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# Recent problems solved by 'rapaljer'

rapaljer answered: 4664 problems
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 Expressions-with-variables/9206: what is the answer for this. instructions- rewrite each expressionusing the distributive property. then simplify1 solutions Answer 4945 by rapaljer(4667)   on 2005-08-31 23:45:49 (Show Source): You can put this solution on YOUR website!We aren't quite THAT good!! You really need to give us a PROBLEM!! You give us the expression first, THEN we can simplify it!! R^2 at SCC
 decimal-numbers/9083: which is an example of a proportion? 2/3, n=1/2, 2/5=a/15,or none of these? (thank you for the help!!!!!!!!!!!!)1 solutions Answer 4944 by rapaljer(4667)   on 2005-08-31 23:38:07 (Show Source): You can put this solution on YOUR website!A ratio of two numbers is like a fraction . A proportion is a ratio of two numbers equal to a ratio of two other numbers: . So, I would say that the ratio is . I suppose if had been written in the form , then that too would have been an example of a proportion. R^2 at SCC
 Points-lines-and-rays/9180: How do you find a vertex angle for a regular octagon?1 solutions Answer 4943 by rapaljer(4667)   on 2005-08-31 23:32:00 (Show Source): You can put this solution on YOUR website!First you need to find the sum of all the angles within a regular octagon. To do this, draw an octagon (8 sides, like a stop sign!), select a vertex (any vertex will do!), and draw diagonals from that vertex to each other vertex in the octagon. These diagonal will divide the octagon into 6 triangles (it's always 2 less than the number of sides in the figure being "diagonalized"). Each triangle has 180 degrees, which multiplied times 6 gives you 1080 degrees. This 1080 degrees represents the sum of the 8 vertex angles of the octagon. To find the size of each angle, divide 1080 by 8, or 135 degrees. R^2 at SCC
 Expressions-with-variables/9182: i have a graph that states number of sales,and total earnings are: 5 \$2.00 10 \$4.00 15 \$6.00 20 \$8.oo so how would i write an equation for that?1 solutions Answer 4942 by rapaljer(4667)   on 2005-08-31 23:23:53 (Show Source): You can put this solution on YOUR website!Earnings = or Earnings = R^2 at SCC
 Complex_Numbers/8979: Hi I am having trouble solving the following problem: x^3-8=0 Can you provide some help in solving this - there are three answers one of which is 2 but I cannot figure out the other two imaginary ones. Thanks Lee1 solutions Answer 4941 by rapaljer(4667)   on 2005-08-31 23:13:01 (Show Source): You can put this solution on YOUR website! Factors into The quadratic factor can be solved by either the quadratic formula, the pluggable solver, or by completing the square. Completing the square is fairly easy: , and of course, x=2!! R^2
 Square-cubic-other-roots/9045: sqrt 8x^5y simplify Is the answer 2x^2 sqrt2xy?1 solutions Answer 4940 by rapaljer(4667)   on 2005-08-31 23:00:12 (Show Source): You can put this solution on YOUR website!Again, Jon's answer should be simplified further, giving YOUR answer: R^2
 Square-cubic-other-roots/9046: These things are hard for me, can you please help? simplify cubed rt 9x^2y * cubed rt 3x^3y^2 Is the answer 3xy cubed rt 3x^2? Thanks1 solutions Answer 4939 by rapaljer(4667)   on 2005-08-31 22:54:09 (Show Source): You can put this solution on YOUR website!In Jon's solution, he didn't simplify the answer completely. If you simplify HIS answer , you will get YOUR answer, which is
 Divisibility_and_Prime_Numbers/9134: I need help on this question. Find the probablilty of drawing a heart or a club from a standard 52 card deck1 solutions Answer 4938 by rapaljer(4667)   on 2005-08-31 22:35:13 (Show Source): You can put this solution on YOUR website!OOps, Jon is going too fast! The answer of 2/4 reduces to 1/2.
 Divisibility_and_Prime_Numbers/8897: what is prime and real numbers?1 solutions Answer 4857 by rapaljer(4667)   on 2005-08-30 07:09:44 (Show Source): You can put this solution on YOUR website!A prime number is a number larger than 1 that cannot be broken down into a product of smaller numbers. A number larger than 1 that CAN be broken down into the product of two or more numbers is said to be a composite number. The number 1 is neither prime nor composite. For examples, 2, 3, 5, 7, 11, etc. are prime numbers since they cannot be broken down. The numbers 4, 6, 8, 9, 10, 12, etc. are composite numbers. Real numbers consist of all numbers whose distance can be measured on the numberline, including whole numbers like 1, 2, 3, 4, etc. 0 and the negative integers like -1, -2, -3, etc. all fractions, and decimals, and even numbers that don't come out even, like etc. See the page on my own website which is not yet a lesson plan for algebra.com (maybe coming soon to algebra.com, who knows!) from Basic Algebra by clicking on my tutor name "rapaljer" anywhere in this website, go to Basic Algebra, look for "Samples of Basic Algebra: One Step at a Time", "Chapter 1," then "Section 1.01 Number Systems." This section may be helpful. R^2 at SCC
 Miscellaneous_Word_Problems/8890: In 1993,10,631,000 vehicles were registered in New Mexico, Maryland, and Georgia. New Mexico had 3,000 less than 2/5ths of the number in Maryland. Georgia has 52,000 less than 4 times the number in New Mexico. how many registered motor vehicles were there in each of these three states?? so far I have the formulas: NM=(MD)(2/5) - 3,000 GA= (NM)(4) - 52,000 MD= 10,613,000 - (NM + GA)1 solutions Answer 4848 by rapaljer(4667)   on 2005-08-30 00:12:19 (Show Source): You can put this solution on YOUR website!It looks right so far. Substitute the first formula for NM into the second equation: GA = 4(NM) - 52000 GA = 4(2/5MD -3000) - 52000 GA = 8/5 MD - 12000 - 52000 GA = 8/5 MD - 64000 Now, substitute THIS GA and the NM into the third equation: MD = 10613000 - (NM + GA) MD = 10613000 - ( 2/5MD -3000 + 8/5 MD -64000) MD = 10613000 - (10/5 MD - 67000) MD = 10613000 - 2MD + 67000 MD = 10680000 - 2MD Add +2MD to each side of the equation: 3MD = 10680000 Divide by 3 MD = 3560000 It's late! I have no idea if this is right or not! It's the UGLIEST problem I've seen in a long time! At least it came out even, right?? Ask me in the morning!! Oops! It IS morning!! R^2 at SCC
 Coordinate-system/8885: what are the cordinates of the x-intercept of the line 2x-5y=6 1 solutions Answer 4847 by rapaljer(4667)   on 2005-08-29 23:57:51 (Show Source): You can put this solution on YOUR website!X-intercept is where y = 0. So, just plug in y=0, 2x - 5y = 6 2x - 5(0) = 6 2x = 6 x=3 If you want the coordinates of the point, that would be (3,0). R^2 at SCC
 Linear-systems/8887: I need help on this equation: y=[x+3]-4= I need the x-intercepts(the negative and positive).....im stuck at that part.. Thanks1 solutions Answer 4846 by rapaljer(4667)   on 2005-08-29 23:54:43 (Show Source): You can put this solution on YOUR website!After I solved the following exercise, it occurred to me that you MAY have meant this to be an absolute value problem!! Did you intentionally use brackets [ ] in the problem? Brackets in a math problem do NOT mean absolute value. Before continuing, let's make sure you MEANT to give me a bracket function. If you meant absolute value, then IGNORE all of this HARD work that I did trying to solve a BRACKET FUNCTION!! Bracket function, the greatest integer function!! What this means is that whatever you get when you substitute a value of x, you round it down to the greatest integer. y= [x+3] -4 means that if x= 0, then y= [0+3] - 4 = 3 - 4 = -1 if x=.5, then y= [.5+3] - 4 = 3 - 4 = -1 if x=1, then y = [1+3] - 4 = 4 - 4 = 0 which is an x-intercept if x=1.5, then y = [1.5+3] - 4 = 4 - 4 = 0 which is also an x-intercept if x=1.9, then y = [1.9+3] - 4 = 4 - 4 = 0 which is also an x-intercept if x=2, then y = [2+3] - 4 = 5 - 4 = 1 In other words, everything between 1 and 2 including the 1 but NOT including the 2 will be x-intercepts. This is called the "unit step function. However, this may NOT have been what you were asking! R^2 at SCC
Inequalities/8888: I have this due tonight can anyone help me out please.....please
graph the following inequalities
y < x + 3
y < -2x + 4

Thank you for anyone who will kindly answer.
1 solutions

Answer 4845 by rapaljer(4667)   on 2005-08-29 23:37:15 (Show Source):
You can put this solution on YOUR website!
Before continuing with the solution, you must realize that both of the lines that you have given must be DOTTED lines, since they involve the symbol "<" or ">". Secondly, you must shade the area BELOW the lines, since you are looking for the areas in which "y < ". Use the graphs given below, but graph BOTH lines on the same xy axes. You are probably looking for the INTERSECTION, which would be the overlapping of the two areas shaded below the two lines. In other words, shade the area below BOTH lines.
The following graphs are thanks to a special solver written by Igor Chudov, the owner of this website. Send HIM the thank the note!!

 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. -3/1 = -3.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/-1 = 3.Slope is -1/-1 = 1. Equation in slope-intercept form: y=1*x+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. 4/2 = 2.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.Slope is -2/1 = -2. Equation in slope-intercept form: y=-2*x+4.

 Polynomials-and-rational-expressions/8886: I've been stuck on this problem for a long time.... How can u factor: 7x2y2+147xy2-504y2= (the 2 means to the 2nd power) Thanks!!1 solutions Answer 4844 by rapaljer(4667)   on 2005-08-29 23:17:21 (Show Source): You can put this solution on YOUR website!Your first step in ANY factoring problem is to take out the common factors! In this expression, each term is divisible by 7 and y^2, so take out a common factor of The trinomial factors if you can find two numbers whose product is -72 and whose difference is 21. Try 24 and -3 R^2 at SCC
 Exponents-negative-and-fractional/8863: I'm so lost on this one. I do remember the order of operations, however this is a very complex formula, I hope I type it well enough or it'll get a completely different meaning and answer. Here goes: Looks like it came through correctly, please help...1 solutions Answer 4842 by rapaljer(4667)   on 2005-08-29 22:28:34 (Show Source): You can put this solution on YOUR website!This is SO INTIMIDATING!! It probably is really easy if you dare to look at it. First, simplify the numerator at the very top: 3*8 is 24, and add 11, which is 35. Second, in the middle, go ahead and multiply the (2t)*(3*8) which is 2t*24 or 48t. Then simplify the fraction that follows, which is and simplifies to 4t. This combines with the 48t, so 48t - 4t = 44t. Third, the denominator at the bottom likewise simplifies, with the 3 and -3 subtracting out, to . The net result is this: divided by Invert and multiply: As you can see the t's all divide out, the 2 divides out, and you are left with . R^2 at SCC P.S. Congratulations on writing that equation in an algebra.com formatted equation!! You must be a math teacher???
 expressions/8869: provide examples on writing algebraic expressions 1 solutions Answer 4841 by rapaljer(4667)   on 2005-08-29 22:14:25 (Show Source): You can put this solution on YOUR website!Can you be a bit more specific? I probably have a lesson plan for you either on algebra.com or on my own website. Check out my own website by clicking on my tutor name "rapaljer" anywhere in this website, go to "Basic Algebra" then look for "Samples of Basic Algebra: One Step at a Time", and look in Chapter 1. This probably has everything from simplifying algebraic expressions Section 1.06 or translating words into algebraic expressions, Section 1.09." Let me know if you don't find what you need. Happy hunting! R^2 at SCC
 Geometric_formulas/8872: how do u find the area of a circle with the radius of 5 and 1/3 feet.1 solutions Answer 4839 by rapaljer(4667)   on 2005-08-29 22:07:56 (Show Source): You can put this solution on YOUR website! In this case, r = 5 1/3 ft, which as an improper fraction is 16/3 feet. Square the numerator, which is 256, and the denominator, which is 9. which can be written as feet. However, some books want you to substitute 3.14 for pi, and calculate the decimal approximation. Do what you need to do! I like leaving it in terms of . R^2 at SCC
 Evaluation_Word_Problems/8874: 60000s plans to use 1150 feet of fence to enclose the rectangular pasture shown below. One side boarders a river where there is already a thick hedge. It needs no fencing. The pasture is in the shape of a rectangle only the widths are marked. a. Let x be the width of the pasture as labeled. Write an expression for the length in terms of x. b. Write an expression for the area of the pasture in terms of x. c. Suppose the pasture must enclose at least 60,000 square feet. Write a sentence relating the area expression in part b to the area the pasture must enclose. 1 solutions Answer 4837 by rapaljer(4667)   on 2005-08-29 21:55:59 (Show Source): You can put this solution on YOUR website!Let x = width of the rectangle. Notice that there are two widths to this rectanglar fence, and only one length, since the other side doesn't need any fence. To find the length, you'll need to start with the total amount of fence, which is 1150, and subtract the TWO widths, which would be 2x, which leaves you the length = 1150 - 2x. b)AREA = WIDTH * LENGTH A = x(1150 - 2x) C) R^2 at SCC
 Equations/8875: -4(-p)(-q)=1 solutions Answer 4835 by rapaljer(4667)   on 2005-08-29 21:48:40 (Show Source): You can put this solution on YOUR website!(In this problem, you really have to watch your p's and q's!!) Since there are an odd number of negative signs in a product or quotient, the answer will be negative. Then multiply 4 times p times q, which would be 4pq, so the final answer is -4pq. R^2 at SCC
 Expressions-with-variables/8877: I am trying to help my daughter & I am so confused by "simplify the variable expression, here is the problem... (5)(-x) what is the answer & how do we do this? please help1 solutions Answer 4833 by rapaljer(4667)   on 2005-08-29 21:45:46 (Show Source): You can put this solution on YOUR website!(5)(-x) Since there is no sign between the 5 and the -x, it means to multiply. Since you are multiplying a postivie times a negative (opposite signs!), the answer is negative, and the product of 5 times x is 5x. Final answer, -5x R^2 at SCC
 Miscellaneous_Word_Problems/8876: A woman is asked her weight. She, appropriately, replies (you should never ask a woman her weight – unless you are really asking for a slap in the face or a divorce) that she weighs 60 lbs plus half her weight. What is her actual weight (in lbs)?1 solutions Answer 4832 by rapaljer(4667)   on 2005-08-29 21:43:26 (Show Source): You can put this solution on YOUR website!The equation is based upon the fact that "Her weight is equal to 60 lbs. plus half her weight." Srart by letting x = thw weight of the woman (if she is like most women I know, in this case, x is REALLY the unknown!) "Her weight is equal to 60 lbs. plus half her weight." You probably don't like that fraction, so just multiply both sides of the equation by 2 and get rid of it. Subtract x from each side, and you get: Check it out: Her weight is 120, which equals 60 plus half of her weight, which is another 60. You might figure out a way to do this intuitively (like in your head), but I like equations. They are reliable! R^2 at SCC
 Triangles/8615: The area for a triangle is (4x squared + 10) squared. the base is 4x-4 and the height is x-3 and the hypotinus is 2x+5. what is x? how do you find what x is?1 solutions Answer 4807 by rapaljer(4667)   on 2005-08-28 23:58:23 (Show Source): You can put this solution on YOUR website!Jennifer's solution is NOT correct! When you add the base and to the height you do NOT get the hypotenuse, as she suggested!! Area of a triangle: Since this seems unreasonable to solve, perhaps you stated the problem wrong!! Recheck the problem. I was thinking that maybe the area is just , without the "squared." Solve by quadratic formula, and it just comes out ugly?? Recheck your copying of the problem to make sure that is correct. R^2 at SCC
 Equations/8603: solve for h. v = 1/3(pie)r(squared)h1 solutions Answer 4801 by rapaljer(4667)   on 2005-08-28 15:13:30 (Show Source): You can put this solution on YOUR website! Eliminate the fractions by multiplying both sides by 3: Now, to solve for h, you need to get rid of the which are being multiplied times the h. So divide both sides of the equation by . R^2 at SCC
 Linear_Equations_And_Systems_Word_Problems/8623: The altitude of a falling rock t seconds after it is dropped is calculated from the polynomial h(t)=-16t^2+200. Find the altitude of the rock 2 seconds after it is dropped. also: A rectangle has a length which is 3 more than its width. Write a polynomial P(x) which expresses the perimeter of this rectangle in terms of the width x.1 solutions Answer 4800 by rapaljer(4667)   on 2005-08-28 15:05:04 (Show Source): You can put this solution on YOUR website!We already did the first question, so here is the second part: Let x= width of the rectangle x+3 = length of the rectangle P = 2(W) + 2(L) P = 2(x) + 2(x+3) P = 2x + 2x + 6 P = 4x + 6 R^2 at SCC
 Linear_Equations_And_Systems_Word_Problems/8617: The altitude of a falling rock t seconds after it is dropped is calculated from the polynomial h(t)= -16t^2+ 200. Find the altitude of the rock 2 seconds after it is dropped. I set up as h=-16(2)(2)+200 =-16(4)+200 =-64+200 = 136 feet help!1 solutions Answer 4799 by rapaljer(4667)   on 2005-08-28 15:00:46 (Show Source): You can put this solution on YOUR website!It looks right to me!! R^2 at SCC
 Mixture_Word_Problems/8643: a chemist has one solution that is 60% chlorinated and another that is 40% chlorinated. How much of each solution is needed to make a 100 L solution that is 50% chlorine? 1 solutions Answer 4798 by rapaljer(4667)   on 2005-08-28 14:56:16 (Show Source): You can put this solution on YOUR website!Normally this is a word problem that must be worked out with an equation (see my Lesson Plan on Word Problems--Coin and Mixture Problems--Part I). However, there is an intuitive solution to this one if you think about it. You are mixing some 60% and some 40% solutions, trying to obtain a 50% solution, which is exactly halfway between the 60% and the 40%. You will obviously need to mix them half and half. The solution is 50 L of each. R^2 at SCC
 Equations/8629: how do you factor out x squared plus 3x?1 solutions Answer 4797 by rapaljer(4667)   on 2005-08-28 14:52:31 (Show Source): You can put this solution on YOUR website! Take out the common factor, which is x: x(x+3) R^2 at SCC
 Functions/8640: I'm sorry. I left out the 7. 2/x + 1/2x = 7 ?1 solutions Answer 4796 by rapaljer(4667)   on 2005-08-28 14:49:33 (Show Source): You can put this solution on YOUR website!Do you mean Assuming that this is the case, the LCD for the entire problem is 2x, so multiply both sides of the equation by 2x: This eliminates all the denominators: 4 + 1 = 14x 5= 14x Divide both sides by 14: x= R^2 at SCC
 Points-lines-and-rays/8620: I need to write the equation of a line with a slop of 0 and a y-intercept of (0,2)and am having problems in general with lines, slopes given different variables. Can you help with the specific and then point me in the right direction so I can finish the rest of my work? Thank you!1 solutions Answer 4787 by rapaljer(4667)   on 2005-08-28 12:38:49 (Show Source): You can put this solution on YOUR website!The slope intercept form of the equation of a line is y = mx+b, where m is the slope and b is the y-intercept. In this case, you are given the slope and the y intercept, so just substitute these numbers into y=mx+b, and you have y=0x + 2 or y=2. Also, a line with slope 0 is always a horizontal line, which is always in the form of y = a number. In this case, the y-intercept is 2, so y = 2. R^2 at SCC
 Miscellaneous_Word_Problems/8616: A board 18 ft long is cut into two pieces. Two feet less than the product of five and the length of the smaller piece is equal to the difference between three times the length of the longer piece and eight. Find the length of each piece. Here's what I've done and I know I don't have it setup right. 5x-2+x+18 6x=20 x=3 1/3 x+3x+8=18 4x=26 x=6 1/21 solutions Answer 4786 by rapaljer(4667)   on 2005-08-28 12:35:08 (Show Source): You can put this solution on YOUR website!The way I did it, always start off by identifying the variables: Let x = length of smaller piece 18-x = length of longer piece The equation is tricky, but just follow the wording of the sentence that is given: 5(smaller) - 2 = 3(longer) - 8 5(x) - 2 = 3(18-x) - 8 5x - 2 = 54 - 3x - 8 5x - 2 = 46 - 3x Add 3x to each side: 5x + 3x - 2 = 46 - 3x + 3x 8x - 2 = 46 Add +2 to each side: 8x = 48 x=6 smaller piece 18-x = 12 longer piece Check: 5(6) -2 = 3(12) - 8 30-2= 36-8 28 = 28 It checks! R^2 at SCC
 Expressions-with-variables/8610: The problem asks me to solve usling any method. 5x+6y=14 y=4x-17 I am not sure which method to use. I tried both but did not come out with the same answer both times! Thanks for your help!1 solutions Answer 4785 by rapaljer(4667)   on 2005-08-28 12:25:06 (Show Source): You can put this solution on YOUR website!Because one of the equations is in the form of y=___ (or also x=____), I think the substitution method is the easiest way. Rewrite the first equation 5x + 6y = 14, and leave a blank space in place of the y. 5x + 6(_____) = 14. In that blank space, substitute the value y from the second equation, that is, 4x-17. 5x + 6(_____) = 14 5x + 6(4x-17) = 14 Now just solve for x. 5x + 24x - 102 = 14 29x - 102 = 14 29x - 102 + 102 = 14 + 102 29x = 116 Divide both sides by 29 x= 4. Now, the easiest place to find y is in the y=___ equation. y=4x- 17 y=4(4) - 17 y = -1 Check in the OTHER equation: 5x+ 6y = 14 5(4) + 6(-1) = 14 20 - 6 = 14 It checks!! R^2 at SCC