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# Recent problems solved by 'KnightOwlTutor'

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 Angles/326743: the ratio of the measures of two complementary angles is 4:5.find the measures of the angles1 solutions Answer 233957 by KnightOwlTutor(293)   on 2010-07-29 08:28:18 (Show Source): You can put this solution on YOUR website!The definition of a complementary angles is that the sum of the angles is equal to 90. thus we have the ratio 4:5. We then set up the problem as follows 4x + 5x=90. Then you would add (4+5)x=9x 9x=90 divide both sides by 9 and x is equal to 10. Then we go back and multiply to find the value of each angle. ie 4(x)=4(10)=40 5(x)=5(10)=50. The angle values are 40 and 50.
 Linear_Algebra/194832: The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side, and the perimeter is 17 in. How long is the third side? If s represents the length of the second side, which of the following represents the length of the third side? s - 5 s - 2 s + 3 1 solutions Answer 146167 by KnightOwlTutor(293)   on 2009-05-05 08:36:09 (Show Source): You can put this solution on YOUR website!Side 2=s side 1=s-5 side 3=s-5+3=s-2 (s)+(s-5)+(s-2)=17 3s-7=17 add 7 to both sides 3s=24 divide both sides by 3 s=6 third side =6-2=4 The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side second side of the triangle =s first side of the triangle is =s-5 3rd side is =(s-5)+3=s-2
 Matrices-and-determiminant/175330: Cramers rule Cant find this problem here Solve the system of equation using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. Parenthesis 2x+3y=41 2x-3y=-13 A Parenthesis is only in the beginning then the two equations top and bottom.. here are the choices I need A. x=7,y=9 B. x=-9,y=7 C. x=-7,y=-9 D. x=9,y=7 I think it is B is that correct? Help1 solutions Answer 130410 by KnightOwlTutor(293)   on 2009-01-07 01:20:56 (Show Source): You can put this solution on YOUR website!If you plug in the x and y values for b you will find it incorrect. x=-9,y=7 2x+3y=41 -18+21=39 2x-3y=-13 -18-21=-39 2x+3y=41 2x-3y=-13 Add each column 4x+0=28 divide both sides by 4 x=7 Plug in the value of 7 for x to get the y value 14+3y=41 Subtract 14 from both sides 3y=27 divide both sides by 3 y=9 Plug in the values of x and y in the second equation (2*7)-(3*9)=-13 -13=-13
 Rectangles/175296: This question is from textbook Geometry Connections How do you find the area and width of a rectangle from diagonal and one side length? This is exactly how the problem is stated in my book: A rectangle has one side length of 11 mm and a diagonal of 61 mm. Draw a diagram of this rectangle (which I've done) and its width and area.1 solutions Answer 130409 by KnightOwlTutor(293)   on 2009-01-07 01:11:00 (Show Source): You can put this solution on YOUR website!A rectangle is composed of 4 right angles. With the diagonal you have created two triangles and better yet 2 right triangles. You would then use the pythagorean therom a^2+b^2=c^2 you already have the value for c=61 and a=11 all you have to do is plug in the numbers 121 +b^2=3721 subract 121 from both sides b^2=3600 b=60 Let us doublecheck 121+3600=3721
 Inequalities/175331: I am trying to find the minimum for f(x)=5x^2-20x+3. i think to find the min. you do -b/2a. In which case i did (-)-20/2(5) and got 2. My teacher said that this answer was incorrect. If you could please tell me where i went wrong it would be much appreciated. thanks!1 solutions Answer 130408 by KnightOwlTutor(293)   on 2009-01-07 01:02:56 (Show Source): You can put this solution on YOUR website!You are trying to get the vertex. In order to do this you need to complete the square f(x)=5x^2-20x+3.Set f(x)=0 0=5x^2-20x+3 Subtract 3 from both sides -3=5x^2-20x Factor out the 5 on the right hand side of the equation -3=5(x^2-4x divide the 4 by 2 and then square it. -3=5(x^2-4x+4) since you added an additonal 20 on the right side -don't forget to multiply the 4 you just added by 5 -3+20=5(x-2)^2 17/5=(x-2)^2 take the square root of each side 17/5sq rt=x-2 sqrt85/5=x-2 add two to both sides x=2sqrt85/5
 Average/175341: 6-3/4÷3=? & 8÷1-1/3=? please help me I'm having the hardest time trying to figure out these type of problems and fractions are my weakness. i've read many fractions problems but i still dan't get it.1 solutions Answer 130405 by KnightOwlTutor(293)   on 2009-01-07 00:46:15 (Show Source): You can put this solution on YOUR website!first you solve for 6-3/4 You need to find the common denominator for both numbers in this case it is four. the number 6 becomes 24/4 you haven't changed the number it is still the same quantity but you can now perform the subtraction part with the fraction.64/4-3/4=21/4 divided by 3=7/4 8 divided by 1 is still eight but we need to find a common denominator to solve the problem in this case it is 3. 24/3-1/3=23/3
 Linear-systems/175338: I am having trouble understanding, "solving systems of equations by graphing." Ex: x+y=6 x-y=4 Then, I started to try and solve and find the ordered pair that worked for both equations. I only got this far, then I get confused: x+y=6 -x -x ______ y=-1x+6 x-y=4 -x -x _______ -y=-1+4 1 solutions Answer 130403 by KnightOwlTutor(293)   on 2009-01-07 00:39:14 (Show Source): You can put this solution on YOUR website!x+y=6 x-y=4 Add each colum and you get 2x (+y-y=0)=6+4 2x=10 divide both sides by two and x=5 if x is 5 then y must equal 1 5+1=6 5-1=4
 Polynomials-and-rational-expressions/175184: please help factor the trinomial completely. 1) 3p^2 -2p - 51 solutions Answer 130292 by KnightOwlTutor(293)   on 2009-01-06 12:11:58 (Show Source): You can put this solution on YOUR website!(3p-5)(p+1)=answer First figure out what are the factors that give u 5 1,5 What are the factors that give u 3 3,1 Based on this we need to find the two numbers from above that will give u -2 3-5=-2
 Money_Word_Problems/175217: Please help. amount of an investment. The amount of an investment of P dollars for t years at simple intrrest rate r is given by A=P + Prt. Please help with rewriting the formula by factoring out the greatest common factor on the right side. and Find A if 8300 is invested for 3yrs at a simple intrest rate of 15% A=8300 + (8300)3(.15) A = 8300 + 3735. A = 12035.00 (is this correct)1 solutions Answer 130291 by KnightOwlTutor(293)   on 2009-01-06 12:07:03 (Show Source): You can put this solution on YOUR website!Awesome job!
 Coordinate-system/175198: Please help me solve this equation: . 1 solutions Answer 130269 by KnightOwlTutor(293)   on 2009-01-06 07:10:53 (Show Source): You can put this solution on YOUR website!4y+5x=2y-3x+16 Subtract 2y from both sides 2y+5x=-3x+16 Subtract 5x to both sides 2y=-8x+16 Divide each term by 2 y=-4x+8 This is a equation of a line.
 Geometry_Word_Problems/175196: a rectangle is three times as long as it is wide . if its length and width are both decresed by 2cm its area is decreased by 36 cm squared . find its original dimensions 1 solutions Answer 130268 by KnightOwlTutor(293)   on 2009-01-06 07:06:46 (Show Source): You can put this solution on YOUR website!We know that the difference between the 2 areas is 36. Therefore we are going to set up the equation of subtracting the two areas to get the original dimensions. x=width of the original rectangle 3x=the length of the original rectangle x-2=width of the smaller rectangle 3x-2=length of the smaller rectangle the area of a rectangle is width X length Area of the original rectangle-Area of smaller rectangle=36 (3x*x)-[(x-2)(3x-2)]=36 Use the foil method 3x^2-2x-6x+4 (3x*x)-[3x^2-2x-6x+4]=36 multply -1 to each term contained within the bracket. Make sure to pay attention to the sign. (+)(-)=(-) (-)(-)=(+) (3x^2-3x^2+2x+6x-4=36 Combine like terms and simplify (2+6)x-4=36 8x-4=36 Add 4 to both sides of the equation 8x=40 divide both sides by 8 x=5 The dimensions of the original rectangle was 5,15 Let us double check our answer the dimensions of the smaller rectangle is 3,13 (3*15)-(3*13)=36 75-39=36
 Rational-functions/174766: This question is from textbook Saxon Algebra 2 Find the inverse of A= (matrix) -3....1 -5....5 if it exists.1 solutions Answer 130140 by KnightOwlTutor(293)   on 2009-01-05 09:09:46 (Show Source): You can put this solution on YOUR website!We know that the matrix has an inverse because the determinant is not equal to zero [-3 1] [-5 5] [a b] [c d] To calculate the determinant ad-bc in this case -15+5=-10 Any Matrix inverse =1/ad-bc[d -b] [-c a] -1/10[5 -1] [5 -3] To double check multiply the matrices together and see if you come up with the identity matrix. [-3 1]-1/10[5 -1] [-5 5] [5 -3] -15+5 3+3 -1/10[-10 0] -25+25 5-15 -1/10[0 -10] [1 0] [0 1] is the identity matrix
Coordinate-system/173829: Graph the line with slope -2/3 passong through the point (-5,5). I cannot do this problem. I have tried and when it comes to math I can't add 3 + 3. The negatives are the worst along with fractions. I just don't understand it.Can anybody figure this out and show me how? Ty in advance. Judy
1 solutions

Answer 128702 by KnightOwlTutor(293)   on 2008-12-17 11:42:31 (Show Source):
You can put this solution on YOUR website!
The general equation for a line is y=mx+c
m= slope
Replace m with -2/3 y=-2/3x +c

Plug in the value for the point
5=-2/3(-5) +c
We are trying to find the y intercept c

5=10/3+c
Subract 10/3 to both sides
15/3 -10/3= c
5/3= c
Let's double check that this is the correct linear equation

5=10/3 +5/3
Therefore the eqation is y=-2/3x+5/3
 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 5/2 = 2.5.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 5/3 = 1.66666666666667.Slope is -2/3 = -0.666666666666667. Equation in slope-intercept form: y=-0.666666666666667*x+1.66666666666667.

 Equations/173791: help me solve this problem please. 4a^2-2[3b-5b(b+4)]1 solutions Answer 128699 by KnightOwlTutor(293)   on 2008-12-17 11:28:44 (Show Source): You can put this solution on YOUR website!4a^2-2[3b-5b(b+4)] the first step is to expand this -5b(b+4)=-5b^2-20b 4a^2-2[3b-5b^2-20b] -2[3b-5b^2-20b]=-6b+10b^2+40b 4a^2-6b+10b^2+40b Combine like terms and simplify 4a^2+34b+10b^2
 Linear_Equations_And_Systems_Word_Problems/173823: a line that passes through (6,2) and has the slpoe of 2 y=2x squared1 solutions Answer 128696 by KnightOwlTutor(293)   on 2008-12-17 11:19:13 (Show Source): You can put this solution on YOUR website!y=2x squared is not a line it is a parabola. Check your equation.
 Square-cubic-other-roots/173511: What is the square root of 28y3 what do i do to slove that question?1 solutions Answer 128372 by KnightOwlTutor(293)   on 2008-12-15 18:29:17 (Show Source): You can put this solution on YOUR website!Break down the #28 into factors 2*2*7 y*y*yThe answer is 2ysqrt 7y You would subtract the exponents.
 Distributive-associative-commutative-properties/173512: distribute: 5(2x-8y)1 solutions Answer 128370 by KnightOwlTutor(293)   on 2008-12-15 18:24:26 (Show Source): You can put this solution on YOUR website!10x-40y
 Graphs/173510: This question is from textbook Essentials Algebra If the slope of a line is m= 4, then the slope of every line perpendicular to it is ________ .1 solutions Answer 128368 by KnightOwlTutor(293)   on 2008-12-15 18:23:39 (Show Source): You can put this solution on YOUR website!The negative inverse of the slope m=-1/4
 Quadratic-relations-and-conic-sections/173486: What is the easiest way to figure out hyperbola's?1 solutions Answer 128366 by KnightOwlTutor(293)   on 2008-12-15 18:21:38 (Show Source): You can put this solution on YOUR website!It is the only conic section that has a - in the equation x^2/a^2-y^2/b^2=1
 Graphs/173506: This question is from textbook Essentials Algebra The equation of the line with slope m= -2 passing through the point (-2,4) is _________ .1 solutions Answer 128364 by KnightOwlTutor(293)   on 2008-12-15 18:19:20 (Show Source): You can put this solution on YOUR website!The general equation of a line is y-mx+c we know the slope of the line y=-2x+c Plug in the point 4=(-2)(-2)+c 4=4 +c subtract 4 from both sides c=0 the equation of the line is y=-2x
 Numbers_Word_Problems/173407: When two-thirds of a number is added to one-fourth of the same number, the result is 8 more than the original number. Find the number.1 solutions Answer 128265 by KnightOwlTutor(293)   on 2008-12-15 07:35:15 (Show Source): You can put this solution on YOUR website!The unknown number is x The equation to solve is 2/3x+1/4x=x+8 The lcd is 12 Therefore multiply each term by 12 8x+3x=12x+96 simplfy terms 11x=12x+96 Subtract 12x from both sides -x=96 divide both sides by -1 x=-96 Let's doublecheck our answer (2(-96)/3} +(-96/4)=-96+8 -64-24=-88
 logarithm/173406: log25 1/251 solutions Answer 128264 by KnightOwlTutor(293)   on 2008-12-15 07:17:09 (Show Source): You can put this solution on YOUR website!log25 1/25= -1 1/25= (25)-1 The log value is the exponent of the base which in this case is 25.
 Quadratic_Equations/173408: This question is from textbook Introductory Algebra Write standard form and identify a, b, and c. 4x^2 + 4 = 2x + 31 solutions Answer 128263 by KnightOwlTutor(293)   on 2008-12-15 07:14:27 (Show Source): You can put this solution on YOUR website!4x^2 + 4 = 2x + 3 Subtract 3 and 2x from both sides 4x^2+1-2x=0 4x^2-2x+1=0 a=4 b=-2 c=1
 Quadratic_Equations/173409: This question is from textbook Introductory Algebra Solve the equation 15r^2 = 3r1 solutions Answer 128261 by KnightOwlTutor(293)   on 2008-12-15 07:10:51 (Show Source): You can put this solution on YOUR website!15r^2 = 3r Subtract 3 r from both sides 15r^2-3r=0 Factor the equation 3r(5r-1)=0 r=0 and r=1/5 these are the solutions to this problem
 Quadratic_Equations/173410: This question is from textbook Introductory Algebra Solve the equation x(x-3) = 401 solutions Answer 128260 by KnightOwlTutor(293)   on 2008-12-15 07:07:28 (Show Source): You can put this solution on YOUR website!x(x-3) = 40 Expand the equation x^2-3X=40 subtract 40 from both sides x^2-3X-40=0 Find possible factors for 40 (40,1) (2,20) (8,5) We see that the 40 has a negative sign which means that one of the factors is negative. Then we find which two factors when added together can give you -3 I can see from the list that the only possible answer is 5,8 (x-8)(x+5)=0 is the factored form of the above equation Therefore the answers are x=8 and x=-5
 Quadratic_Equations/173413: This question is from textbook Introductory Algebra Solve the equation by completing the square p2 + 3p - 9 = 01 solutions Answer 128258 by KnightOwlTutor(293)   on 2008-12-15 07:00:48 (Show Source): You can put this solution on YOUR website!p2 + 3p - 9 = 0. Add 9 to both sides of the equation p2 + 3p=9 Divide the coefficient of the p term(=3) term by 2 and square the resultant value and add to both sides of the equation p2 +3p +(3/2)^2= 9 +(3/2)^2 This makes the quadratic equation a perfect square (p+3/2)^2=9 +9/4 Simplify the left side of the equation (p+3/2)^2=36/4+9/4=45/4 (p+3/2)^2=45/4 Take the square root of both sides p+3/2= + or -3sqrt5/2 subtract 3/2 from both sides p=-3/2+3sqrt5/2 or p=-3/2-3sqrt5/2
 logarithm/172870: the log base is in parenteses right after the log Log(2) (x-8) + Log(2) (x+4) = 51 solutions Answer 127897 by KnightOwlTutor(293)   on 2008-12-13 06:02:42 (Show Source): You can put this solution on YOUR website!Change form to exponent (x-8)(x+4=2^5=32 Use FOIL to ge x^2-4x=0 factorx(x-4)=0 x=0 or 4 In logs you only use + numbers Therefore 4 is the correct answer.
A ball is thrown upward with an initial velocity of 30 feet per second from a point that is 24
feet above the ground. The height h (in feet) of the ball at time t (in seconds) after it is
thrown is
h= -16t^2 + 30t + 24
Find the time when the ball hits the ground.
1 solutions

Answer 127896 by KnightOwlTutor(293)   on 2008-12-13 05:47:11 (Show Source):
You can put this solution on YOUR website!
Set the equation to 0. When the ball hits the ground the distance is 0. Then use the quadratic formula.
 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=2436 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.604870334906633, 2.47987033490663. Here's your graph:
t=2.8

Find zeros for the function:
g(x) = 6 - x^2 -5x
h(x) = x^2 + 6x + 12
1 solutions

Answer 127578 by KnightOwlTutor(293)   on 2008-12-11 08:28:37 (Show Source):
You can put this solution on YOUR website!
 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=1 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3, -2. Here's your graph:

 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 : . The discriminant -12 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -12 is + or - . The solution is Here's your graph:

 Linear-equations/172710: Please help!!! Natalie spends 90 minutes doing her mant and english homework. The time she spends on her math homework is a function of the time she spends on her english homework.1 solutions Answer 127577 by KnightOwlTutor(293)   on 2008-12-11 08:22:52 (Show Source): You can put this solution on YOUR website!The equation is y=90-x x=time she spends on her English HW y= time that she spends on her Math HW
 logarithm/172715: ln 9.3 = ln e^(.047x)1 solutions Answer 127576 by KnightOwlTutor(293)   on 2008-12-11 08:20:14 (Show Source): You can put this solution on YOUR website!ln 9.3 = ln e^(.047x) 2.23001=.047x Divide both sides by 0.047 47.4471=x Let's doublecheck our answer 9.3=e^2.23