLE THAT MEASURES 74 DEGREES. WHAT KIND OF TRIANGLE IS IT?1 solutions Answer 302474 by nerdybill(6959)   on 2011-04-18 10:13:31 (Show Source): You can put this solution on YOUR website!Because one angle is 90 degrees, we conclude that it is a "Right Triangle"
 test/437295: What is the value of the discriminant of the equation 6x^2-5x-3=0?1 solutions Answer 302471 by nerdybill(6959)   on 2011-04-18 10:11:07 (Show Source): You can put this solution on YOUR website!What is the value of the discriminant of the equation 6x^2-5x-3=0? discriminant is b^2 - 4ac (-5)^2 - 4(6)(-3) 25 - (24)(-3) 25 + 72 97
 test/437296: How many solutions does 5x^2-2x+3 have?1 solutions Answer 302470 by nerdybill(6959)   on 2011-04-18 10:08:57 (Show Source): You can put this solution on YOUR website!5x^2-2x+3 we calculate the discriminant: b^2-4ac (-2)^2-4(5)(3) 4-4(15) 4-60 -56 Since the discriminant is negative we conclude that there are "two complex solutions"
test/437282: what are the solutions of
4x^2-16x=16x-39
1 solutions

Answer 302458 by nerdybill(6959)   on 2011-04-18 09:40:56 (Show Source):
You can put this solution on YOUR website!
4x^2-16x=16x-39
4x^2-32x=-39
4x^2-32x+39 = 0
solve using the quadratic formula to get:
x = {6.5, 1.5}
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=400 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.5, 1.5. Here's your graph:

test/436577: 0.6x^2=1.2x+0.6
1 solutions

Answer 302053 by nerdybill(6959)   on 2011-04-16 11:42:11 (Show Source):
You can put this solution on YOUR website!
0.6x^2=1.2x+0.6
multiply by 10 to rid ourselves of decimal points:
6x^2=12x+6
divide both sides by 6:
x^2=2x+1
move everything to the left:
x^2-2x-1=0
can't factor so apply the quadratic formula to get:
x = {2.41, -0.41}
.
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=8 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.41421356237309, -0.414213562373095. Here's your graph:

 Miscellaneous_Word_Problems/436580: 80% is equivalent to 1 solutions Answer 302052 by nerdybill(6959)   on 2011-04-16 11:33:50 (Show Source): You can put this solution on YOUR website!% is "per one hundred" so, we can write 80% as 80/100 8/10 4/5 (or, .80)
 Linear-equations/436578: a4-b4 a to the power of 4 minus b to the power of 4 1 solutions Answer 302051 by nerdybill(6959)   on 2011-04-16 11:30:13 (Show Source): You can put this solution on YOUR website!Think: "difference of squares" . can be rewritten as: which factors out as: but, you're still not done. The term on the left is another "difference of squares":
 Complex_Numbers/436549: A holding pen fro cattle must be square and have a diagonal length of 140 meters. A: Find the length of a side of the pen? (Symplify your answer. An exact answer using radicals as needed) B: The area of the pen in square meters is?1 solutions Answer 302028 by nerdybill(6959)   on 2011-04-16 09:44:03 (Show Source): You can put this solution on YOUR website!A holding pen fro cattle must be square and have a diagonal length of 140 meters. A: Find the length of a side of the pen? (Symplify your answer. An exact answer using radicals as needed) Let x = length of one side of square then applying Pythagorean theorem: meters . B: The area of the pen in square meters is? area is then x^2 square meters
 Numbers_Word_Problems/436543: what is the equation for seventy-two is two more than the product of ten and a number?1 solutions Answer 302026 by nerdybill(6959)   on 2011-04-16 09:36:48 (Show Source): You can put this solution on YOUR website!what is the equation for seventy-two is two more than the product of ten and a number? . Let x = the number then 72 = 10x+2
 Equations/436547: Two numbres have a sum of 185. If one number is x, represent the other number as an algabraic expression in x.1 solutions Answer 302025 by nerdybill(6959)   on 2011-04-16 09:34:27 (Show Source): You can put this solution on YOUR website!Two numbres have a sum of 185. If one number is x, represent the other number as an algabraic expression in x. . Let x = "one number" then the "other" number is 185-x (this is what they're looking for)
 Miscellaneous_Word_Problems/436546: A rare isotope of a nuclear material is very unstable, decaying at a rate of 12% each second. Find how much isotope remains 10 seconds after 4 grams of the isotope is created. Use y=4(2.7)^0.12t, where t represents time in seconds.. There would be how many grams of the isotope. (Round to the nearest tenth as needed)1 solutions Answer 302024 by nerdybill(6959)   on 2011-04-16 09:32:01 (Show Source): You can put this solution on YOUR website!A rare isotope of a nuclear material is very unstable, decaying at a rate of 12% each second. Find how much isotope remains 10 seconds after 4 grams of the isotope is created. Use y=4(2.7)^0.12t, where t represents time in seconds.. . In the given equation: (I think you need a negative sign) y=4(2.7)^-0.12t y is the amount (grams) left after t (seconds) . simply replace t with 10 and equate: y=4(2.7)^-0.12t y=4(2.7)^-0.12(10) y=4(2.7)^-1.2 y=4(0.30364) y=1.2 grams
 logarithm/436328: How would I rewrite 1/2log s + 5 log q as a logarithm of a single quantity?1 solutions Answer 301860 by nerdybill(6959)   on 2011-04-15 15:00:50 (Show Source): You can put this solution on YOUR website!applying "log rules":
 Exponential-and-logarithmic-functions/436260: solve for x log(base 10)X+log(base 10)(X+1) = log(base 10)121 solutions Answer 301823 by nerdybill(6959)   on 2011-04-15 12:02:19 (Show Source): You can put this solution on YOUR website!log(base 10)X+log(base 10)(X+1) = log(base 10)12 log(base 10)X(X+1) = log(base 10)12 X(X+1) = 12 X^2+X = 12 X^2+X-12 = 0 (X+4)(X-3) = 0 X = {-4,3} Throw out the negative solution (extraneous) leaving: X = 3
 Exponential-and-logarithmic-functions/436263: solve for x 3-ln(x-2) = 51 solutions Answer 301821 by nerdybill(6959)   on 2011-04-15 12:00:30 (Show Source): You can put this solution on YOUR website!3-ln(x-2) = 5 3 = 5+ln(x-2) -2 = ln(x-2) e^(-2) = x-2 e^(-2) + 2 = x 2.135 = x
 test/436213: Solve equation by factoring x^4+10=7x^21 solutions Answer 301803 by nerdybill(6959)   on 2011-04-15 10:51:03 (Show Source): You can put this solution on YOUR website!x^4+10=7x^2 x^4-7x^2+10=0 . Let z = x^2 then we can write: z^2-7z+10=0 (z-2)(z-5)=0 z = {2, 5} . but, since z=x^2 x = {sqrt(2), sqrt(5)}
 Polynomials-and-rational-expressions/436209: What i the domain of the rational expression f(x)= x-5 over 2x+3 1 solutions Answer 301799 by nerdybill(6959)   on 2011-04-15 10:30:11 (Show Source): You can put this solution on YOUR website!What i the domain of the rational expression f(x)= x-5 over 2x+3 . The "domain" specifies the range of numbers for x. x can assume all numbers except when denominator is zero. so set 2x+3 to zero and solve for x (only value x can't take): 2x+3 = 0 2x = -3 x = -3/2 . domain then is all real numbers except -3/2 or (-oo, -3/2) U (-3/2, +oo) where oo is infinity
 Expressions-with-variables/436198: (4x + 6) (x - 5) + (6x - 2) (x - 5) please factor the expression1 solutions Answer 301791 by nerdybill(6959)   on 2011-04-15 09:30:56 (Show Source): You can put this solution on YOUR website!(4x + 6)(x - 5) + (6x - 2)(x - 5) (x - 5)[(4x + 6) + (6x - 2)] (x-5)[2(2x + 3) + 2(3x - 1)] 2(x-5)[(2x + 3) + (3x - 1)]
 Quadratic_Equations/435900: solve the equation n^2+6n+4=0 by compleating the square1 solutions Answer 301633 by nerdybill(6959)   on 2011-04-14 17:09:09 (Show Source): You can put this solution on YOUR website!n^2+6n+4=0 n^2+6n = -4 take 1/2 b-coefficient, square it, and add it to both sides: n^2+6n+9 = -4+9 (n+3)(n+3) = 5 (n+3)^2 = 5 n+3 = sqrt(5) n = +-sqrt(5) - 3 . n = {-0.764, -5.236}
 Quadratic_Equations/435903: find the roots of the equation x^2-3x+2=0 by using the quadratic equation1 solutions Answer 301632 by nerdybill(6959)   on 2011-04-14 17:05:08 (Show Source): You can put this solution on YOUR website!x^2-3x+2=0 factoring the left: (x-2)(x-1) = 0 . then, setting each term on the left to zero we get: x = {2, 1}