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# Recent problems solved by 'vleith'

vleith answered: 2822 problems
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 Angles/148270: Judy is driving along a highway that is climbing a steady 9-degree slope. After driving for 2 miles along this road, how much altitude has Judy gained? How far must she travel in order to gain a mile of altitude? thank you very much! 1 solutions Answer 108670 by vleith(2825)   on 2008-07-14 18:38:51 (Show Source): You can put this solution on YOUR website!Sin is defined as opposite/hypotenuse. Draw a right triangle with one point at the origin. Draw the hypotenuse (h) with an angle of 9 degrees above the x axis. The "altitude" gained is given by At 2 miles, we have = 0.312 miles How far must one go to be an altitude of 1 mile?
 Exponents-negative-and-fractional/148139: This question is from textbook algebra: the easy way 41: 4(3+x)+10= -11(x-6)+1 43:3x+21=-2x+11 45:6x+4=2x whenever i experiance any of these types of questions im not sure how to solve for x when there is an x on both sides of the equation. Given that the book that im using does not go over how to do these types of equations im at lost of how to do it, any help trying to solve these equations is greatly appreciated by me, thank you. -Brian.1 solutions Answer 108536 by vleith(2825)   on 2008-07-13 19:47:59 (Show Source): You can put this solution on YOUR website!The way to solve these types of problems is to get all the constants on one side and all the terms with x in them on the other. Then simplfy. Let's do the first one 41: 4(3+x)+10= -11(x-6)+1 First expand both sides using distribution 12+4x + 10 = -11x + 66 + 1 Now combine like terms 22 + 4x = 67 - 11x Now get the constants on one side and the x terms on the other 4x + 11x = 67 - 22 Combine like terms again 15x = 55 Now isolate x by diving both sides by 15 x = 55/15 = 11/3 Check you answer by using 11/3 as x in the original problem and verifying that both sides are equal 43 is easier. 3x+21 = -2x + 11 same steps. get constants on one side, x term on the other 3x + 2x = 11 - 21 combine like terms 5x = -10 x = -2 I bet you can do 45 now. Give it a go and ing me if you cant get it
 Angles/148135: Find the equation of a line passing through the origin that makes an angle of 52 degrees with the x axis. 1 solutions Answer 108535 by vleith(2825)   on 2008-07-13 19:42:19 (Show Source): You can put this solution on YOUR website!Th easiest thing to do is find the tangent of 52. Then realize that is sin/cos or y/x. Thus the slope of a line through the origin will be equal to the tangent(52). Tangent(52) = 1.28 y = 1.28x
 Rational-functions/148081: Divide using long division: 6x^3 + 19x^2 + x - 10 / 3x^2 - 11x - 6 + -4/2x - 11 solutions Answer 108528 by vleith(2825)   on 2008-07-13 18:53:19 (Show Source): You can put this solution on YOUR website!See --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
 sets-and-operations/148101: This question is from textbook A Survey Mathematics with Applications I'm just learning how to do these and need a little help please? pts) Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set a) A ∩ B b) A ∩ C c) A U C d) B U C e) (A U B) ∩ C f) A U (B U C) g) (A ∩ B) ∩ C h) (A ∩ B) U C 1 solutions Answer 108525 by vleith(2825)   on 2008-07-13 18:50:50 (Show Source): You can put this solution on YOUR website!a) A ∩ B means what is in both A and B. {3} is in both b) A ∩ C means what is both A and C. Again only {3} is in both c) A U C means what is in either A or C. {1 2 3 5 7} d) B U C means what is in either B or C {3 4 5 6 7} e) (A U B) ∩ C means what is in either A or B and also in C AUB = {1 2 3 4 5 6} what is also in C? {3 5} f) A U (B U C) what is in any of the three {1 2 3 4 5 6 7} g) (A ∩ B) ∩ C what is in each of the three {3} h) (A ∩ B) U C look at answer a above. Now what either in that or in C? {3 5 7} does this help any?
 logarithm/148113: This question is from textbook functions modeling change evaluate with out a calculator: 2lne^41 solutions Answer 108523 by vleith(2825)   on 2008-07-13 18:41:08 (Show Source): You can put this solution on YOUR website!Given
 Linear-systems/148128: Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She averaged 75 MPH along the route from Albuquerque to Roswell and averaged 70 MPH from Roswell to Carlsbad. She covered the entire 220 miles in 3 hours. How long did she take to drive from Albuquerque to Roswell? I started by making a table DISTANCE RATE TIME 270 75 3hrs 270 70 3hrs but the problems that I was coming up with did not make sense to me. Am I going about thie correctly? 1 solutions Answer 108521 by vleith(2825)   on 2008-07-13 18:38:26 (Show Source): You can put this solution on YOUR website!You need to break the trip into two parts. The total trip is 220. The total time is 3 hours. Let the distance from Albuquerque to Roswell be x (watch out for aliens in Roswell). Then the distance from Roswell to Carlsbad is The time for each leg is given by The time to Roswell is The time to Carlsbad is The total time is 3 hours. So the distance to Roswell is 150 miles. At an average speed of 75 mph, the drive to roswell takes 2 hours.
 Numbers_Word_Problems/148126: I'm not sure if i selected the correct type of question for the subject but I need help on a "Number Problem" The book I have does not explain how to solve, it just has them in the back as a question. The sum of two numbers is 27 and there difference is 20. Find the numbers. How would you start this problem?1 solutions Answer 108519 by vleith(2825)   on 2008-07-13 18:23:00 (Show Source): You can put this solution on YOUR website!This is a classic algebra problem. Let the two numbers be represented as x and y. You are given: the sum is 27 their difference is 20 You can use substitution or elimination to solve these. See http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations for a nice video that covers different ways to solve systems like this. We'll use elimination to solve add these two equations ----------------- Now that you know one number, use that to solve for the other one You can verify the answers by substituting back into the original two equations.
 Rational-functions/148124: Simplify 1 solutions Answer 108515 by vleith(2825)   on 2008-07-13 18:15:30 (Show Source):
 Polynomials-and-rational-expressions/148060: How to simplify this expression? (2m+3n/2m^2-5mn-12n^2)/(2m^2-7mn-4n^2/m^2-8mn+16n^2)1 solutions Answer 108449 by vleith(2825)   on 2008-07-13 07:59:47 (Show Source): You can put this solution on YOUR website!Find the factors for the quadratic terms and then cancel to simplify. = = = Now cancel what you can, remembering that dividing by a fraction is just the same as multiplying by that fractions inverse. Ping if you cant get it
 Geometry_proofs/148059: 1) The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral. Prove that the quadrilateral is a parallelogram. (Show that line AB ll line DC and line AD ll BC) 2) The points T(-1,4), E(2,4), and D(2,-1) are vertices of a triangle. Prove that the triangle is a right triangle. (Find the slopes of line TE, line ED and line TD.) 3) The points L(3,1), O(2,-3), V(-2,-2) and E(-1,2) are vertices of a rhombus. Show that the diagonal are perpendicular. 4) Solve y = mx + b for x. Use the result to find x in y = 4x – 5 when y = 3.1 solutions Answer 108445 by vleith(2825)   on 2008-07-13 06:12:05 (Show Source): You can put this solution on YOUR website!I'll show you how to do question 1. Questions 2 and 3 are use the same technique - so you can solve them. 1) (The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral. Prove that the quadrilateral is a parallelogram. You need to remember that parallel lines have the same slope and perpendicular lines have slopes that are negative reciprocal (the product of the slopes of two perpendicular lines equals -1. So find the slopes is the segments AB and CD. Then find the slopes of segments BC and DA. slope when given two points. Slope of AB is given by = Slope of CD is given by = Both are 0, so they are parallel Slope of BC is given by = Slope of DA is given by = Both are -2/3, so they are parallel too. A figure with two sets of parallel lines is a a prallelogram 2) For problem two, find the slopes of the three segments. Then verify that two of those slopes have a product of -1. 3)For problem three, find the slopes of the segments LV and OE. The show they have a product of -1 4) Solve for x Solve when y = 3, m=4 and b = -5
 Money_Word_Problems/148058: How much should be invested at 8% compounded semiannually in order to have \$5000 at the end of 8 years? a. \$4215.27 b. \$9364.91 c. \$2669.54 d. \$3048.781 solutions Answer 108444 by vleith(2825)   on 2008-07-13 05:57:08 (Show Source): You can put this solution on YOUR website!The future value of money using compound interest is given by: Where F is the future value P is the present value r s the annual interest rate n is the number of compounding per year t is the total number of compoundings This problem asks for the present value (P)of a future sum (F=5000), when the interest is 8%(r=0.08) compounded semi-annually (n=2) for a length of 8 years (t = 8*n = 16). Solving for P: The answer is C Read this for more info -->http://www.purplemath.com/modules/expofcns4.htm
 Linear_Equations_And_Systems_Word_Problems/147925: Express the following statements in terms of algebraic symbols. Q:The three angles A,B,C of a triangle ABC if angle A exceeds twice angle B by 20. please and thank you1 solutions Answer 108300 by vleith(2825)   on 2008-07-11 14:25:46 (Show Source): You can put this solution on YOUR website!We know the sum of the angels in a triangle is 180. Given: A = 2B + 20 Then C = 180 - A - B C = 180 - (2B+20) - B C = 180 - 2B - 20 - B C = 160 - 3B So, the angles are: A = 2B+20 B = B C = 160 - 3B Make sense?
 Trigonometry-basics/147846: trig identities- i need help proving that this identity is true (sin2x/ 1+cos2x) * (cosx/1+cosx) = tan(x/2)1 solutions Answer 108229 by vleith(2825)   on 2008-07-10 19:03:02 (Show Source): You can put this solution on YOUR website!Assume you have double angle and half angle identities already 'in your bag of trick'. See http://homepage.mac.com/shelleywalsh/MathArt/DoubleHalf.html Namely sin(2x) = 2sin(x)cos(x) cos(2x) = 2cos^2(x)-1 tan(x/2) = sin(x)/(1+cos(x)) Now let's start at the top (sin2x/ 1+cos2x) * (cosx/1+cosx) = ((2sin(x)cos(x)) / (1 + (2cos^2(x)-1)) * (cosx/1+cosx) = ((2sin(x)cos(x)) / (2cos^2(x)) * (cosx/1+cosx) = ((sin(x)cos^2(x)) / (cos^2(x)) * 1/(1+cosx) = sin(x) * 1/(1+cosx) = sin(x)/(1+cosx) = tan(x/2)
 Human-and-algebraic-language/147852: Hank and Sally went shopping for school supplies at the local discount store. Hank realized that the price of two pencils was the same as a blue pen. When checking out, Sally paid \$15 for the ten pencils and five pens for Hank and her. What was the price for one pen and the price for one pencil? My Work so far: 2p = 1b (p=pencil; b=blue pen) 15= 10p + 5b1 solutions Answer 108222 by vleith(2825)   on 2008-07-10 18:39:57 (Show Source): You can put this solution on YOUR website!so far so good. 2p = 1b (p=pencil; b=blue pen) 15= 10p + 5b Now substitute using 2p=b 15 = 10p + 5(2p) 15 = 10P + 10p 15 = 20p 3/4 = p pencils are \$0.75 each pens are 2p = 2*(0.75) = \$1.50 Check your answer. Is 10*0.75 + 5*(1.50) = 15?
 expressions/147855: Evaluate the expression 17-(-x)- -10 when x=31 solutions Answer 108220 by vleith(2825)   on 2008-07-10 18:36:34 (Show Source): You can put this solution on YOUR website!Given Evaluate at x=3 Remember that subtracting a negative is the same as adding a positive
 percentage/147857: from point a to point b elevation drops 2.6 feet. total distance from a to b is 560 feet.at what percent does this flow.1 solutions Answer 108219 by vleith(2825)   on 2008-07-10 18:33:40 (Show Source): You can put this solution on YOUR website!To find percent grade, divide the part by the whole and multiply by 100. % = % = % grade
 Miscellaneous_Word_Problems/147688: one has two 20oz cups of water filled to the brim, and a empty 14 oz cup and a empty 8 oz cup, without dropping any i need 6oz in the 14 and 6 oz in the 8 oz cup. Should take only 6 steps to complete.1 solutions Answer 108101 by vleith(2825)   on 2008-07-09 15:38:12 (Show Source): You can put this solution on YOUR website!1) Pour from 20 into 14 filling it. Leaves 6 in the 20 2) Pour from 14 into 8 filling it. Leaves 6 in the 14 3) Drink the 8 oz contents 4) Pour 6 from the 20 into the 8 If you cant drink any 1) pour from 20 into the 8. leaves 12 and 8 2) Pour from other 20 into the 14. leaves 6 and 14 3) Pour 12 into 6. leaves empty and 18 4) Pour 8 into empty. Leaves empty 8 and 8 in 20 5) Pour from 14 into 8 until 8 is full. leaves 8 and 14 with 6 in it (one done) 6) Pour from 8 into 18 until full. Leaves 6 in 8 (other one done) and a full 20. When we are done, we have a full 20, 6 in 8, 6 in 14 and 8 in the other 20. total 40. we are golden.
 Linear-equations/147648: Solve each system by the addition method. Indicate whether each system is dependent, inconsistent, or dependent. x+3(y-1)=11 2(x-y)+8y = 28 1 solutions Answer 108024 by vleith(2825)   on 2008-07-09 06:48:07 (Show Source): You can put this solution on YOUR website! These two lines can be represented by the same line. So they are dependent
 Human-and-algebraic-language/147633: Suppose you have 12 coins that total 32 cents. Some of the coins are nickels and the rest are pennies. How many of each coin do you have? 1 solutions Answer 108022 by vleith(2825)   on 2008-07-09 06:43:44 (Show Source): You can put this solution on YOUR website!Let p be the pennies and n be nickles Use elmination, subtract these two equations So you have 5 nickles and pennies
Angles/147652: The sum of the measures of two obtuse angle is 215.The sum of three-fifths of the supplement of the smaller angle and two-thirds the supplement of the larger angle is 91. Find the measure of the two angles.
1 solutions

Answer 108021 by vleith(2825)   on 2008-07-09 06:38:50 (Show Source):
You can put this solution on YOUR website!
Let the two angels be a and b
a+b = 215
We are also given a second set of information
The supplement of an angle plus the angle is always 180.
We are told

Now solve using

To get a = 95 and b = 120

 Expressions-with-variables/147651: EVALUATE: a-13 when a =33 2 =3y when y=81 solutions Answer 108020 by vleith(2825)   on 2008-07-09 06:28:09 (Show Source): You can put this solution on YOUR website!Given the function evaluate that function when a = 33 Take the function and plug in the value for a. Now do the arithmetic. What is 33-13? I don't understand the second one. 2=3y when y=8 doesn't make sense
 Geometry_proofs/147489: Can two of the angle bisectors of a tirangle intersect perpendicularly? Explain. (i think the answer is yes, for a right triangle? but i don't know why)1 solutions Answer 107869 by vleith(2825)   on 2008-07-07 20:43:11 (Show Source): You can put this solution on YOUR website!I don't think so. Start with a right triangle. At the non-right angle vertices, double the angles. What are the resulting angles? Let's say that one angle was alpha, then the other angle must be 90-alpha. If we double alpha, we get 2alpha. If we double (90-alpha), we get (180-2alpha). The sum of the anlges inside a triangle is 180. Let's add our two angles so far. 180-2alpha + 2alpha = 180. So we already have 180 degrees. The other vertex doesn't exist (the lines are parallel).
 Exponents/147490: What is the greatest positive integer n such that 2^n is a factor of 12^10? I don't even know where to start!!!1 solutions Answer 107868 by vleith(2825)   on 2008-07-07 20:33:30 (Show Source): You can put this solution on YOUR website!I am thinking this: We are being asked to find the largest value of n such that is an integer = 2 will never factor into 3, since both are prime. So the largest number for n is the largest one that still results in being an integer. What is the smallest number that still is a positive integer? well, that's 1. So what value of n results in is 1? n = 20
 Geometry_proofs/147491: Given rectangle ABCD, let P be the point outside ABCD that makes triangle CDP equilateral, and let Q be the point outside ABCD that makes triangle BCQ equilateral. Prove that triangle APQ is also equilateral. Would APQ be equilateral if ABCD was a parallelogram? I happen to be very, very lost in this specific problem. I understand that it is equilateral, but unfortunately, I don't know how to prove it! Thanks!1 solutions Answer 107867 by vleith(2825)   on 2008-07-07 20:22:34 (Show Source): You can put this solution on YOUR website!Draw the picture. Mark the two sets of congruent sides in the rectangle. Then layout the two equilateral triangles and mark the sides that are congruent with the two different sets in the rectangle. You end up with a rectangle with two triangles and only two different lengths for the various segments. Remember that side-angle-side (SSA) is one means to establish congruent triangles. Now: The angles in the original rectangle are all 90 degree each. The angles in equilateral triangles are 60 degrees each. Triangles ADP, ABQ and CPQ are all congruent using SSA. How do we get that? Angle ADP is 90+60 = 150. Segment AD and DP as sides Angle ABQ is also 90+60. Again BC and AB as sides Angle PCQ = 360 - 60 - 90 - 60 = 150. Sides are CQ and CP So we have 3 congruent triangles. Hence the thrid side of each is the same length. And the triangle composed of those three sides must be equilateral. Not so for parallelogram
 expressions/147474: 19-(2x+3)=2(x+3)+x please tell me if i did this right. 19-2x-3=2x+6+x 16-2x=3x+6 10-2x=3x 10=5x x=21 solutions Answer 107859 by vleith(2825)   on 2008-07-07 18:58:46 (Show Source): You can put this solution on YOUR website!You did. well done. Use this to check if you need to http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic
 Graphs/147472: For each of the following inequalities indicate whether the boundary line should be dashed or solid. x+y<2 2x<-y 2x-y>3 x+y>1 y>2 4x-2y+1>0 2>x-y 1 solutions Answer 107858 by vleith(2825)   on 2008-07-07 18:56:19 (Show Source): You can put this solution on YOUR website!Use solid lines when there is an equal sign as part of the expression. None of these equations have an equal sign, so none use solid lines
 Polynomials-and-rational-expressions/147437: x+3(divisor) divided by 5xcubed+5xsquared-32x-10 (dividend). Not sure how to work out this problem in long division.1 solutions Answer 107857 by vleith(2825)   on 2008-07-07 18:53:00 (Show Source): You can put this solution on YOUR website!Use this --> http://www.calc101.com/webMathematica/long-divide.jsp
Quadratic_Equations/147469: Let's put an equation with that curve. Use y = x2-8x+7
a. What is the value of the discriminant? Review Lesson 3.05.
b. What types of roots will this equation have? Ex: two complex roots, one repeated root, two real rational roots or two real irrational roots? Review Lesson 3.05.
c. Find the roots by factoring and solving. Review Lesson 3.04.
d. Find the roots by using the quadratic equation. Review Lesson 3.04.
e. Find the roots by graphing and using the tracking tool.
1 solutions

Answer 107856 by vleith(2825)   on 2008-07-07 18:50:49 (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=36 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 7, 1. Here's your graph:

 Parallelograms/147464: I have a parallelogram (rv lot)45 feet by 30 feet with angle of 60 degrees..question is...will my rv of 40 feet by 10 feet fit on lot without crossing boundries? 1 solutions Answer 107846 by vleith(2825)   on 2008-07-07 16:06:54 (Show Source): You can put this solution on YOUR website!I think that's a trick question. Sure it will ... if you park it at a 60 degree angle. If you have to park it 'straight', then we have to do a little math. Draw your parallelogram, 45 feet and 30 feet with 60 degree angle between the 30 and 45 sides. Drop a line from one end of the a 45 foot side down. Make it perpendicular to the 30 foot base line. Now take 45 *cos(60) to see how long the side of the resulting right triangle is. Take 45*sin(60) to see how long the other side is. Then make the call about whether the rv can fit
 expressions/147466: a mechanic earns a salary of \$350 a week plus he gets \$10 for every oil change he carries out. a) write an eqation to represent the total weekly earnings E, when C oil changes are done. 1 solutions Answer 107845 by vleith(2825)   on 2008-07-07 15:58:56 (Show Source): You can put this solution on YOUR website! Earning is the flat 350 + \$10 for each oil change