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Numbers_Word_Problems/498392: One number is four times another number. the larger number is also 87 more than the smaller number. what are the numbers? 1 solutions Answer 337018 by solver91311(16868)   on 2011-09-15 16:30:41 (Show Source): You can put this solution on YOUR website! Let represent the smaller number. Then: Solve for , then calculate John My calculator said it, I believe it, that settles it

real-numbers/497707: can you name the subsets of the real numbers to which each number belongs? 3/4 -8 45,368 -2/3 1 solutions Answer 336834 by solver91311(16868)   on 2011-09-14 16:57:25 (Show Source): You can put this solution on YOUR website! If a number cannot be represented by the quotient of two integers, then the number is Irrational. The number isn't insane, but it cannot be represented as a ratio. If a number can be represented by the ratio of two integers, the number is Rational. The positive and negative whole numbers are the Integers. Non-negative whole numbers are the Natural numbers. (Actually, there are varying opinions on the exact definition of the set of Whole Numbers and the set of Natural numbers. Whole Numbers could mean Natural Numbers in the sense of positive integers, i.e. . Or Whole Numbers could mean Natural Numbers in the sense of non-negative integers, i.e. . Or Whole Numbers could be used to mean the entire set of Integers, i.e. ) Note that Natural numbers are a proper subset of the Integers which, in turn, is a proper subset of the Rationals. 45,368 is Natural, Whole, Integer, AND Rational. -8 is Whole (maybe), Integer, and Rational All fractions and explicitly stated decimals, even those that repeat forever, are Rational. Everything else is Irational. Any number that is the root of a non-zero polynomial function with rational coefficients is an Algebraic number. Any other number is a Trancendental number. Only one of the numbers in your list is Trancendental. Can you find it? John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/497705: How do you find the center of a rectangle garden, without using any measurements? 1 solutions Answer 336810 by solver91311(16868)   on 2011-09-14 15:36:50 (Show Source): You can put this solution on YOUR website! Drive a stake into the ground at one corner. Tie a string to the stake. Go to the diagonally opposite corner and drive another stake into the ground. Tie the other end of your string to the second stake, making the string nice and taut. Repeat the process for the other two corners of your rectangle. The point where the two strings cross is the center. John My calculator said it, I believe it, that settles it

Linear-equations/497697: Find the equation of the line described. Write the equation in slope-intercept form. (-5,3) (5,-3) The equation of the line is 1 solutions Answer 336808 by solver91311(16868)   on 2011-09-14 15:32:03 (Show Source): You can put this solution on YOUR website! Use the two-point form of an equation of a line. where and are the coordinates of the given points. Once you have substituted values and done the indicated arithmetic, solve for . That is to say arrange your equation into (Slope-Intercept) form. John My calculator said it, I believe it, that settles it

Linear-equations/497694: Perpendicular to x=1 through the point (1,3) 1 solutions Answer 336805 by solver91311(16868)   on 2011-09-14 15:24:07 (Show Source): You can put this solution on YOUR website! The equation represents a vertical line consisting of all ordered pairs where the coordinate is equal to 1. A line perpendicular to a vertical line is a horizontal line. Horizontal lines have the characteristic that the coordinates of every ordered pair contained in the set of ordered pairs that is the vertical line are identical. Since the desired perpendicular must pass through the point , that coordinate must be 3. John My calculator said it, I believe it, that settles it

Probability-and-statistics/497681: 16 marbles total/ 2green and 3 whites. if one is drawn it is not repalce. what is the probability of this. thanks 1 solutions Answer 336801 by solver91311(16868)   on 2011-09-14 15:17:51 (Show Source): You can put this solution on YOUR website! You have described a collection of marbles that total 16. Then you say 2 green and 3 white. If you mean that 2 of the 16 marbles are green, 3 of them are white, and 11 of them are some other color, then what is the without replacement draw for which you want to calculate the probability? On the other hand, if you want the probability of drawing 2 green and 3 white from a collection of 16 without replacement, then you need to describe the numbers of the various colors that make up the 16 in the container. And do take the time to proofread your post before sending it. We only have the written word with which to communicate, hence the niceties of spelling, grammar, and punctuation are essential for this system to work. John My calculator said it, I believe it, that settles it

Quadratic_Equations/497684: give exact and approximate solutions to three decimal places. x^2+16x+64=4 what are the exact solutions? x= Thank You For Your Time 1 solutions Answer 336798 by solver91311(16868)   on 2011-09-14 15:08:55 (Show Source): You can put this solution on YOUR website! Add -4 to both sides Factor. Hint: 6 times 10 = 60 and 6 plus 10 = 16. Apply the Zero Product Rule to find the two solutions. Since the quadratic factors over the rationals, the roots are rational and exact. That is, there is no need for a numerical approximation for a solution set element that can be represented exactly numerically. John My calculator said it, I believe it, that settles it

Rational-functions/497679: the width of a retangle is 1ft less than the length, the area is 30ft^2. find the length and the width. the width is: the length is: 1 solutions Answer 336793 by solver91311(16868)   on 2011-09-14 15:00:47 (Show Source): You can put this solution on YOUR website! Just off the top of my head, I would guess 5 feet by 6 feet. But let's check on my intuition. Let represent the width. Then must represent the length. And since the area is 30 square feet: Solve the quadratic for , then calculate . Was my guess correct? Extra Credit. Solve the same problem using to represent the length and to represent the width. John My calculator said it, I believe it, that settles it

Equations/497680: the sum of two times a number and 5 is 11 1 solutions Answer 336791 by solver91311(16868)   on 2011-09-14 14:53:48 (Show Source): You can put this solution on YOUR website! I wouldn't plan on making any money off of that truly delightful and fascinating tidbit of information. What exactly is your question? You do realize, do you not, that this is Algebra.com and NOT the Psychic Hot Line? John My calculator said it, I believe it, that settles it

Square-cubic-other-roots/497614: I need help solving this problem please! An aquarium has a volume of 1320 in. cubed. The aquarium has a height of 20 in. and a length of 5 more in. than the base. Find the length and base of the aquarium. Thank you(: 1 solutions Answer 336767 by solver91311(16868)   on 2011-09-14 12:54:36 (Show Source): You can put this solution on YOUR website! Divide 1320 by the given height. That will give you the area of the base. You misused "base" since that would refer to the entire rectangle that has a length and a width. I'm going to presume that you meant length is 5 inches longer than the width. Let represent the width. Then represents the length. And let represent the area you calculated in the first step. Then: Simplify and solve the resulting quadratic for , then calculate . Hint: The quadratic is factorable: -6 times 11 is -66. John My calculator said it, I believe it, that settles it

Triangles/497613: If two sides of a triangle measure 30 and 60, which of the following cannot be the measure of the third side? 1 solutions Answer 336766 by solver91311(16868)   on 2011-09-14 12:47:13 (Show Source): You can put this solution on YOUR website! Impossible to tell since you didn't provide "the following." This is Algebra.com, not the Psychic Hot Line. However, this is probably a Triangle Inequality problem, so if one of your answers is a number larger than the sum of the measures of the two given sides, that's the one you want. John My calculator said it, I believe it, that settles it

Circles/497609: The distance around a circular park is 2.4 mi. How many acres does it contain? One square mile contains 640 acres 1 solutions Answer 336764 by solver91311(16868)   on 2011-09-14 12:43:58 (Show Source): You can put this solution on YOUR website! The area of a circle is given by: The radius of a circle given the circumference is: Combining these facts: Which simplifies to: Plug in your value for the circumference (the "distance around") and do the arithmetic to get the area in square miles. Multiply the area in square miles by 640 acres per square mile. Round to the nearest 10th because your given measurement was to the nearest tenth. John My calculator said it, I believe it, that settles it

Rate-of-work-word-problems/497605: 1) working together , it takes 2 roofers 4 hours to put a new roof on. If the first roofer can do the job by himself in 6 hours. how many hours will it take to the second roofer to do the job by himself? 2) With both cold water and hot ater faucets open, it takes 9 mins t ofill a bathtub. How long will it take to fill the tub with just the hot water faucet? 3) A bus leaves Valdosta, Georgia at 10 am travelling norht on 1-75 at an average rate of 63 miles per hour. At the same time a car leaves Valdosta, travelling south on i-75 at an average rate of 72 miles per hour. At what time will they be at 675 miles apart? 4) Rapid City is 360 miles from Sioux Falls. At 6 am freight train leaves Rapid City for Sioux Falls and at the same time a passenger train leaves Sioux Falls for Rapid City. The 2 trains meet at 9am if the freight train travels 3/5 of the speed of the passenget train how fast does the passenger train travels? 5) Jack Leaves his home in Atlanta, travellilng north on i-75 at an average rate of 45 miles per hour. 2 hours later his wife Frances leaves home and takes the same route travelling at an average rate of 60 miles pr hour HOw long will it take Frances to catch Jack? 1 solutions Answer 336763 by solver91311(16868)   on 2011-09-14 12:30:33 (Show Source): You can put this solution on YOUR website! Where did you get the idea that you could drop your whole homework assignment in here and then just walk off expecting someone to do your work for you? Not happening. 1. One question per post. 2. Show the work you have done so far. 3. Describe the difficulty you are having. 4. The more work you do first, the more help you are going to get. The limiting position on the other end is zero. John My calculator said it, I believe it, that settles it

Distributive-associative-commutative-properties/497603: What is -9(y-9) rewritten in distributive property? 1 solutions Answer 336761 by solver91311(16868)   on 2011-09-14 12:22:06 (Show Source): You can put this solution on YOUR website! The distributive property is: For your problem: You can do your own arithmetic. John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/497602: The difference between the two numbers is a whole number less than 2? 1 solutions Answer 336760 by solver91311(16868)   on 2011-09-14 12:15:39 (Show Source): You can put this solution on YOUR website! I wouldn't plan on making any money off of that truly delightful and fascinating tidbit of information. What did you want to do with it? I saw the question mark, but what exactly is your question? You do realize, do you not, that is is Algebra.com -- it is NOT the Psychic Hot Line. John My calculator said it, I believe it, that settles it

Linear-equations/497269: How do I solve these equations? Can you please explain the steps. 1/2(x+4) = 1/3 (3x-6) and 5/2 X = -10 for the first one I don't understand the end when the steps show it going back into parentheses 1 solutions Answer 336702 by solver91311(16868)   on 2011-09-13 21:39:13 (Show Source): You can put this solution on YOUR website! Let's start by getting rid of those pesky fractions. Notice that we have a denominator of 2 on one side and a denominator of 3 on the other side. 2 times 3 is 6, so let's multiply the whole schmierkδse by 6. Now use the distributive property to get rid of the parentheses: Add -6x to both sides: Add -12 to both sides: Multiply both sides by One problem per post. John My calculator said it, I believe it, that settles it

Linear-equations/497259: in slope intercept form write an equation for a line that is perpendicular to the line and passes through the point y=3x-7;(0,4) 1 solutions Answer 336699 by solver91311(16868)   on 2011-09-13 21:28:50 (Show Source): You can put this solution on YOUR website! Step 1: Determine the slope of the line described by the given equation. Since the given equation is in slope intercept form, the slope of the line described by that equation is the coefficient on . Step 2: Determine the slope of the desired line. The slopes of perpendicular lines are negative reciprocals. That is: Hence, calculate the negative reciprocal of the slope value determined in step 1. Step 3: Use the point-slope form of an equation of a line: where are the coordinates of the given point and is the calculated slope from step 2. Step 4: Rearrange your result in to slope-intercept from, namely: John My calculator said it, I believe it, that settles it

Trigonometry-basics/497224: find all values of x when x is greater than or equal to 0 degrees and less than 360 degrees. tan^2x+3secx+3=0 1 solutions Answer 336696 by solver91311(16868)   on 2011-09-13 21:11:03 (Show Source): You can put this solution on YOUR website! Multiply by Substitute from the Pythagorean Identity: Collect terms: Let and substitute: Factor: Substitute back: or Use the Unit Circle: to determine that: or or If you want it in degrees you can multiply by John My calculator said it, I believe it, that settles it

Angles/497223: I have two parallel lines with a transversal running through it. At the top (the lines are horizontal and the transversal is vertical) i have to find the measure of an angle coming of the top parallel line. The information i have to find it is that it equals 4x-30. How should i do this?? 1 solutions Answer 336692 by solver91311(16868)   on 2011-09-13 20:53:32 (Show Source): You can put this solution on YOUR website! Either you didn't give all of the information that is on the diagram, or this problem cannot be solved. However, you can use these facts: Vertical angles are equal. Opposite exterior and opposite interior angles are equal. The sum of supplementary angles is 180. John My calculator said it, I believe it, that settles it

Equations/497175: |4x+9|+3=11 Need to know the correct steps. Thank You 1 solutions Answer 336688 by solver91311(16868)   on 2011-09-13 20:43:59 (Show Source): You can put this solution on YOUR website! Solve for to get the first element of the solution set. Solve for to get the second element of the solution set. John My calculator said it, I believe it, that settles it

Polygons/497188: Find the number of sides in a polygon whose sum of the interior angles is 1440. 1 solutions Answer 336682 by solver91311(16868)   on 2011-09-13 20:23:02 (Show Source): You can put this solution on YOUR website! Divide by 180 and add 3. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/497161: A stained - glass window is being designed in the shape of a rectangle surmounted by a semicircle, as shown in the figure. The width of the window is to be 3 feet, but the height h is yet to be determined. If 4 ft2 of glass is to be used, find the height h. (Round your answer to the nearest hundredth.) 1 solutions Answer 336678 by solver91311(16868)   on 2011-09-13 20:15:47 (Show Source): You can put this solution on YOUR website! If you mean that the overall area of both the rectangle and the surmounting semi-circle is supposed to be 4 ft², then this is mighty weird looking stained glass window. Since you didn't provide a dimension for the diameter of the semicircle, I have to assume that it is the same as the width of the rectangle. I'm also assuming that is the missing dimension of the rectangle since it cannot possibly be the overall height of the window. The area of a semicircle with a diameter of 3 feet and therefore a radius of 1.5 feet is . That means only of the given area remains for the rectangle. Divided by 3, that leaves a height of less than feet for the rectangle part of the window -- not even 2 inches. Standing back, you probably wouldn't notice that there was a rectanglual part of the window. John My calculator said it, I believe it, that settles it

Complex_Numbers/497133: Solve the equation by completing the square. 4x2 − 16x + 13 = 0 what i got: -1 plus/minus square root -3 /2 I'm having trouble finalizing my answer. Thank you. Your help is appreciated ! 1 solutions Answer 336671 by solver91311(16868)   on 2011-09-13 19:51:56 (Show Source): You can put this solution on YOUR website! Let's follow the process and maybe you can figure out where you went astray. Step 1: Constant term to the RHS: Step 2: Divide by the lead coefficient: Step 3: Divide the 1st degree term coefficient by 2. Add the square of that result to both sides: -4 divided by 2 is -2. -2 squared is 4. Add 4 to both sides: Step 4: Factor the perfect square trinomial in the LHS and do the arithmetic in the RHS: Step 5: Take the root of both sides: Step 6: Add the opposite of the LHS constant to both sides: Which you could render, if you were so inclined: John My calculator said it, I believe it, that settles it

Trigonometry-basics/497100: Find the exact value of each of the remaining trigonometric functions of theta. Costheata=-12/13, theta in quadrant 2. Sin theta= Tan theta= Cot theta= Secant theta= Cosecant theta= Please help?? 1 solutions Answer 336660 by solver91311(16868)   on 2011-09-13 19:32:59 (Show Source): You can put this solution on YOUR website! If then . Since we know , we can determine that and therefore , taking the positive side because sin is positive in QII, we have From there, the rest are easy: , , , and John My calculator said it, I believe it, that settles it

Percentage-and-ratio-word-problems/497088: I have tried setting this word problem into a table a few different ways, just not sure I am doing it right... A landscaper needs to mix a 75% pesticide solution with 30 gallons of a 25% pesticide solution to obtain a 60% pesticide solution. How many gallons of the 75% solution must be used? I got 31.5 gallons? Can that be right? Thank you! 1 solutions Answer 336649 by solver91311(16868)   on 2011-09-13 19:14:56 (Show Source): You can put this solution on YOUR website! Can it be right? Well, let's see: Your claim is that you need to mix 31.5 gallons of 75% solution with 30 gallons of 25% solution to make 61.5 gallons of 60%. And the answer to the question you posed is a big resounding NO. Now, for the treasure map to the answer to the real question: Let represent the amout of 75% solution, then the resulting amount of 60% solution must be plus the 30 gallons of 25% solution. Therefore: Solve for . John My calculator said it, I believe it, that settles it

Length-and-distance/497081: The midpoint of UV is (5,-11) The coordinate of one endpoint are U(3,5) Find the coordinate of endpoint V. Please explain 1 solutions Answer 336647 by solver91311(16868)   on 2011-09-13 19:01:34 (Show Source): You can put this solution on YOUR website! Use the midpoint formulas. and Substitute the given coordinates for and (presuming the midpoint is labeled M for lack of a better guess), . Then solve for and John My calculator said it, I believe it, that settles it

Linear_Algebra/497082: x square divided by 4-x 1 solutions Answer 336646 by solver91311(16868)   on 2011-09-13 18:57:41 (Show Source): You can put this solution on YOUR website! What about it? Is there a question here in our immediate future? Or were we just supposed to guess what you want? John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/497061: I really need help with this as fast as possible thanks alot! What are all the possible rational zeros for f(x) = x3 + 8x + 6? ±1, ±6 ±1, ±2, ±6 ±1, ±2, ±3, ±6 ±1, ±2, ±3, ±6, ±12 What are all the possible rational zeros for f(x) = 6x3 + 6x2 – 15x – 2? ±1, ±2, ±1/2, ±1/3, ±2/3, ±1/6 ±1, ±2, ±1/3, ±2/3 ±1, ±2, ±3 ±1, ±2, ±3, ±6 Identify all the rational zeros for f(x) = x3 + 4x2 – 3x – 18. 1, –3, –6 –1, 2, –9 2, –3, –3 –1, –3, 6 Identify all the rational zeros for f(x) = x3 – x2 – 8x + 12. 2, 2, –3 2, –2, 3 –1, 3, 4 1, –3, 4 Identify all the rational zeros for f(x) = x3 + 4x2 – 2x + 15. 1 3 –5 1, 3, –5 How many positive real zeros does the function f(x) = x4 + x3 – 7x – 1 have? 3 or 1 1 2 or 0 0 How many negative real zeros does the function f(x) = x5 + x4 – x2 – x + 1 have? 4, 2, or 0 3 2 or 0 3 or 1 How many imaginary zeros does the function f(x) = 3x4 + 2x3 + 4x + 7 have? 0 2 or 0 4 or 2 4, 2, or 0 Identify the real zeros for the function f(x) = x3 – 3x2 – 53x – 9. 1, –3, –3 –1, 1, 9 Identify the real zeros to the nearest tenth for the function f(x) = x3 – 6x – 9. 3.0 –0.6, 1.4 .8, 2.0 –1.2, .4, 3.0 Identify all zeros for the function f(x) = x3 – 6x2 + 10x – 8. 1, 2, 4 2, 2, 4 4, 1 + i, 1 – i 4, 2 + i, 2 – i 1 solutions Answer 336645 by solver91311(16868)   on 2011-09-13 18:55:00 (Show Source): You can put this solution on YOUR website! Re-read the instructions for posting on this site, especially the instruction that says "One question per post." What is NOT going to happen is for someone to do your whole homework assignment, or worse, your test, for you. Here are a couple of rules to help you though. Rational zeros of a polynomial function, if they exist, must be of the form where is an integer factor of the constant term and is an integer factor of the lead coefficient. A polynomial function of degree has exactly zeros, some of which may be complex. Complex zeros ALWAYS show up as conjugate pairs, that is, if is a zero, then must also be a zero. A corollary to the above is that polynomial functions of odd degree must have at least one real zero. Using the first rule I gave you, you can use either polynomial long division or synthetic division to determine if a potential rational zero is actually a zero of the given polynomial. The quotient of a successful division that identifies a zero can be couched as a lesser degree polynomial funcition. Continue the process until you cannot find any more rational roots or you end up with a quadratic quotient that you can solve with the quadratic formula. In fact, if you get down to a quartic or a cubic, there are general formulas for these too, but you don't have any where you will need to go to those lengths. If you are a little rusty on your poly long division or synthetic division, check out: Purple Math Polynomial Long Division Purple Math Synthetic Division To determine the number of real zeros use Descartes' Rule of Signs Purple Math Descartes' Rule of Signs John My calculator said it, I believe it, that settles it

Problems-with-consecutive-odd-even-integers/497047: Find the number. i am w whole number greater then 10 but less than 20. The sum of my digits is 7. i am an even number. what number am i? Also, explain how you figure this question out 1 solutions Answer 336640 by solver91311(16868)   on 2011-09-13 18:31:45 (Show Source): You can put this solution on YOUR website! If the number is greater than 10 but less than 20, then the 10s digit has to be 1. If the sum of the digits in a two digit number is 7, and one of the digits is a 1 -- I'll let you take it from here. John My calculator said it, I believe it, that settles it

Equations/497038: If xyz=20, find the value of (6z)(x/2)(12y) 1 solutions Answer 336634 by solver91311(16868)   on 2011-09-13 18:22:17 (Show Source): You can put this solution on YOUR website! This is a commutative and associative property problem. Now all you have to do is substitute the value you know for and do the arithmetic. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/497034: The variable, y varies directly with x. If y=15 when x equals 20, what is y when x=52? 1 solutions Answer 336630 by solver91311(16868)   on 2011-09-13 18:14:24 (Show Source): You can put this solution on YOUR website! If varies directly with , then Substitute the given initial condition values for and , then solve for the value of that results. Re-write using the above determined value of Then you can solve for given any value of . John My calculator said it, I believe it, that settles it