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# Recent problems solved by 'solver91311'

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 Polynomials-and-rational-expressions/273690: JACK USUALLY MOWS HIS LAWN IN 6 HOURS. MARYILYN CAN MOW THE SAME YARD IN 5 HOURS. HOW MUCH TIME WOULD IT TAKE THEM TO MOW THE LAWN TOGETHER?1 solutions Answer 199908 by solver91311(18785)   on 2010-02-24 11:27:45 (Show Source): You can put this solution on YOUR website! Why do you feel the need to shout? Typing in all caps is the electronic equivalent of shouting and is therefore both annoying and rude. If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John
 Equations/273700: I need help with the following problem, including the steps needed to get to the answer. Thanks so much!! Find the value of c to make a perfect square.1 solutions Answer 199904 by solver91311(18785)   on 2010-02-24 11:24:48 (Show Source): You can put this solution on YOUR website! In general, is a perfect square if and only if So divide -18 by 2 and square the result. John
 Polynomials-and-rational-expressions/273699: I need help with the following problem please, including the steps to get to the answer if needed... thanks!! Factor the polynomial . If the polynomial cannot be factored, write PRIME.1 solutions Answer 199901 by solver91311(18785)   on 2010-02-24 11:21:43 (Show Source): You can put this solution on YOUR website! In general, is not factorable over the reals, and I think that is what you mean here. Therefore your answer is PRIME. However, IS factorable over the complex numbers. Where is the imaginary number defined by John
 Equations/273697: Can you please help with the following problem including the steps!! Thanks!! to divide 7 over x+2 by x-2 over 14, you can multiply 7 over x+2 by:1 solutions Answer 199897 by solver91311(18785)   on 2010-02-24 11:15:38 (Show Source): You can put this solution on YOUR website! Just like any other fraction division problem -- invert and multiply. John
 Angles/273585: How does an angle complementary to an angle mesuring 27 degrees, look like?1 solutions Answer 199803 by solver91311(18785)   on 2010-02-24 01:32:58 (Show Source): You can put this solution on YOUR website! The sum of two complementary angles is 90 degrees. John
 Equations/273561: What is the proper method to solve 7x+10y=-13 3x-2y=71 solutions Answer 199795 by solver91311(18785)   on 2010-02-23 23:30:14 (Show Source): You can put this solution on YOUR website! There is no "proper" method to solve this system. You can use Substitution, Elimination, or Cramer's rule. All of these methods, properly performed, will lead to the correct solution set of this system. For my money, the elimination method seems like the quickest and easiest. Just multiply the 2nd equation by 5... John
 Numbers_Word_Problems/273557: Suppose that you square two consecutive whole numbers and subtract the smaller square from the larger. Is it possible that the difference is an even number?1 solutions Answer 199787 by solver91311(18785)   on 2010-02-23 23:05:36 (Show Source): You can put this solution on YOUR website! No Let represent the smaller of the two consecutive integers. Then represents the larger. Square the larger: Square the smaller: Subtract the smaller square from the larger: If is an integer, must be odd. John
 Complex_Numbers/273552: How do i solve z=4+3i?1 solutions Answer 199784 by solver91311(18785)   on 2010-02-23 22:53:16 (Show Source): You can put this solution on YOUR website! What's to solve? It is just a simple statement that is a complex number, specifically John
 Angles/273423: The question is about a supplementary angle. There is angle 1 and angle y. The question says"Represent angle 1 in terms of y." 1 solutions Answer 199768 by solver91311(18785)   on 2010-02-23 19:48:53 (Show Source): You can put this solution on YOUR website! Presuming angle 1 and angle y are supplementary, then John
 Linear-equations/273435: Given the piecewise function f(x)={(5x+1for3 ≤ x < 7, 3x-5 for7≤ x <10 determine f(9). 1 solutions Answer 199766 by solver91311(18785)   on 2010-02-23 19:46:30 (Show Source): You can put this solution on YOUR website! Since 9 is in the interval , You can do your own arithmetic. John
 Age_Word_Problems/273450: Jack's dad is 40 years old. Jack is 14 years old. How old will each of them be when his dad is twice as old as Jack1 solutions Answer 199764 by solver91311(18785)   on 2010-02-23 19:42:13 (Show Source): You can put this solution on YOUR website! Let represent the number of years between now and the time that Dad is twice as old as Jack, then: is the age Dad will be and is the age Jack will be and these two ages are related thus: Solve for and then add that amount to each of their ages. John
 Word_Problems_With_Coins/273447: Please can u answer all Thanks in advance 4. Joe Shmoe bought some $0.32 and$0.38 stamps. He bought 42 stamps in all, and paid $14.82 for them. How many stamps of each kind did he buy? 5. For a school play, 390 tickets valued at$2568 were sold. Some cost $5 and some cost$8. How many tickets of each kind were sold? 6. Romeo bought a mixture of $0.25,$0.50 and $0.75 Valentines. The number of$0.25 Valentines are 3 more than twice the number of $0.50 Valentines. The number of$0.75 Valentines was 1 less than the number of $0.50 ones. If he spent$5.25 all together, how many Valentines of each kind did he buy?1 solutions Answer 199758 by solver91311(18785)   on 2010-02-23 19:31:41 (Show Source): You can put this solution on YOUR website! No, I won't answer all. I'll show you how to do one of them, and the others are done in the same manner. Let represent the number of 32 cent stamps and let represent the number of 38 cent stamps. The value of all of the 32 cent stamps is then cents. Likewise, the value of all of the 38 cent stamps is cents. Since we know there are 42 stamps we can say: And since we know the value of all of the stamps is $14.82, which is to say 1482 cents, we can say: Solve the first equation for either of the variables: And then substitute: Now all you have to do is solve for . The value of follows directly. The other two problems are solved in the same way. Create an equation that describes the numbers of things and then an equation that describes the value of things. In the third problem, use for the 50 cent valentines. Then is the number of 25 cent valentines and is the number of 75 cent valentines. Don't forget to change$5.25 to 525 cents. John
 Travel_Word_Problems/273443: Joseph can finish a project in 10 hours and Aaron can do the same project in 8 hours. How long will it take to finish the project together? Thank you.1 solutions Answer 199757 by solver91311(18785)   on 2010-02-23 19:20:33 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John
 Graphs/273440: How do you solve a problem that asks for the equation in standard form, only giving you the following info : (4,2); m = -31 solutions Answer 199756 by solver91311(18785)   on 2010-02-23 19:16:22 (Show Source): You can put this solution on YOUR website! Use the point-slope form of the equation of a line: where are the coordinates of the given point and is the given slope So, for and Now all you have to do is put it into standard form by manipulating it to look like: John
 Angles/273428: If the sum of the measures of two angles is 90 degrees, the angles are complementary. if the measure of an angle is A degree, the measure of the complement is (90 - A degree). Find the angle whose measure is 3 greater than twice the measure of its complement.1 solutions Answer 199753 by solver91311(18785)   on 2010-02-23 19:10:01 (Show Source): You can put this solution on YOUR website! The measure of the angle: The measure of the complement: Twice the measure of the complement: Three greater: So: Just solve for A John
 Geometry_proofs/273408: how do you classify a shape as a sqaure,rectangle, rhombus,or parllelogram?1 solutions Answer 199748 by solver91311(18785)   on 2010-02-23 18:16:47 (Show Source): You can put this solution on YOUR website! A parallelogram is a quadrilateral (four-sided) polygon with two pairs of parallel sides. A rhombus is a parallelogram with all 4 sides of equal measure. A rectangle is a parallelogram with four vertices that are right angles. It is sufficient to prove that one vertex has a right angle because if it does, the other three have to be right angles as well. (In any parallelogram opposite angles are equal and adjacent angles are supplementary -- so if one angle is 90, the opposite is 90 and both adjacent angles are also 90 because 180 - 90 is 90.) A square is either a rectangle with all 4 sides of equal measure, or a rhombus with 4 vertices that are right angles. Again, proof of one right angle is sufficient. John
 Volume/273405: How many gallons do i need to fill a 5 foot by 6 foot space thats 6 inches tall1 solutions Answer 199746 by solver91311(18785)   on 2010-02-23 18:10:26 (Show Source): You can put this solution on YOUR website! A gallon of what? A US liquid gallon is 231 cubic inches or approximately 0.134 cubic feet. Which is to say approximately 7.48 gallons per cubic foot. So presuming you want to fill the space with liquid, your space having a volume of 5 times 6 times 0.5 = 15 cubic feet, you would need 15 times 7.48 which is approximately 112.2 gallons. If you are filling the space with dry (aka corn) gallons, 268.8025 cubic inches, or 6.43 gallons per cubic foot, you only need about 96.5 gallons -- give or take. John
 Polygons/273403: if two of the line segments of a polygon are parallel what is the least number of sides it could have1 solutions Answer 199738 by solver91311(18785)   on 2010-02-23 17:55:19 (Show Source): You can put this solution on YOUR website! The polygon with the least number of sides is a triangle. Since no triangle can have parallel sides, 3 is excluded as an answer. Rhombi and parallelograms, their special cases of squares and rectangles, and trapezoids are all quadrilaterals with at least one pair of parallel sides. Hence if two of the line segments of a polygon are parallel, the fewest number of sides is 4. John
 Parallelograms/273387: in parallelogram abcd, if angle A = 50 find angle C1 solutions Answer 199735 by solver91311(18785)   on 2010-02-23 17:48:07 (Show Source): You can put this solution on YOUR website! Opposite angles of a parallelogram are equal. Adjacent angles of a parallelogram are supplementary. John
 Percentage-and-ratio-word-problems/273377: if jane paints a house in 4 hours and john paints the same house in 6 hours how long will it take them both to paint the house?1 solutions Answer 199716 by solver91311(18785)   on 2010-02-23 17:08:33 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John
 Rectangles/273321: the length of a rectangle is twice as long as its width. Express the area of the rectangle as a function of its perimeter1 solutions Answer 199714 by solver91311(18785)   on 2010-02-23 17:01:10 (Show Source): You can put this solution on YOUR website! The first thing we know is that The next thing we know is that the perimeter of a rectangle is given by: Substituting we discover that: or The area of a rectangle is given by: Substituting: Check the answer for reasonability: Consider a 2' by 4' rectangle. The area is 8 ft². The perimeter is 2 times 4 plus 2 times 2 equals 8 plus 4 equals 12' Seems to work. John
 Polynomials-and-rational-expressions/273348: Hi. I'm trying to solve x^2-5x+6=0. Thank you.1 solutions Answer 199706 by solver91311(18785)   on 2010-02-23 16:22:30 (Show Source): You can put this solution on YOUR website! Let's start with a hint: Let me know if that does it for you or if you need more help. John
 Linear-equations/273307: Find an equation of the line having the given slope and containing the given point. m= -3,(4,8) The answer book gives the answer as -3x+20. I understand how they got the -3x because the question says the m=-3. The formula is y=mx+b. How did they get the +20? Can you show me how? Thank you jpa1 solutions Answer 199700 by solver91311(18785)   on 2010-02-23 16:03:56 (Show Source): You can put this solution on YOUR website! through (4, 8) Use the point-slope form of the equation of a line to derive the desired equation: where are the coordinates of the given point and is the slope of the given line. So: Simplification is left as an exercise for the student. John
 Rational-functions/273335: write an equation for each line through negative 2 and 1 and parallel to y= negative 3x plus 1 1 solutions Answer 199699 by solver91311(18785)   on 2010-02-23 15:57:01 (Show Source): You can put this solution on YOUR website! I think you want a line through (-2, 1) parallel to The slope of a line is the coefficient on when the equation is in slope-intercept form. Parallel lines have equal slopes. So use the point-slope form of the equation of a line to derive the desired equation: where are the coordinates of the given point and is the slope of the given line. So: Simplification is left as an exercise for the student. John
 Travel_Word_Problems/273339: what is the average speed of a vehicle that covers 250 miles in 2.5 hours1 solutions Answer 199697 by solver91311(18785)   on 2010-02-23 15:44:59 (Show Source): You can put this solution on YOUR website! Distance equals rate times time: Therefore rate equals distance divided by time: John
 Coordinate-system/273159: Find the value(s) of x so that the distance between the points A(3, 5) and B(x, 8) is 5 units. i have tried using the distance formula AB = (x2 – x1)2 + (y2 – y1)2 with a square root on all of the equation and substituting the values and working back using the balance method, but I got the wrong answer. the answer is 7 or -1. How can I solve this question?1 solutions Answer 199579 by solver91311(18785)   on 2010-02-23 01:47:59 (Show Source): You can put this solution on YOUR website! Square both sides: Simplify: Factor and solve the quadratic. Both roots are valid solutions. John
 Permutations/273156: In the United Kingdom's National Lottery you must correctly select a group of 6 numbers from 49. Suppose that the contest were changed to selecting 7 numbers. How many more ways would there be to select the numbers?1 solutions Answer 199578 by solver91311(18785)   on 2010-02-23 01:36:24 (Show Source): You can put this solution on YOUR website! John
 Inequalities/273161: Solve: (x-5)(x+3)<=0 Thanks!1 solutions Answer 199577 by solver91311(18785)   on 2010-02-23 01:31:06 (Show Source): You can put this solution on YOUR website! Critical points are at (0,5) and (1,-3). These two points separate the -axis into three regions. Select -values from each of the three regions that are not the critical point -values. Let Let Let So: On the interval [-3,5] John
 Complex_Numbers/273148: how do you write the problem 3i(2-3i) in a+bi form?1 solutions Answer 199568 by solver91311(18785)   on 2010-02-23 00:03:11 (Show Source): You can put this solution on YOUR website! Use the distributive property: Remember: John
 Permutations/273140: in many lotteries, contestants choose 6 out of 50 numbers, without replacement. find the probability of winning this kind of lottery with one set of numbers.1 solutions Answer 199565 by solver91311(18785)   on 2010-02-22 23:51:26 (Show Source): You can put this solution on YOUR website! The numerator of your probability fraction is 1 and the denominator is the number of ways to select 6 things from 50 things. The number of ways to select things from things, , is calculated by: For your problem: You can do your own arithmetic. John
 Linear-equations/273142: find the value of C such that each pair of points is 5 units apart (0,C) (3,1)1 solutions Answer 199564 by solver91311(18785)   on 2010-02-22 23:44:05 (Show Source): You can put this solution on YOUR website! Use the distance formula: Solve: For And the question is mis-stated. It should read: "Find the values of C..." John