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# Recent problems solved by 'Alan3354'

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 Pythagorean-theorem/292483: A 37-inch-square TV is on sale at the local electronics store. If 37 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen.1 solutions Answer 211245 by Alan3354(30993)   on 2010-04-15 09:34:34 (Show Source): You can put this solution on YOUR website!A 37-inch-square TV is on sale at the local electronics store. If 37 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen. ----------------------- I've never seen a square screen, but s =~ 26.16 inches ------------------- ------------------- For modern TV's, the width to height ratio is 16:9. Using that: But, for modern TV's, the width to height ratio is 16:9. Using that: u =~ 2.016 inches width = 16u =~ 32.25 inches height = 9u =~ 18.14 inches ----------------------------- Don't buy the square one. Tho the screen area is larger, the format is not compatible.
 Exponents-negative-and-fractional/292384: -1/5)x to the -1/5 times x to the -1/4 what i tried: 1/x to the 1/5 times 1/x to the 1/4 = 1/x to the 1/20 the answer is supposed to be 1/x to the 9/201 solutions Answer 211202 by Alan3354(30993)   on 2010-04-14 22:00:06 (Show Source): You can put this solution on YOUR website! Add the exponents = = =
 Trigonometry-basics/292282: (4+4i)^51 solutions Answer 211201 by Alan3354(30993)   on 2010-04-14 21:55:53 (Show Source): You can put this solution on YOUR website!(4+4i)^5 ------------ -->(4sqrt(2)cis(45))^5 = 4096sqrt(2)cis(225) = 4096sqrt(2)*(-sqrt(2)/2 + i(-sqrt(2)/2) = -4096 - 4096i =
 Triangles/292378: The sum of two numbers is 20, and the sum of their squares is 208. Find the numbers.1 solutions Answer 211197 by Alan3354(30993)   on 2010-04-14 21:29:53 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 20, and the sum of their squares is 208. Find the numbers. -------------- x+y = 20 (x - 12)*(x - 8) = 0 x = 8 y = 12
 Divisibility_and_Prime_Numbers/292365: is 2 divisible by 32 1 solutions Answer 211190 by Alan3354(30993)   on 2010-04-14 21:09:09 (Show Source): You can put this solution on YOUR website!2/32 = 1/16 = 0.0625 It is, unless you mean evenly divisible (an integer result).
 Polygons/292337: the measure of each angle of this regular polygon is 135 degrees. what is it?1 solutions Answer 211188 by Alan3354(30993)   on 2010-04-14 21:05:54 (Show Source): You can put this solution on YOUR website!135º is the interior angle, so the exterior is 45º (180-135) The sum of exterior angles for any polygon is 360º 360/45 = 8 It's an octagon, or a STOP sign
 decimal-numbers/292276: what is the greatest decimal with hundredths that will round to 0.5 when rounded to the nearest tenth?1 solutions Answer 211165 by Alan3354(30993)   on 2010-04-14 18:28:11 (Show Source): You can put this solution on YOUR website!0.49
 Linear-equations/292254: how do I solve In7/In31 solutions Answer 211164 by Alan3354(30993)   on 2010-04-14 18:25:55 (Show Source): You can put this solution on YOUR website!Use a calculator
 Surface-area/292271: What is the ratio of 4ft to 4yd1 solutions Answer 211163 by Alan3354(30993)   on 2010-04-14 18:15:48 (Show Source): You can put this solution on YOUR website!1 to 3
 Percentage-and-ratio-word-problems/292269: Why is \$10 to \$20 a 100% increase, while \$20 to \$10 is a 50% decrease. Explain your answer.1 solutions Answer 211160 by Alan3354(30993)   on 2010-04-14 18:05:33 (Show Source): You can put this solution on YOUR website!Why is \$10 to \$20 a 100% increase, while \$20 to \$10 is a 50% decrease. Explain your answer. -------------- It's based on what the change is from. From 10 to 20 starts with 10. 10/10 is 100% From 20 to 10 starts with 20. 10/20 is 50% ----------------- What you start with is the base. If you try to do it any other way, it's a lot less meaningful.
 Square-cubic-other-roots/292261: Factor completely. If the polynomial is prime, state this. x3 + 3x2 - 28x 1 solutions Answer 211159 by Alan3354(30993)   on 2010-04-14 18:03:07 (Show Source): You can put this solution on YOUR website!28 = 7*4 3 = 7 - 4 There are 2 hints.
 Probability-and-statistics/292242: There are 15 balls in a rectangular box 5 are red, 6 are yellow and the rest is green. If 2 balls are selected at random without replacement one after the other, what is the probability that they are: a) both green (b) of the same color. 1 solutions Answer 211156 by Alan3354(30993)   on 2010-04-14 17:49:33 (Show Source): You can put this solution on YOUR website!There are 15 balls in a rectangular box 5 are red, 6 are yellow and the rest is green. If 2 balls are selected at random without replacement one after the other, what is the probability that they are: a) both green There are 4 green balls, 15 balls total. The 1st is 4/15, the 2nd is 3/14. (4/15)*(3/14) = 2/35 (b) of the same color. That can be: 2 red (5/15)*(4/14) = 20/210 2 yellow (6/15)*(5/14) = 30/210 2 green = 12/210 ------------------ Add those up = 62/210 = 31/105
 Polynomials-and-rational-expressions/292250: what is the polynomial degree to 5x to the 4th power 1 solutions Answer 211153 by Alan3354(30993)   on 2010-04-14 17:29:05 (Show Source): You can put this solution on YOUR website!It's 4.
 Divisibility_and_Prime_Numbers/292247: I don't understand how to determine whether a natural number is divisible. In example: is 235 divisible by 2,3, 5?1 solutions Answer 211152 by Alan3354(30993)   on 2010-04-14 17:25:49 (Show Source): You can put this solution on YOUR website!I don't understand how to determine whether a natural number is divisible. In example: is 235 divisible by 2,3, 5? ------------------ You can use a calculator. 235 = 5*47 ------------ Any number ending in 5 or 0 is divisible by 5. If it's even, it's divisible by 2.
 Linear-equations/292220: What is the equation in slope-interaction form for the line passing through each pair of points? (9,-1) and (6,-2) (12,5) and (-4,1) 1 solutions Answer 211147 by Alan3354(30993)   on 2010-04-14 17:11:08 (Show Source): You can put this solution on YOUR website!Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ Another approach using determinants: |x y 1| |2 1 1| = 0 |3 5 1| -------- x(1-5) - y(2-3) + 1(10-3) = 0 -4x + y + 7 = 0 y = 4x - 7 --------- For further assistance, or to check your work, email me via the thank you note or at MoralLoophole@aol.com
 Graphs/292234: Please help me solve this question as soon as you can: Thanks so much in advance!!!! 1 solutions Answer 211141 by Alan3354(30993)   on 2010-04-14 16:52:11 (Show Source): You can put this solution on YOUR website!Did you try to factor it? 10 will be either 1*10 or 5*2. All coefficients are positive. You try it.
 Polygons/292236: how would you simplify the product 3w(w+2)1 solutions Answer 211140 by Alan3354(30993)   on 2010-04-14 16:51:04 (Show Source): You can put this solution on YOUR website!It cannot be simplified much, if any. Simplified can be a matter of opinion.
 Polynomials-and-rational-expressions/292174: How would I solve for this division problem? (x^3 + x^2 - 10x - 6) / (x - 3)1 solutions Answer 211136 by Alan3354(30993)   on 2010-04-14 16:42:08 (Show Source): You can put this solution on YOUR website!It's not an equation, there's nothing to solve. "Solve for" applies to a variable, as in "solve for x", but that does not apply here. ----------- This can only be simplified, or reduced, by dividing the denominator into the numerator.
 Problems-with-consecutive-odd-even-integers/292230: Solve by factoring and using the principle of zero. x^2- 7x=01 solutions Answer 211135 by Alan3354(30993)   on 2010-04-14 16:32:28 (Show Source): You can put this solution on YOUR website!Factor out x.
 expressions/292196: Please explain how to get my answer to 2x-7x=-401 solutions Answer 211128 by Alan3354(30993)   on 2010-04-14 15:27:49 (Show Source): You can put this solution on YOUR website!2x-7x=-40 ------------ 2x-7x = -5x -5x = -40 Divide by -5 x = -40/-5 x = 8
 Rectangles/292198: find the area of a rectangle that measures 17 yards by 29 yards 1 solutions Answer 211127 by Alan3354(30993)   on 2010-04-14 15:26:14 (Show Source): You can put this solution on YOUR website!You have only 2 numbers. Give it a try.
 Polynomials-and-rational-expressions/292116: Find the polynominal using real coefficents. Degree 4; zeros ;2 multiplicity 2,4i I got x^4-4x^3-3x^2-40+208 but it is wrong. I am confused can someone please help? 1 solutions Answer 211100 by Alan3354(30993)   on 2010-04-14 11:34:46 (Show Source): You can put this solution on YOUR website!Find the polynominal using real coefficents. Degree 4; zeros ;2 multiplicity 2,4i I got x^4-4x^3-3x^2-40+208 but it is wrong. I am confused can someone please help? ------------- Complex roots come in conjugate pairs, so -4i is also a root. If you mean the multiplicity of the the 2 root is 2: (x-2)*(x-2)*(x+4i)*(x-4i) = =
 Linear-systems/292113: how do you simplify linear equations like y=3/2x+21 solutions Answer 211096 by Alan3354(30993)   on 2010-04-14 11:13:05 (Show Source): You can put this solution on YOUR website!how do you simplify linear equations like y=3/2x+2 -------------- That's as simple as that one gets. It's in slope-intercept form. It can by put into "standard form" y=3/2x+2 2y = 3x + 4 3x - 2y = -4 or 3x - 2y + 4 = 0 ------------------ Standard form has the x and y terms on the same side, and uses integers. "Simplified" can be a matter of opinion.
Quadratic_Equations/291689: A ball is projected into the air. Its height at time t is given by the equation h = -16t^2 + 60x +1. When will the height be 8 feet?

1 solutions

Answer 211094 by Alan3354(30993)   on 2010-04-14 10:43:54 (Show Source):
You can put this solution on YOUR website!
A ball is projected into the air. Its height at time t is given by the equation h = -16t^2 + 60x +1. When will the height be 8 feet?
-----------------
When h = 8
8 = -16t^2 + 60t + 1 (I think you meant 60t, not 60x)
-16t^ + 60t - 7 = 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=3152 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.120541394047725, 3.62945860595227. Here's your graph:

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x1 and x2 are the values of t.
There are 2 of them, 8 feet going up, and 8 feet coming back down.

 Probability-and-statistics/292102: A box contains exactly 5 red, 4 blue, and 3 green balls. If two balls are selected at random one after the other without replacing the first, what is the probability that the first one is red and the second one is green?1 solutions Answer 211093 by Alan3354(30993)   on 2010-04-14 10:31:40 (Show Source): You can put this solution on YOUR website!A box contains exactly 5 red, 4 blue, and 3 green balls. If two balls are selected at random one after the other without replacing the first, what is the probability that the first one is red and the second one is green? ----------------- A total of 12 balls. 5 of 12 chances for the 1st ball being red. 11 balls are left. 3 of 11 chances for the 2nd ball being green. (5/12)*(3/11) = 5/44
 Square-cubic-other-roots/292103: Square root property. x2 (x squares) = 7x 1 solutions Answer 211092 by Alan3354(30993)   on 2010-04-14 10:29:05 (Show Source): You can put this solution on YOUR website! x(x-7) = 0 x = 0 x = 7 --------- PS It's x squared, not squares. Typos can be forgiven, but not knowing could mean the end of the world.
 Rate-of-work-word-problems/292091: It takes Sal 5 hours to paint a house. It takes Tom 3 hours to paint the same house. How long will it take to paint the house if both of them work together?1 solutions Answer 211088 by Alan3354(30993)   on 2010-04-14 09:45:46 (Show Source): You can put this solution on YOUR website!It takes Sal 5 hours to paint a house. It takes Tom 3 hours to paint the same house. How long will it take to paint the house if both of them work together? ---------------------- If you add the hours, it's 8 hours. Doesn't seem right, unless they drink a lot of beer and watch TV. --------------------------- Use the reciprocals, then you can add them. Sal does 1/5 of the house per hour. Tom does 1/3 per hour. Together, they do 1/5 + 1/3 per hour = 8/15 8/15 house per hour --> 15/8 hours per house. 15/8 is it, or 1.875 hours. -------------------------- There's a shortcut, product/sum 3*5/(3+5) = 15/8
 logarithm/292093: Solve the equation, log9 (b + 4) - log9 (b - 3) = log9 8. I tried to figure out a couple of ways; and came up with the answer that b=4. Is this answer correct? 1 solutions Answer 211086 by Alan3354(30993)   on 2010-04-14 09:33:03 (Show Source): You can put this solution on YOUR website!Solve the equation, log9 (b + 4) - log9 (b - 3) = log9 8. I tried to figure out a couple of ways; and came up with the answer that b=4. Is this answer correct? -------------- Sub 4, see if it's correct: Since the base is consistent, log(8) - log(1) = log(8) log(1) = 0 for any base, so it's correct.
 logarithm/292086: solve 8^x < 25. Are these the correct steps?- 8^x<25 log8 25 < x....is this the answer? thank you1 solutions Answer 211084 by Alan3354(30993)   on 2010-04-14 09:29:13 (Show Source): You can put this solution on YOUR website!solve 8^x < 25. Are these the correct steps?- 8^x<25 log8 25 < x....is this the answer? ----------------- x < ~ 1.54795
 Angles/292078: what are the angles sizes if one is 5 more times than 41 solutions Answer 211081 by Alan3354(30993)   on 2010-04-14 09:01:56 (Show Source): You can put this solution on YOUR website!I don't know what that means. I don't think it's my fault.
 Trigonometry-basics/291907: solve for the exact trigonometric value: sin theta = 2/5, 0 degrees < theta < 90 degrees; csc theta1 solutions Answer 211003 by Alan3354(30993)   on 2010-04-13 21:40:57 (Show Source): You can put this solution on YOUR website!csc = 1/sin csc = 5/2 --------- theta =~ 23.578º, no exact value for it