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# Recent problems solved by 'scott8148'

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 Triangles/92988: If a base angle of an isoceles triangle is 16 degrees more than half of the measure of its vertex angle, than the vertex angle is ? degrees? Please show solution using equation. Thank You!1 solutions Answer 67780 by scott8148(6628)   on 2007-08-17 16:55:27 (Show Source): You can put this solution on YOUR website!let x=vertex angle the angles of a triangle (ANY TRIANGLE) sum to 180 degrees ... the 2 base angles of an isoceles triangle are equal so, ((x/2)+16)+((x/2)+16)+x=180 ... 2x+32=180 ... 2x=148 ... x=74
 Circles/93066: This question is from textbook you are in charge of constructing a fence around the running track at a high school. the fence is to be built around the track so that there is a uniform gap between the outside edge of the track and the fence. what is the maximum width of the gap between the track and the fence if no more than 630 meters of fencing is used?1 solutions Answer 67778 by scott8148(6628)   on 2007-08-17 15:46:15 (Show Source): You can put this solution on YOUR website!VERY difficult to answer without knowing the size and shape of the track
 Inequalities/92719: Question: Solve: How do i solve this? Do i need a chart?1 solutions Answer 67670 by scott8148(6628)   on 2007-08-16 15:30:21 (Show Source): You can put this solution on YOUR website!find the roots of the equality 6x^2+5x=4 ... 6x^2+5x-4=0 ... factoring gives (3x+4)(2x-1)=0 ... so the roots are -3/4 and 1/2 the roots are the "boundry points" between solutions ... in this case, the three ranges are <-3/4, between -3/4 and 1/2, and >1/2 test a range by choosing a value in it ... 0 is between -3/4 and 1/2 ... 6(0^2)+5(0)<4 ... 0<4 so x must be between -3/4 and 1/2 testing the other ranges will show no solution; this is because the "boundry points" are between solutions and non-solutions (-3/4) < x < (1/2)
 Trigonometry-basics/92871: This question is from textbook Finie Mathematics The dot product 3 1 4 x 2 -1 5 is:1 solutions Answer 67666 by scott8148(6628)   on 2007-08-16 14:47:05 (Show Source): You can put this solution on YOUR website!the dot product is multiplying the row elements by the corresponding column elements and summing the results (3*2)+(1*-1)+(4*5)=6-1+20=25
 logarithm/92976: 2^x+2 - 2^x = 48 Please explain the steps. Thanks.1 solutions Answer 67665 by scott8148(6628)   on 2007-08-16 14:35:43 (Show Source): You can put this solution on YOUR website!by rules of exponents, 2^(x+2)=(2^x)(2^2) ... so 4(2^x)-2^x=48 ... 3(2^x)=48 ... 2^x=16 ... so x=4 2*2*2*2=16
 Expressions-with-variables/92918: Hey this is Debbie and I am having trouble understanding this. For these linear functions complete the table of values by substitution. b=a+3 a 0 1 2 3 4 5 10 b I am having trouble working how to do substitution because I forgot how to do it.Must help appreciated.1 solutions Answer 67632 by scott8148(6628)   on 2007-08-16 11:30:51 (Show Source): You can put this solution on YOUR website!substitution means put the (a) value into the equation where (a) is and you will get a numerical value for (b) then put the (b) value in the table next to the (a) value that you used to get it
 Linear-equations/92938: In the x,y plane, what is perpendicular to the graph of the linear equation 3x-4y=0 I've done this over and over but i can't figure it out. The answer is supposed to be y=-(4/3)x+12 but i keep getting y=(3/4)x+0. Thank you for your help!1 solutions Answer 67631 by scott8148(6628)   on 2007-08-16 11:23:19 (Show Source): You can put this solution on YOUR website!perpendicular means that the slopes are negative reciprocals of each other the original line has a slope of 3/4, so the perpendicular line has a slope of -4/3 3x-4y=0 ... -4y=-3x+0 ... y=(3/4)x+0 (y=mx+b) can't tell where the 12 comes from ... judging from the question, the 12 could be any number - it is the slope that's important
 Radicals/92904: 2 over square root of 3 plus the square root of 2. Rationalize the denominator. Mike1 solutions Answer 67599 by scott8148(6628)   on 2007-08-16 00:04:54 (Show Source): You can put this solution on YOUR website!this is what you wrote ... rationalize by multiplying by ... this gives if you meant ... rationalize by multiplying by the conjugate ... this gives or
 Age_Word_Problems/92909: Two less than 6 times Harriet's age is the same as 10 more than twice her age. Find her age. I have no idea where to start.1 solutions Answer 67598 by scott8148(6628)   on 2007-08-15 23:45:50 (Show Source): You can put this solution on YOUR website!let h=Harriet's age "Two less than 6 times Harriet's age" ... 6h-2 "is the same as" ... = "10 more than twice her age" ... 2h+10 6h-2=2h+10 ... 4h=12 ... h=3
 Equations/92844: I really need help on this problem. I haven't taken algebra in years so im a little rusty. Q: What is the remainder when x^3+5x^2-6x+10 is divided by x+3? The book says that the answer is 46 but i'm not sure how to get that. Thanks alot. 1 solutions Answer 67596 by scott8148(6628)   on 2007-08-15 23:35:15 (Show Source): You can put this solution on YOUR website!remember long division? ... you can use the same technique with polynomials 372 is the same as 3(10^2)+7(10)+2 ... just like 3x^2+7x+2 so, dividing x+3 into x^3+5x^2-6x+10 ... x goes into x^3, x^2 times ... (x^2)(x+3) is x^3+3x^2 (x^3+5x^2-6x+10)-(x^3+3x^2) is 2x^2-6x+10 ... x goes into 2x^2, 2x times ... (2x)(x+3) is 2x^2+6x (2x^2-6x+10)-(2x^2+6x) is -12x+10 ... x goes into 12x+10, -12 times ... (-12)(x+3) is -12x-36 (12x+10)-(-12x-36) is 46 ... this is the remainder (it is not divisible by x) this is done like long division ... with all the same power terms lined up vertically not the case here, but if you were missing a term; like x^3+x-7 (no x^2 term); you would put in a zero for a place holder x^3+0x^2+x-7 ... to keep things properly aligned
 Radicals/92843: Simplify by combining like terms sqrt of 63 - 2 sqrt of 28 + 5 sqrt of 7 Thank you - Hope this makes sense1 solutions Answer 67595 by scott8148(6628)   on 2007-08-15 23:01:43 (Show Source): You can put this solution on YOUR website! ... ... ...
 Quadratic_Equations/92892: I am having major problems with this word problem and need some help The length of a rectangle is 3cm more than 2 times its width. If the area of the rectangle is 99cm^2, Find the dimensions of the rectangle to the nearst thousandth. Thanks a million1 solutions Answer 67594 by scott8148(6628)   on 2007-08-15 22:48:05 (Show Source): You can put this solution on YOUR website!L=2W+3 ... area=L*W ... 99=(2W+3)W ... 2W^2+3W-99=0 ... using quadratic formula gives ... W=6.325 and W=-7.825 ... negative value is unrealistic L=2W+3 ... L=2(6.3255)+3 ... L=15.651 ... extra digit in W for precision in calculating L
 Linear_Equations_And_Systems_Word_Problems/92760: Solve the system by addition. 2x + 4y = 3 4x – 2y = 1 A) (1/2, 1/2) B) (1/3, 1/3) C) (1/4, 1/4) D)(1/5, 1/5) 1 solutions Answer 67564 by scott8148(6628)   on 2007-08-15 17:40:00 (Show Source): You can put this solution on YOUR website!multiplying the second equation by 2 and adding the result to the first equation gives (2x+4y)+2(4x-2y)=3+2(1) 2x+4y+8x-4y=3+2 ... 10x=5 ... x=1/2 ... 2(1/2)+4y=3 ... 1+4y=3 ... 4y=2 ... y=1/2 ... answer A)
 Graphs/92759: find the slope of the passing through the following points: (2, 0) and (0, -4) A. 2 B. -2 C. 1/2 D. -1/2 Thank you for any help...1 solutions Answer 67563 by scott8148(6628)   on 2007-08-15 17:33:09 (Show Source): You can put this solution on YOUR website!the slope of a line is the change in y (RISE or vertical) divided by the change in x (RUN or horizontal) the formula is m=(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are two points ... m=(-4-0)/(0-2)=-4/-2=2 ... answer A. "RISE over RUN" is a good memory helper
 Linear_Equations_And_Systems_Word_Problems/92757: Evaluate 2m - 5n / (over or divided by) n +3p if m = –2, n = 4, and p = –1. A) –24 B) 24 C) –16 D) 16 Ok, I am not getting any answer here, can you help please? thank you 1 solutions Answer 67562 by scott8148(6628)   on 2007-08-15 17:23:49 (Show Source): You can put this solution on YOUR website!(2(-2)-5(4))/(4+3(-1)) ... (-4-20)/(4-3) ... -24/1 ... -24 ... looks like A) if you are using a calculator, it may be a good idea to use parentheses liberally without parentheses, you get three terms 2m, -5n/n, and 3p ... evaluating this gives -4-5-3 or -12
 Graphs/92758: Find the slope of the line that passes through these points (0,-4) I do not seem to understand how this is done can you help?1 solutions Answer 67546 by scott8148(6628)   on 2007-08-15 16:25:07 (Show Source): You can put this solution on YOUR website!you need two points to determine the slope of a line ... you have only provided one perhaps this is the reason you can't understand the problem?
 Travel_Word_Problems/92765: Could someone please help me with setting this problem up and figuring it out? I have tried and cannot come up with anything. Algebra is my worst subject. Thanks for any help. Two planes set out at 3pm from the same airfield headed in the same direction. The average speed of the first plane is 250 mph slower than twice the speed of the second plane. In 3hr. the first plane is 300 mi. ahead of the second plane. How far did the second plane travel? Thanks for your time.1 solutions Answer 67543 by scott8148(6628)   on 2007-08-15 16:21:38 (Show Source): You can put this solution on YOUR website!r*t=d ... let r and d be the rate and distance of the second plane ... 3r=d or r=d/3 for first plane ... 3(2r-250)=d+300 substituting d/3 for r gives 3(2(d/3)-250)=d+300 ... 2d-750=d+300 ... d=1050
 Money_Word_Problems/92784: I ask this question and someone answered; however, the answers was not posted with the question. So, does anyone have the answer to this question? Two planes set out at 3pm from the same airfield headed in the same direction. The average speed of the first plane is 250mph slower than twice the speed of the second plane. In 3hrs. the first plane is 300 miles ahead of the second plane. How far did the second plane travel?: 1 solutions Answer 67540 by scott8148(6628)   on 2007-08-15 16:12:07 (Show Source): You can put this solution on YOUR website!r*t=d ... let r and d be the rate and distance of the second plane ... 3r=d or r=d/3 for first plane ... 3(2r-250)=d+300 substituting d/3 for r gives 3(2(d/3)-250)=d+300 ... 2d-750=d+300 ... d=1050
 Miscellaneous_Word_Problems/92767: HI, I am wondering if you could check this question to see if I have it right. The cost to a landscape architect for a 25-gallon tree is \$65.00 Find the selling price of the tree when the markup rate used by the architect is 30%. I got \$19.50. Could you let me know if this is correct or not. Thanks for all your time.1 solutions Answer 67537 by scott8148(6628)   on 2007-08-15 15:56:50 (Show Source): You can put this solution on YOUR website!you have correctly calculated the architect's markup ... the selling price is the architect's cost PLUS the markup
 Trigonometry-basics/92731: This question is from textbook Algebra and Trigonometry A rectangle is placed under the parabolic arch given by f(x)=27-3x squared by using a point (x,y) on the parabola, as shown. Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen.1 solutions Answer 67527 by scott8148(6628)   on 2007-08-15 12:12:31 (Show Source): You can put this solution on YOUR website!area equals length*width ... in this case, x-dimension*y-dimension ... the y-dimension is f(x) since the parabola is centered on the y-axis, the x-dimension is 2x ... so a=(f(x))*2x ... (27-3x^2)2x ... 54x-6x^3
 Trigonometry-basics/92728: This question is from textbook Algebra and Trigonometry The polynomial f(x) divided x-3 results in a quotient of x squared+3x-5 with the remainder of 2. Find f(3).1 solutions Answer 67526 by scott8148(6628)   on 2007-08-15 12:01:39 (Show Source): You can put this solution on YOUR website!undoing the division gives (x-3)(x^2+3x-5)+2 ... x^3+3x^2-5x-3x^2-9x+15+2 ... f(x)=x^3-14x+17 f(3)=3^3-14(3)+17=27-42+17=2 this is an example of the remainder theorem; which states that when you divide f(x) by (x-a) the remainder equals f(a)
 Trigonometry-basics/92729: This question is from textbook Algebra and Trigonometry Find the vertical asymptote of the rational function: f(x)=3x-12/4x-21 solutions Answer 67525 by scott8148(6628)   on 2007-08-15 11:45:09 (Show Source): You can put this solution on YOUR website!when x=0; the denominator of the second term (12/4x) becomes zero, resulting in an undefined quantity on either side of zero, the second term has a large + or - value ... this results in a vertical asymptote at x=0
 expressions/92745: I'm trying to help my daughter answer a question on her homework. Every way she's tried is the only ways I know to do it also. The instructions are: please place inclusion symbols to make the following true. 44 * 5 - 3 + 2 = 10 She's came up with 90, -263, -6581 solutions Answer 67523 by scott8148(6628)   on 2007-08-15 11:33:13 (Show Source): You can put this solution on YOUR website!not sure if this is legitimate, but it works ... 44*(5-(3+2))=1(0)
 Coordinate-system/92657: In the xy-plane, line l passes through the origin and is perpendicular to the line 4x+y=k, where k is a constant. If the two lines intersect at the point (t,t+1), what is the value of t?1 solutions Answer 67499 by scott8148(6628)   on 2007-08-14 22:39:56 (Show Source): You can put this solution on YOUR website!perpendicular lines have slopes that are negative reciprocals, so the slope of line 1 is -1/(-4) or 1/4 it passes through the origin so the equation is y=x/4 ... substituting gives t+1=t/4 ... 4t+4=t ... 3t=-4 ... t=-4/3
 Geometric_formulas/92674: This question is from textbook prentice hall mathematics geometry use the table and inductive reasoning. make a conjecture about each value. Question: What is the sum of the first 6 positve even numbers. and the sum of the first 100 positive numbers. here is the table 2 =2=1*2 2+4 =6=2*3 2+4+6 =12=3*4 2+4+6+8 =20=4*5 2+4+6+8+10 =30=5*61 solutions Answer 67497 by scott8148(6628)   on 2007-08-14 22:04:13 (Show Source): You can put this solution on YOUR website!the next step (6th) in the table would be for 6 numbers, giving a sum of 6*7 or 42 if you think about the first 100 positive numbers; 1+100=101, 2+99=101, 3+98=101, etc. there will be 50 such pairs ... so the sum is 101*50 or 5050
 Volume/92614: A right circular cylinder with radius 5 and height 4 has volume v. In terms of v, what is the volume of a right circular cylinder with radius 5 and height 8? (A) v + 4 (B) 2v (C) 4v (D)6v (E)8v1 solutions Answer 67495 by scott8148(6628)   on 2007-08-14 21:52:37 (Show Source): You can put this solution on YOUR website!the second cylinder has the same radius as the first (they are equally big "around") the second one is twice as long ... if you cut it in half, it would make two of the first cylinder so it must have twice the volume ... answer (B)
 Polynomials-and-rational-expressions/92532: I am having a little trouble getting the correct answer to this problem. Factor completely. 1 solutions Answer 67371 by scott8148(6628)   on 2007-08-13 21:46:05 (Show Source): You can put this solution on YOUR website!this is the difference of two squares ... the first three terms are a perfect square, as is the last term (3x+2y)^2-(5)^2 ... (3x+2y+5)(3x+2y-5)
 Linear_Equations_And_Systems_Word_Problems/92540: I am just drawing a blank on what the 2 equations would be for this problem. Once I get them. I can solve the problem. Simone can build a treehouse in 15 hours. Working together Simone and Tyrese can build a treehouse in 7 hours. How many hours would Tyrese take to build the treehouse working alone? I have S=15 S+T=7 but I know this isn't correct. Please help1 solutions Answer 67368 by scott8148(6628)   on 2007-08-13 21:38:22 (Show Source): You can put this solution on YOUR website!with work problems, the trick is to see what fraction of the job is done by each person if Simone can build a treehouse in 15 hours, then in 7 hours she builds 7/15 of the treehouse this means Tyrese builds 8/15 of the tree house in 7 hours ... so 7 is to 8/15 as x is to 15/15 (or 1 whole treehouse)
 Miscellaneous_Word_Problems/92432: I'd really appreciate your input on this problem. Tom and David both collected a total of 480 marbles. Tom stacked each column with 6 marbles. and David stacked each column with 9 marbles. They stacked 72 columns together. Write an equation using this information. Well, i came up with 56 columns for Tom; and 16 columns for David which equal 72 together. Tom collected 56columns x 6marbles=336 David collected 16columns x 9marbles=144 Tom plus David=480marbles. But, how do i write an equation for these numbers??1 solutions Answer 67300 by scott8148(6628)   on 2007-08-12 22:33:44 (Show Source): You can put this solution on YOUR website!start by defining variables ... let t=Tom's marbles, let d=David's marbles ... then write equations "Tom and David both collected a total of 480 marbles" ... t+d=480 "Tom stacked each column with 6 marbles. and David stacked each column with 9 marbles. They stacked 72 columns together" ... (t/6)+(d/9)=72 this gives you two equations and two unknowns ... the easiest solution method is probably substitution
 Rational-functions/92388: simplify (3x^2+7x-40)+(x+5) a. 3x+2 b. 3x+8 c. 3x-2 d. 3x-8 my test is tomorrow and i still dont understand how to work this kind of problem. i've tried to divide but it hasnt given me one of the choices i have for answers. please help?1 solutions Answer 67218 by scott8148(6628)   on 2007-08-12 13:57:37 (Show Source): You can put this solution on YOUR website!if the two expressions are divided (rather than added as indicated); then factoring can help (3x^2+7x-40)/(x+5) ... ((3x-8)(x+5))/(x+5)=(3x-8) what type of division did you try? long division can be done with these expressions