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# Recent problems solved by 'scott8148'

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 Pythagorean-theorem/385091: My question is on the Pythagorean Theorom The question asks: Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5.She askes you to find the other leg of the triangle without using paper and pencil. What is your answer. I tried solving it by subtracting 5 from 13 because of the one rule that says the sum of the two legs will equal the hypotenuse if it is a right triangle, but I am not sure if that works for this. Thank you 1 solutions Answer 272502 by scott8148(6628)   on 2010-12-12 19:00:26 (Show Source): You can put this solution on YOUR website!the "rule" is ___ the SQUARE of the hypotenuse equals the sum of the SQUARES of the other two sides 5^2 + x^2 = 13^2
 Quadratic_Equations/384812: for the equation 25x^2 - kx = -4, find k so that the equation has exactly one rational root.1 solutions Answer 272394 by scott8148(6628)   on 2010-12-12 12:53:27 (Show Source): You can put this solution on YOUR website!25x^2 - kx + 4 = 0 (5x - 2)^2 = 0 use FOIL to find k
 Quadratic-relations-and-conic-sections/384828: Write an equation of a circle with center (-3,7) and radius 8.1 solutions Answer 272392 by scott8148(6628)   on 2010-12-12 12:47:19 (Show Source): You can put this solution on YOUR website!a general equation for a circle centered at (h,k) with a radius of r is ___ (x - h)^2 + (y - k)^2 = r^2
 Quadratic_Equations/384820: factor 28x^2-23x-15 into factors with integer coefficients, if posible.1 solutions Answer 272391 by scott8148(6628)   on 2010-12-12 12:44:46 (Show Source): You can put this solution on YOUR website!(7x + 3)(4x - 5)
 Circles/384036: in navigational terms, a minute is one sixtieth of a degree, and a second is one sixtieth of a minute. to the nearest foot, what is the length of a one-second arc on the equator?1 solutions Answer 272188 by scott8148(6628)   on 2010-12-11 14:55:01 (Show Source): You can put this solution on YOUR website!the circumference of the Earth is 40,000 km (the original definition of a meter was the distance from the equator to the pole, divided by 10,000,000) 2.54 cm = 1 in. 4E9 cm * (1 in / 2.54 cm) * (1 ft / 12 in) = circumference in feet divide the circumference by ___ 360º * (60 min / º) * (60 sec / min)
 Travel_Word_Problems/383968: 89. Penny tossing. If a penny is thrown downward at 30 ft/sec from the bridge at Royal Gorge, Colorado, how long does it take to reach the Arkansas River 1000 ft below?1 solutions Answer 272183 by scott8148(6628)   on 2010-12-11 14:38:48 (Show Source): You can put this solution on YOUR website!neglecting air resistance ___ h = 16t^2 + 30t ___ 1000 = 16t^2 + 30t 16t^2 + 30t - 1000 = 0 ___ 8t^2 + 15t - 500 = 0 use the quadratic formula to find t ___ the positive solution is the one you want
 Linear-equations/384174: Find the equation of a line with y-intercept -4 and perpendicular to 2x+3y=5.1 solutions Answer 271952 by scott8148(6628)   on 2010-12-10 13:39:01 (Show Source): You can put this solution on YOUR website!to quickly find a perpendicular line ___ swap the x and y coefficients , and change one of their signs 3x - 2y = 5 is perpendicular to 2x + 3y = 5 the y-int is -4 , so plug in to find the correct constant term 3(0) - 2(-4) = 8 the new equation is ___ 3x - 2y = 8
 Rectangles/384176: Solve by factoring and using the principle of zero products: 2x^2-11x+15=0 OK I done this before but with the quadratic and square rooting I'm lost I done this much so far Please help I'm so lost with this 2(x-2)(x+2)-11+15 then add 11 on both sides which would be 2x2=4 and 15+11 =4 -11+11=0 this is my third sending!! hopefully i get some help1 solutions Answer 271945 by scott8148(6628)   on 2010-12-10 13:29:24 (Show Source): You can put this solution on YOUR website!you have to FOIL two binomial factors to get 2x^2-11x+15 so the x terms of the binomials multiply to 2x^2 ___ like 2x and x the constant terms multiply to 15 ___ 3 & 5 , and 1 & 15 are the choices look at the center (x) term coefficient ___ it is negative this means that the factors of 15 must be negative ___ -3 & -5 , and -1 & -15 now the "tricky" part ___ the factors of the squared term (2x^2) are multiplied with the factors of the constant term (15) to end up with the coefficient of the x term (-11) you have to mix & match to get the right combination 2x * -3 = -6x x * -5 = -5x -5x + -6x = -11x so the factors are ___ (2x - 5)(x - 3) = 0 2x - 5 = 0 ___ 2x = 5 ___ x = 5/2 x - 3 = 0 ___ x = 3
 Miscellaneous_Word_Problems/383999: how much solution must be removed from 50ml of 30% acid solution and replaced with pure water to produce a 20% solution?1 solutions Answer 271834 by scott8148(6628)   on 2010-12-10 00:59:55 (Show Source): You can put this solution on YOUR website!(50 - x)(30%) + (x)(0%) = (50)(20%)
 Polynomials-and-rational-expressions/384018: Factor completely. 10w^6 + 32w^5 + 6w^41 solutions Answer 271833 by scott8148(6628)   on 2010-12-10 00:57:03 (Show Source): You can put this solution on YOUR website!(2w^4)(5w^2 + 8w + 3) (2w^4)(5w + 3)(w + 1)
 Polynomials-and-rational-expressions/384017: Factor. 5z^2 - 16z + 121 solutions Answer 271831 by scott8148(6628)   on 2010-12-10 00:54:22 (Show Source): You can put this solution on YOUR website!(5z - 6)(z - 2)
 Miscellaneous_Word_Problems/384016: PLEASE HELP ME I URGENTLY NEED IMMEDIATE HELP ON THIS PROBLEM: " Ms. Martin was researching the cost of financing \$125,000 for a home. She found that the monthly payment for a 6.875% loan for 30 years would be \$821.16 per month. She found that the monthly payment for a 6.875% loan for 20 years would be \$959.77 per month" 1)write and solve an equation to find the amount of interest she would pay altogether for the 30-year loan. Thank yo SO much for your help!( could yall please show work so i understand better?)1 solutions Answer 271830 by scott8148(6628)   on 2010-12-10 00:52:22 (Show Source): You can put this solution on YOUR website!interest = payments - principle for 30 yr ___ i = (30 * 12 * 821.16) - 125000 for 20 yr ___ i = (20 * 12 * 959.77) - 125000
 Miscellaneous_Word_Problems/384053: Hello, im really having trouble understanding my homework on the absolute maximum and minimum values of a function. The problem that i am on right now is g(x)= -x^2+2x+8. Thank you for your help in advance!1 solutions Answer 271824 by scott8148(6628)   on 2010-12-10 00:40:18 (Show Source): You can put this solution on YOUR website!the max/min of a parabola is the vertex , which is on the axis of symmetry general equation for the axis of symmetry ___ x = -b / (2a) in this case ___ x = (-2) / (2 * (-1)) = (-2) / (-2) = 1 plug into the function to find the vertex ___ g(x) = -(1)^2 + 2(1) + 8 = 9 ___ the vertex is (1,9) the coefficient of the squared term is negative , so the parabola opens downward this means that the vertex is an absolute maximum
 Quadratic-relations-and-conic-sections/384054: The directions for the assignment are as follows: Write an equation for the circle the satisfys each set of conditions. center (0,5) radius one unit1 solutions Answer 271822 by scott8148(6628)   on 2010-12-10 00:29:45 (Show Source): You can put this solution on YOUR website!the general equation for a circle of radius r , centered at (h,k) is ___ (x - h)^2 + (y - k)^2 = r^2
 Functions/383533: y = 25(-7x-4)^64 I really need some help finding the domain and range on this one. Any help would be greatly appreciated.1 solutions Answer 271756 by scott8148(6628)   on 2010-12-09 20:09:13 (Show Source): You can put this solution on YOUR website!there is no (possible) division by zero or anything "strange" , so the domain (x-values) is all real numbers the quantity in parentheses is raised to an even power (64) , this means the result cannot be less than zero so the range (y-values) is all real numbers greater than or equal to zero
 Age_Word_Problems/383801: michelle is 19 years older than her brother doug. 6 years fro now, michelle will be twice as old as doug. how old is each person now?1 solutions Answer 271753 by scott8148(6628)   on 2010-12-09 19:57:48 (Show Source): You can put this solution on YOUR website!"michelle is 19 years older than her brother doug" ___ m = d + 19 "6 years fro now, michelle will be twice as old as doug" ___ m + 6 = 2(d + 6) substituting the equivalent value for m ___ (d + 19) + 6 = 2d + 12 13 = d substituting ___ m = (13) + 19 = 32
 Money_Word_Problems/383842: I have 41 coins that are all nickels and dimes (n and d). The value of the coins is \$3.65. What is a system of equations to solve this?1 solutions Answer 271748 by scott8148(6628)   on 2010-12-09 19:45:19 (Show Source): You can put this solution on YOUR website!n + d = 41 5n + 10d = 365
 Mixture_Word_Problems/383850: How much of an alloy that is 40% copper should be mixed with 500 ounces of an alloy that is 70% copper in order to get an alloy that is 60%1 solutions Answer 271747 by scott8148(6628)   on 2010-12-09 19:43:35 (Show Source): You can put this solution on YOUR website!(x)(40%) + (500)(70%) = (500 + x)(60%)
 Travel_Word_Problems/383768: x=420 over t and x +10=420 over t-1 dont know what to do next..1 solutions Answer 271745 by scott8148(6628)   on 2010-12-09 19:41:52 (Show Source): You can put this solution on YOUR website!substituting ___ (420 / t) + 10 = 420 / (t - 1) multiplying by t(t-1) ___ 420t - 420 + 10t^2 - 10t = 420t t^2 - t - 42 = 0 factoring ___ (t + 6)(t - 7) = 0 t + 6 = 0 ___ t = -6 , x = -70 t - 7 = 0 ___ t = 7 , x = 60
 Functions/383070: find an equation of a parabola whose vertex is (-4,6) and has a solution point of (1,81). Thanks for the help in advance really need it ha.1 solutions Answer 271407 by scott8148(6628)   on 2010-12-08 18:57:32 (Show Source): You can put this solution on YOUR website!the general vertex form is ___ y = a(x - h)^2 + k , where (h,k) is the vertex to find a , plug in the given point ___ 81 = a(1 - -4)^2 + 6 75 = a(5)^2 ___ 3 = a y = 3(x + 4)^2 + 6 more commonly ___ y = 3x^2 + 24x + 54
 Circles/382993: find the radius of the circle defined by the equation: 3x^2+3y^2+12x-12x-48=01 solutions Answer 271406 by scott8148(6628)   on 2010-12-08 18:40:44 (Show Source): You can put this solution on YOUR website!dividing by 3 and adding 16___ x^2 + y^2 + 4x - 4y = 16 completing the squares ___ x^2 + 4x + 4 + y^2 - 4y + 4 = 16 + 4 + 4 (x + 2)^2 + (y - 2)^2 = 24 r = sqrt(24) = 2 sqrt(6)
 Miscellaneous_Word_Problems/382544: you are in a roomful of 35 students people every one is asked to shake hands with everyone how many handshakes will there be 1 solutions Answer 271066 by scott8148(6628)   on 2010-12-07 18:37:38 (Show Source): You can put this solution on YOUR website!all 35 people will shake hands with the 34 other people in the room ___ BUT ___ Jim shaking with Sue is the same as Sue shaking with Jim so ___ 35 * 34 * (1/2)
 Travel_Word_Problems/382546: i sailed west to hawaii againts the wind at a speed of 12 knots/hour. when i returned, i sailed the same route with the wind at a speed of 18 knots/hour. what was my average speed for the entire trip?1 solutions Answer 271065 by scott8148(6628)   on 2010-12-07 18:27:58 (Show Source): You can put this solution on YOUR website!the distance isn't given because it has no bearing on the answer that means we can choose a convenient "working" distance , like 36 nautical miles time to H ___ 36/12 = 3 return time ___ 36/18 = 2 total time is 5 hr and total distance is 72 nautical miles average speed is 72/5 or 14.4 knots/hr
 Quadratic_Equations/382523: Hello, My instructions were to "Graph the quadratic function. Label the vertex and axis of symmetry. " However, i dont understand this problem: I tried using the -b/2a formula , and i got the answer 3. Then i made a t-chart, to get other points to make my parabola, but the numbers were very off, (one of my 'y' coordinates came out to 32) . I dont think i did it right, and im not good at algebra what so ever, so i am absolutely positive i got it all wrong. Thank you in advance, Jackie1 solutions Answer 271064 by scott8148(6628)   on 2010-12-07 18:17:56 (Show Source): You can put this solution on YOUR website!it looks like you're doing fine you found the axis of symmetry (x = 3) ; and when x=-2 , y=32 the vertex is on the axis of symmetry - just find the value of y FYI ___ the roots (x-intercepts) are 0 and 6
 Exponential-and-logarithmic-functions/382538: What would the answer be if y=6500(85.7)^3? Ive tried this equation many times on my calculator, and I get 4,091,248,155. For the question I have, it seems to be too large of a number. (A COMPUTER VALUED AT \$6500 DEPRECIATES 14.3% EACH YEAR. WRITE A FUNCTION THAT MODELS THE VALUE OF THE COMPUTER AND FIND WHAT THE COMPUTER WOULD BE WORTH IN 3 YEARS.) Thanks!1 solutions Answer 271061 by scott8148(6628)   on 2010-12-07 18:02:06 (Show Source): You can put this solution on YOUR website!your equation is fine ___ with the exception of a misplaced decimal point ___ 85.7% ?
 Geometry_Word_Problems/382506: crown point is due south of merrilville,which is due west of winfield.of winfield is 13 miles from crown point and merrillville is 2 miles farther from winfield than twice its distance from crown point,how far is it from crown point to merrillville? I need help setting up this problem to solve and solving it please.1 solutions Answer 271060 by scott8148(6628)   on 2010-12-07 17:59:09 (Show Source): You can put this solution on YOUR website!the 3 places form a right triangle , with m at the right angle and c->w as the hypotenuse by Pythagoras , (c->m)^2 + (m->w)^2 = (c->w)^2 x^2 + (2x + 2)^2 = 13^2 ___ x^2 + 4x^2 + 8x + 4 = 169 5x^2 + 8x - 165 = 0 factoring ___ (5x + 33)(x - 5) = 0 x - 5 = 0 ___ x = 5
 Triangles/382356: The Area of a right triangle is 36. The base is 2 times the height. What is the base and height? Looking for an answer pretty quick. 1 solutions Answer 271030 by scott8148(6628)   on 2010-12-07 15:56:44 (Show Source): You can put this solution on YOUR website!(1/2)(x)(2x) = 36 x^2 = 36 x = 6 base is 12 , height is 6
 Linear_Equations_And_Systems_Word_Problems/382379: I need help with Problems Using Systems in Three Variables A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 3 bags of potato chips, and 2 soft drinks for \$5.50. The price of a hot dog is \$0.75 more than the price of a bag of potato chips. The cost of a soft drink is \$1.75 less than the price of two hot dogs. Find the cost of each item. Thank you soooo Much!!! =)1 solutions Answer 271029 by scott8148(6628)   on 2010-12-07 15:49:05 (Show Source): You can put this solution on YOUR website!"2 hot dogs, 3 bags of potato chips, and 2 soft drinks for \$5.50" ___ 2h + 3p + 2s = 550 "The price of a hot dog is \$0.75 more than the price of a bag of potato chips" ___ h = p + 75 ___ h - 75 = p "The cost of a soft drink is \$1.75 less than the price of two hot dogs" ___ s = 2h - 175 you know the price of hot dogs relative to the other foods , so solve for h and use the result to find the others substituting the equivalent values into the 1st equation ___ 2h + 3(h - 75) + 2(2h - 175) = 550 2h + 3h - 225 + 4h - 350 = 550 ___ 9h = 1125 ___ h = 125 (125) - 75 = p ___ 50 = p s = 2(125 - 175) = 75
 Graphs/382095: please help me find the general form of the equation of this circle center at the point (-3,1) and tangent to the y-axis1 solutions Answer 270891 by scott8148(6628)   on 2010-12-06 23:04:40 (Show Source): You can put this solution on YOUR website!being tangent to the y-axis means the radius is 3 (distance from x=-3 to x=0) using the general equation ___ (x + 3)^2 + (y - 1)^2 = 3^2
 Linear-equations/382098: y=-2x-3 directions say Use the slope m and the y-intercept b to graph the following equation. how the heck do i do this? I have tried subtracting -2x from both sides but its not right, please explain this to me. I need help asap as this is due tommorow morning.1 solutions Answer 270889 by scott8148(6628)   on 2010-12-06 23:00:15 (Show Source): You can put this solution on YOUR website!the general slope-intercept form is ___ y = mx + b , where m is the slope and b is the y-intercept in this case , the slope is -2 and the y-intercept is -3 graph by starting at a known point (the intercept) , -3 on the y-axis {coordinates (0,-3)} generate the line using the slope of -2 ___ this means that for every unit that x increases , y decreases 2 units (x and y change in opposite directions) x = 1 , then y = -5 x = -1 , then y = -1 x = 3 , then y = -9 x = -4 , then y = 5
 Age_Word_Problems/381919: Can you guide me through this age problem that requires two variable"Mrs. Bruce lacks one year from being five times as old as her son. Five years from now she will lack One year from being 3 time as old as her son will be then.Find each of their ages" 1 solutions Answer 270833 by scott8148(6628)   on 2010-12-06 19:26:29 (Show Source): You can put this solution on YOUR website!"Mrs. Bruce lacks one year from being five times as old as her son" so if you add one to her age , she will equal 5 times the son ___ B + 1 = 5s ___ B = 5s - 1 "Five years from now she will lack One year from being 3 time as old as her son will be then" same technique , different numbers ___ (B + 5) + 1 = 3(s + 5) ___ B + 6 = 3s + 15 ___ B = 3s + 9 substituting the B equivalent from the 1st equation into the 2nd equation ___ (5s - 1) = 3s + 9 2s = 10 ___ s = 5 B = 3(5) + 9 ___ B = 24