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# Recent problems solved by 'rapaljer'

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 Miscellaneous_Word_Problems/15378: A rectangle has a perimeter of centimeters.The length of the rectangle is 11 centimeters longer than triple the width. Find the dimensions of the rectangle1 solutions Answer 7613 by rapaljer(4667)   on 2005-10-14 20:35:03 (Show Source): You can put this solution on YOUR website!Unless you give us the perimeter of the rectangle, we can't give you the dimensions. We just aren't quite THAT good!! R^2 at SCC
 Geometry_Word_Problems/15375: What are the dimensions of a cube if the volume is 1728 cubic in. and has a surface area of 888 square in.1 solutions Answer 7612 by rapaljer(4667)   on 2005-10-14 20:11:44 (Show Source): You can put this solution on YOUR website!If a cube has a volume of 1728 cubic inches, you don't need to know the surface area in order to find the dimensions of the cube. Let x = side of the cube. inches . As a check each side has area = 12*12 = 144. There are 6 sides, so total surface area is 864 square inches. It must NOT be a cube. Are you sure this is stated correctly? I don't see how it can be a CUBE. Someone correct me if I'm wrong!! R^2 at SCC
 Quadratic_Equations/14834: i have a worded problem that i cannot do. it goes like this: A triangles base is x cm and the height is 3cm shorter than the base if the area is 20 what is the value of x. I have worked out the answer but i dont know how to get to it. please help me1 solutions Answer 7611 by rapaljer(4667)   on 2005-10-14 20:01:10 (Show Source): You can put this solution on YOUR website!Let x = base of triangle x-3 = height of triangle Area = Multiply both sides by 2 to clear the fraction: Quadratic equation, so set equal to zero: x=8 base x-3= 5 height Reject x=-5, since the base of a triangle cannot be negative. R^2 at SCC
 Geometry_Word_Problems/15119: the supplement of an angle measures 25 degrees more than twice its complement. Find the measure of the angle. My work: 180-x= 2(90-x) 180-x= 180-2x 180+x=180 x=1 BUT, x is suppposed to be equal to 25 inthe answer key. Thank you. 1 solutions Answer 7610 by rapaljer(4667)   on 2005-10-14 19:48:03 (Show Source): You can put this solution on YOUR website!I would let x = the complement, since that is at the end of the first sentence. 2x + 25 = the supplement The equation is based upon the fact that if you subtract the supplement minus the complement, you get 90 degrees. 2x + 25 - x = 90 x + 25 = 90 x= 65 complement 90-x = 25 = the angle There may be easier ways to do this if we think about it, but at least this works to solve the problem. OH! I see it!! THE WAY YOU DID IT IS CORRECT!! YOU JUST FORGOT THE 25. Your equation: 180-x= 2(90-x) Should have been: 180-x= 2(90-x)+ 25 This works!! x= 25. R^2 at SCC
 Geometry_Word_Problems/15373: Consider an isosceles triangle ABC with lengths of AB=AC=1 and angle BAC =36 degrees. Find the length of BC. Hint: construct angle bisector of angle ABC>1 solutions Answer 7609 by rapaljer(4667)   on 2005-10-14 19:34:33 (Show Source): You can put this solution on YOUR website!The angle bisector of angle BAC is perpendicular to side BC, so it forms a right triangle with angle at point A of 18 degrees, and hypotenuse AB=1. Therefore, sin 18 = , where x = half of the side BC. Be sure your calculator is in degree mode and calculate sin 18 = .3090. Double this value to obtain BC = .618 approximately. R^2 at SCC
 Polygons/15311: Please help me to find a genral rule for calculating the sum of angles for any n- sided polygon... Help its homework and needed by Sunday the 16th of October Cheers, 1 solutions Answer 7600 by rapaljer(4667)   on 2005-10-14 08:15:38 (Show Source): You can put this solution on YOUR website!Start with a rectangle for an example, and draw a diagonal. Notice that you have a 4 sided figure, and there are 2 triangles, each with a sum of 180 degrees for a total of 2*180 = 360 degrees. Next, draw a pentagon, and from any given vertex, draw the two diagonals from that vertex to the other vertices. Notice that you have a 5 sided figure, with two diagonals. There are 3 triangles, each with sum of 180 degrees for a total of 3*180 = 540 degrees. Next, draw a hexagon, and from any given vertex, draw the three diagonals from that vertex to the other vertices. Notice that you have a 6 sided figure, with three diagonals. There are 4 triangles, each with sum of 180 degrees for a total of 4*180 = 720 degrees. Now, notice the pattern. If there are n sides, there will be two less triangles than sides, which is n-2 triangles, and the sum of the angles will be (n-2)* 180 degrees. The formula for the sum of the angles of a polygon with n sides is 180(n-2). R^2 at SCC
 Miscellaneous_Word_Problems/15313: janie has 3 different shirts, 3 different pairs of shoes, and 2 different skirts how many different outfits can janie make1 solutions Answer 7598 by rapaljer(4667)   on 2005-10-14 07:53:28 (Show Source): You can put this solution on YOUR website!By the fundamental counting principle, just multiply 3 times 3 times 2 = 18 different outfits. R^2 at SCC
 Percentage-and-ratio-word-problems/15312: what is the answer for 56 1/2:7 2/31 solutions Answer 7596 by rapaljer(4667)   on 2005-10-14 07:51:15 (Show Source): You can put this solution on YOUR website!Change both mixed fractions to improper fractions: 56 1/2:7 2/3 (2*56 +1)/2 : (3*7 +2)/3 113/2 : 23/3 The ratio of two numbers can be written as a division problem: 113/2 divided by 23/3 113/2 * 3/23 Nothing divides out or reduces, so multiply numerators and denominators: 339/46 R^2 at SCC
 Angles/13168: what is the answer to 87degrres? 1 solutions Answer 7588 by rapaljer(4667)   on 2005-10-13 23:54:57 (Show Source): You can put this solution on YOUR website!Turn on the air conditioner!
 Angles/15300: IF TWO ANGLES OF A TRIANGLE MEASURE 30 AND 70 DEGREES WHAT IS THE NUMBER OF DEGREES OF THE THIRD ANGLE OF THE TRIANGEL?1 solutions Answer 7587 by rapaljer(4667)   on 2005-10-13 23:51:19 (Show Source): You can put this solution on YOUR website!The sum of the three angles of the triangle must be 180 degrees. If two of the angles are 30 and 70 (which adds up to 100 degrees), what would you have to add to 100 degrees to get 180 degrees? You can probably figure this out in your head, right? Did you get 80 degrees? Does it check? Does it all add up to 180 degrees? R^2 at SCC
 Complex_Numbers/15302: (a) -8+i (b) 5+5i1 solutions Answer 7586 by rapaljer(4667)   on 2005-10-13 23:47:43 (Show Source): You can put this solution on YOUR website!And what would you like to do with these complex numbers??? R^2 at SCC
 Mixture_Word_Problems/15293: How many liters of antifreeze must be added to 5 liters of water to make no less than a 60% solution and no more than an 80% solution?1 solutions Answer 7585 by rapaljer(4667)   on 2005-10-13 23:32:18 (Show Source): You can put this solution on YOUR website!x = amount of antifreeze at 100% 5 = amount of water at 0% x+5 = total mixture at 60% or 80% x = .6(x+5) x = .6x + 3.0 x - .6x = 3.0 1.0x - .6x = 3.0 .4x = 3.0 x = 3.0/.4 = 30/4 = 7.5 liters for the minimum of 60% x = .8(x+5) x = .8x + 4.0 x - .8x = 4.0 1.0x - .8x = 4.0 .2x = 4.0 x = 4.0/.2 = 40/2 = 20 liters for the maximum of 80% In other words, you should use between 7.5 and 20 liters (inclusive!) of antifreeze. R^2 at SCC
 Angles/15284: The sum of the measures of two angles is 120 degrees .If the measure of one of the angles is five times that of the other ,which statment is true 1-- the angles are supplementary 2-- the angles are complementary 3-- both angles are acute 4-- one angle is an acute angle and the other is an obtuse angle1 solutions Answer 7584 by rapaljer(4667)   on 2005-10-13 23:20:53 (Show Source): You can put this solution on YOUR website!Let x = smaller angle 5x = larger angle x + 5x = 120 6x = 120 x= 20 degrees -- smaller angle 5x = 100 degrees -- larger angle Now consider the choices. 1. They are NOT supplementary since they do not add up to 180 degrees. 2. They are NOT complementary since they do not add up to 90 degrees. 3. They are NOT both acute since the larger angle is larger than 90 degrees. 4. One angle is acute and the other is obtuse. This is true. R^2 at SCC
 Coordinate-system/15290: a line passes through a(1,-3) and b(2,7) write the equation of a line perpendicular to a. how would you go about solving this problem? 1 solutions Answer 7583 by rapaljer(4667)   on 2005-10-13 23:14:25 (Show Source): You can put this solution on YOUR website!First find the slope of the given line: The slope of a line perpendicular to this line is tne negative reciprocal of the slope of this line. So, the slope of a line perpendicular to this line has a slope of . The equation of a line that is perpendicular to the line between these two points will be in the form where b is the y-intercept of the line. Notice that there are many, many (in fact, infinitely many) lines that are perpendicular to this line segment, and to determine which particular line you are looking for, more information must be given in the problem. Final answer, . R^2 at SCC
 Mixture_Word_Problems/15294: If a plumber charges \$110 for 3 hours and \$160 for 5 hours. In keeping this rate how much will he charge for 8 hours?1 solutions Answer 7582 by rapaljer(4667)   on 2005-10-13 23:03:50 (Show Source): You can put this solution on YOUR website!It would appear that the plumber charges \$50 for the additional two hours from 3 hours to 5 hours, which is \$25 per additional hour. At this rate, for an additional 3 hours, he/she would be charging an additional \$75, added to the \$160, for a total of \$235. R^2 at SCC
 Angles/15288: two angles are supplementary and congruent. how many degrees are in the measure of each angle?1 solutions Answer 7581 by rapaljer(4667)   on 2005-10-13 22:01:58 (Show Source): You can put this solution on YOUR website!If two angles are congruent, then that means the measure of the angles is the same. If they are supplementary, then they add up to 180 degrees. So, x+ x = 180 2x = 180 x= 90 degrees. R^2 at SCC
 Distributive-associative-commutative-properties/15291: angle a is 4 times as large as angle b and angle c is 20 degrees less than angle b...what does each angle equal?1 solutions Answer 7580 by rapaljer(4667)   on 2005-10-13 21:58:07 (Show Source): You can put this solution on YOUR website!Since angle a is given in terms of angle b and angle c is given in terms of angle b, everything is in terms of angle b, so let x = angle b. Let x = angle b 4x = angle a x-20 = angle c The sum of the angles is 180 degrees. x + 4x + x - 20 = 180 6x - 20 = 180 6x = 200 {Note: Answer doesn't come out even, but then that's life sometimes!) x= 200/6 = 100/3 = 33 1/3 degrees -- angle b 4x = 400/3 = 133 1/3 degrees -- angle a x-20 = 33 1/3 - 20 = 13 1/3 degress -- angle c Check: 33 1/3 + 133 1/3 + 13 1/3 = 180 degrees It checks! R^2 at SCC Check:
 Functions/15292: f(x)=ax+b b(b(b(x)))=8x+21 how do I solve?1 solutions Answer 7578 by rapaljer(4667)   on 2005-10-13 21:51:16 (Show Source): You can put this solution on YOUR website!Where did you get this one?? Do you by any chance mean f(f(f(x))) = 8x + 21? This would be a very interesting problem. If it is, please re-post it, or send me an Email. I'm not sure what you mean by b(b(b(x))). R^2 at SCC
 absolute-value/15279: How could i figure this out? - 4( | 5 - 12 | ) = 1 solutions Answer 7577 by rapaljer(4667)   on 2005-10-13 20:57:15 (Show Source): You can put this solution on YOUR website!This looks like an absolute value problem (although it does look strangely like the previous problem that I posted a solution for!). This is the product of -4 times the result of taking the absolute value of 5-12. First take the 5-12 which is -7. Next take the absolute value of -7, which would be 7. Last step, take -4 times 7, and you have a final answer -28. The moral here is to be REALLY careful in writing your math problems, because sometimes a minor difference or sloppiness in writing the problem can end up with a completely different result!! R^2 at SCC
 absolute-value/15278: How could i figure this out? - 4( l 5 - 12 l ) = 1 solutions Answer 7576 by rapaljer(4667)   on 2005-10-13 20:52:55 (Show Source): You can put this solution on YOUR website!This looks like a -4 multiplied by the difference (15-121). Am I reading this right? So take 15-121 which is -106, and multiply this times -4. Remember that a negative times a negative is a positive. The final answer is 424. R^2 at SCC
 Equations/15275: MR.SELL BOUGHT THREE DOGHNUTS AND A 44-OUNCE THERMAL CUP OF COFFE ONHIS WAY TO SCHOOL. IF THE COFFE COST WAS \$1.95 AND THE TOTAL OF HIS PURCHASE [BEFOERE TAX] WAS \$3.60, HOW MUCH DID EACH DOUGHNUT COST?1 solutions Answer 7575 by rapaljer(4667)   on 2005-10-13 20:49:13 (Show Source): You can put this solution on YOUR website!Let x = cost of each doughnut 3x + 1.95 = 3.60 3x + 1.95-1.95 = 3.60-1.95 3x =1.65 Divide by 3 x = \$.55 R^2 at SCC
 Angles/15274: two angles are complementary.The mesure of one angle is twice the mesure of the other angle. what is the smaller of the two angles?1 solutions Answer 7573 by rapaljer(4667)   on 2005-10-13 20:45:04 (Show Source): You can put this solution on YOUR website!Let x = smaller angle 2x = larger angle Sum of the angles = 90 degrees x+ 2x = 90 3x = 90 x= 30 degrees -- smaller angle 2x = 60 degrees -- larger angle Sum of the angles 30 + 60 = 90 It checks! R^2 at SCC
 Linear_Algebra/15263: Sarah is visting a friend about two miles away from her house. she sees a hot-air balloon directly above her house. Sara estimates that the angel of elevation formed by the hot-air balloon is about 15 degrees. about how high is the hot-air balloon? 1 solutions Answer 7572 by rapaljer(4667)   on 2005-10-13 20:41:30 (Show Source): You can put this solution on YOUR website!This figure is a right triangle with the balloon at a height of x miles above Sara's house. The base of the triangle represents the distance from Sara's house to where Sara is at her friend's house. The angle from Sara's friend's house to the balloon is 15 degrees, so trigonometry is required. tan 15 = x/2 Multiply both sides by 2: 2 tan 15 = x Are calculators allowed here? Be sure you are in degree mode! x = 2 tan 15 = .535898 . . . In case you want that in feet, multiply by 5280 (don't round it off until AFTER you do the calculation!!) about 2830 feet. R^2 at SCC
 real-numbers/15273: how many integers between 10 and 100 have exactly one digit equal to 31 solutions Answer 7570 by rapaljer(4667)   on 2005-10-13 20:29:45 (Show Source): You can put this solution on YOUR website!Let's count them: First the units digit equal to 3: 13, 23, (NOT 33 since it has two digits equal to 3), 43, 53, 63, 73, 83, 93 Next, the ten's digit equal to 3: 30, 31, 32, 34, 35, 36, 37, 38, 39 Total equals 8 + 9 = 17 R^2 at SCC
 Angles/15271: the mesures of two complementary angles are represented by x+5 and 4x-15 find the value of x1 solutions Answer 7568 by rapaljer(4667)   on 2005-10-13 20:25:28 (Show Source): You can put this solution on YOUR website!Complementary angles means that the sum of the angles equals 90 degrees. x+5 + 4x -15 = 90 5x -10 = 90 5x - 10 + 10 = 90 + 10 5x = 100 x= 20 degrees-- Final answer! However, as a check, let's find the two angles and see if they add up to 90 degrees. x+5 = 25 degrees 4x-15= 80-15 = 65 degrees 25 + 65 = 90 It checks! R^2 at SCC
 Mixture_Word_Problems/15270: Bob has twice as much money as Anthony. Anthony has \$7 more than Lisa. Together they have \$73. How much does each have? 1 solutions Answer 7567 by rapaljer(4667)   on 2005-10-13 20:21:21 (Show Source): You can put this solution on YOUR website!First, notice that Bob's money is given in terms of Anthony, and Anthony's money is given in terms of Lisa. So, let x = the quantity at the end of all of this, which is Lisa. Let x = amount of money of Lisa x+ 7 = amount of money of Anthony 2(x+7) = amount of money of Bob The equation is that the sum of all these amounts = 73 x + x+7 + 2(x+7) = 73 x + x + 7 + 2x + 14 = 73 4x + 21 = 73 4x + 21 - 21 = 73 -21 4x = 52 x= \$13 Lisa x+ 7 = \$20 Anthony 2(x+7) = \$40 Bob Check: 13+20 + 40 = 73 It checks! R^2 at SCC
 Proportions/15267: HOW TO SOLVE THE RATIO OF 2 TO 5=(?)%1 solutions Answer 7566 by rapaljer(4667)   on 2005-10-13 20:15:20 (Show Source): You can put this solution on YOUR website!Express the fraction 2/5 as a decimal by dividing 5 into 2.00 (you get .40), and then convert the decimal to a percent, by moving the decimal two places to the right. This means that .40 = 40%. Another way to do this particular problem is to start with the fraction 2/5 and multiply the numerator and denominator by 2. This gives the very special fraction 4/10, which as a decimal would be .4 or .40. Then convert to a percent as above .40 = 40%. R^2 at SCC
 Linear-equations/15268: I have a question concerning functions. How would you go about solving this problem: f(f(2)) and f(2f(1))1 solutions Answer 7564 by rapaljer(4667)   on 2005-10-13 20:10:43 (Show Source): You can put this solution on YOUR website!You need more information for this problem. What is f(x)? There must be a formula that you forgot to give us. R^2 at SCC
 Angles/15255: if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle1 solutions Answer 7563 by rapaljer(4667)   on 2005-10-13 20:08:46 (Show Source): You can put this solution on YOUR website!If two angles are complmentary, then the sum of those angles is 90 degrees. Since the sum of all three angles must be 180 degrees, the third angle must be 180-90 = 90 degrees. R62 at SCC
 Quadratic_Equations/15139: the length of a rectangle is 3cm.greater than its width. its area is 70sq.cm, find itsdimension1 solutions Answer 7544 by rapaljer(4667)   on 2005-10-13 16:25:40 (Show Source): You can put this solution on YOUR website!Let x = width of the rectangle x+3 = length of the rectangle Area = L*W x(x+3)= 70 x=-10 Reject, since width of a rectangle can't be negative x= 7 cm Width x+ 3 = 10 cm Length Check: Area= 7*10= 70 sq.cm. R^2 at SCC
 Graphs/15185: I am having problems graphing inequalitys on a plane. I never know which side to shade. I just don't understand this concept.1 solutions Answer 7543 by rapaljer(4667)   on 2005-10-13 16:15:19 (Show Source): You can put this solution on YOUR website!The rule that I use is not the way most people teaching math use, but I like it. Whenever you have an equation with a POSITIVE coefficient of y > or >= , you must shade ABOVE the line. POSITIVE coefficient of y < or <= , you must shade BELOW the line. That's as simple as it gets! Examples: 2x+3y < 6 Shade Below 2x+3y > 6 Shade Above 2x+3y >= 6 Shade Above 2x+3y <= 6 Shade Below So, what if you have a NEGATIVE COEFFICIENT of Y? Well, if you multiply both sides of an inequality by a negative, this reverses the inequality, and therefore it REVERSES the RULE!! 2x - 3y < 6 same as -2x+3y> -6 Shade Above!! See if that helps. If you need more, I might be able to send you a section from my book in a word file. R^2 at SCC