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Recent problems solved by 'nerdybill'

nerdybill answered: 6957 problems
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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): You can put this solution on YOUR website!

Inequalities/437741: what is the answer to x/5 < 1/3 1 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-5 1 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} . Details of quadratic follows: 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} . details of quadratic follows: 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)12 1 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) = 5 1 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^2 1 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 expression 1 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 square 1 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 equation 1 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}