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 Numbers_Word_Problems/94158: 1) When is the sum of any three consecutive numbers odd? when is it even? 2)I am a 2-digit prime number. the sum of my digits is 5, and the difference between them is 3. What number am I? Please help me answer these questions1 solutions Answer 68569 by Earlsdon(6294)   on 2007-08-24 13:56:51 (Show Source): You can put this solution on YOUR website!1) The sum of three consecutive numbers is odd when the first of these three numbers is even. (8+9+10 = 27) The sum of three consecutive numbers is even when the first of these three numbers is odd. (15+16+17 = 48) 2) Let x = the tens digit and y = the units digit, then: x+y = 5 x-y = 3 or x = y+3 Substitute into the above equation. y+3+y = 5 2y+3 = 5 2y = 2 y = 1 This is the units digit. x = y+3 x = 1+3 = 4 This is the tens digit. The number is 41, a prime number.
 Expressions-with-variables/94159: Please help simplify the following expression:[6x^3/3x^4]^2 I thought it was 4/x^2,but it isn't. Thank you kathy1 solutions Answer 68568 by Earlsdon(6294)   on 2007-08-24 13:46:37 (Show Source): You can put this solution on YOUR website!Simplify: = Now, unless the problem is not as you have written it, this is the answer!
 Polynomials-and-rational-expressions/94156: I am having some problems with this problems The product of two consecutive postive even integers is 288. Find the integers Thank you1 solutions Answer 68565 by Earlsdon(6294)   on 2007-08-24 11:31:34 (Show Source): You can put this solution on YOUR website!Let x = the first positive even integer, then x+2 is the next consecutive positive integer. The product of these two = 288. So we can set up the equation to solve for x: Apply the distributive property to the left side. Subtract 288 from both sides. Factor the left side. Apply the zero products principle. or so... x = 16 or x = -18 but you want the positive integer only, so... x = 16 this is the first positive even integer. x+2 = 18 This is the next consecutive positive even integer. Check: (16)(18) = 288
 Graphs/94039: I need to find the equation of the line that passes through (6,-1) and has an undefined slope. Then i need to graph it. If you could please tell me step by step how I would go about doing that I would be very grateful.1 solutions Answer 68461 by Earlsdon(6294)   on 2007-08-23 18:11:50 (Show Source): You can put this solution on YOUR website!First, if a line has an undefined slope, this means that it is a vertical line. If it passes through the point (6, -1) then you can draw a vertical line through this point and you will have it.
 Expressions-with-variables/94037: Please help me to solve 2x+3=5x+8.1 solutions Answer 68458 by Earlsdon(6294)   on 2007-08-23 17:46:00 (Show Source): You can put this solution on YOUR website!Solve: Collect the variable, x, on one side of the equation by subtracting 2x from both sides. Now isolate the variable term by subtracting 8 from both sides. Finally, divide both sides by 3 to get the variable alone. or
 Polynomials-and-rational-expressions/93928: Divide this trinomial (8x^3-6x^2+2x)/(4x+1)1 solutions Answer 68405 by Earlsdon(6294)   on 2007-08-22 23:36:36 (Show Source): You can put this solution on YOUR website!Divide: Use long division or synthetic division. with a remainder of -1
 Square-cubic-other-roots/93940: Evaluate: (-100)^1/21 solutions Answer 68404 by Earlsdon(6294)   on 2007-08-22 23:08:07 (Show Source): You can put this solution on YOUR website!Evaluate: =
 Expressions-with-variables/93939: How do I solve this for x: ax-2=bx+51 solutions Answer 68403 by Earlsdon(6294)   on 2007-08-22 23:03:53 (Show Source): You can put this solution on YOUR website!Try this: Subtract bx from both sides. Now add 2 to both sides. Factor an x from the lefthand side. Finally, divide both sides by (a-b) ...and you're done!
 Sequences-and-series/93753: This question is from textbook please help solve for x the problem is log(little x)32 = 51 solutions Answer 68304 by Earlsdon(6294)   on 2007-08-22 12:11:34 (Show Source): You can put this solution on YOUR website!Solve for x: You can rewrite this in exponential form thus: can be written as: in this problem, you'd get: can be written as: but we can express 32 as , so... Here we can apply the property of exponential functions: If (for n not = 0} then , so... If then
 Linear-equations/93739: Please help. Solve by substiution. 8x-4y=16 y=2x-4 1 solutions Answer 68300 by Earlsdon(6294)   on 2007-08-22 11:14:15 (Show Source): You can put this solution on YOUR website!Solve by substitution: Substitute this value of y into the first equation and solve for x. Simplify. Combine like-terms. This result indicates that the two equations represent the very same line and there are an infinity of solutions. The system is a "consistent system" and the equations are "dependent equations".
 Polynomials-and-rational-expressions/93693: I am having some problems with these problems Simplify: (m^4)^3(m^2)^9 over (m^3)^2 and also Find the value of the polynomial -X^2+10x_10 when X=-5 Thank you1 solutions Answer 68272 by Earlsdon(6294)   on 2007-08-22 00:12:36 (Show Source): You can put this solution on YOUR website!1) Simplify: = = = 2) Evaluate: when x = -5 Substitute -5 for x = -85
 Polynomials-and-rational-expressions/93710: This question is from textbook Beginning Algebra 49x exponent8 - 35x exponent6 - 56x exponent3 over 7x exponent31 solutions Answer 68270 by Earlsdon(6294)   on 2007-08-21 23:56:46 (Show Source): You can put this solution on YOUR website!Simplify: Factor from the numerator. Cancel the indicated factors.
 Systems-of-equations/93712: please help to solve this one I now have grey hair given f(x)=5x to the 2nd-3x+1, find f(-2). thank you 1 solutions Answer 68268 by Earlsdon(6294)   on 2007-08-21 23:48:12 (Show Source): You can put this solution on YOUR website!Sorry 'bout your grey hair! find You just replace x with -2
 Exponents/93711: This question is from textbook Beginning Algebra binomial squared to multiply: (6x+5)exponent2 my work: (6x+5)(6x+5)= 36xexponent2 + 30x + 30x + 25= 36xexponent2 + 60xexponent2 + 25= 96xexponent4 + 251 solutions Answer 68267 by Earlsdon(6294)   on 2007-08-21 23:42:30 (Show Source): You can put this solution on YOUR website!Er...not quite! Your first step was fine. but... not so...
 Functions/93578: Need some help with this problem. Given g(s) = - sē + 5 find f(-4) and f(4a) Thank you for your time, David.1 solutions Answer 68153 by Earlsdon(6294)   on 2007-08-21 12:20:00 (Show Source): You can put this solution on YOUR website!Well, you've given us ? then you ask for f(-4) and f(4a) ??? You will have to give us the function statement for f(?) Please re-post the problem so that is clear.
 Equations/93577: What is the simpliest form of: (9-b^2)/(b^2-b-6)1 solutions Answer 68152 by Earlsdon(6294)   on 2007-08-21 12:15:25 (Show Source): You can put this solution on YOUR website!Simplify: In the numerator, factor a -1 and rearrange the terms. Now factor the binomial in the numerator and factor the trinomial in the denominator. Cancel the indicated factors.
 Quadratic_Equations/93430: This question is from textbook If x varies inversely as y and x = 2 when y = 8, find x when y = 15. PLEASE HELP1 solutions Answer 68016 by Earlsdon(6294)   on 2007-08-20 15:34:12 (Show Source): You can put this solution on YOUR website!You can write this relationship (formula) as: x varies inversely (upsidedownwardly ?) as y which really means that if y goes up then x goes down and vice versa. The k is called the proportionality constant. We need to determine the value of k. This can be done with the help of the given information that x = 2 when y = 8. Substituting these values into the above equation allows us to solve for k. Multiply both sides by 8. so... Now our formula looks like this: Now we are ready to answer the question: What is x when y = 15.
 Quadratic_Equations/93340: Problem: From the information below,write an equation and then solve the equation. My mother is three times as old as my sister. If the difference between their ages is 22 years, find both of their ages. 1 solutions Answer 67963 by Earlsdon(6294)   on 2007-08-19 19:15:07 (Show Source): You can put this solution on YOUR website!Let M = mother's age and S = sister's age. From the problem description, you can write: M = 3S Mother's age is three times sister's age. M-S = 22 The difference in their ages is 22. In this equation, substitute M = 3S. 3S-S = 22 2S = 22 S = 11 M = 3(11) M = 33 Mother's age is 33 years. Sister's age is 11 years.
 Linear-equations/93334: Hi I am needing a little help on some algebra. Could you help me solve this: Is the point (-120,-99) on the graph of the line. Y=4/5x-3? Explain why or why not. I have tried and can't come up with anything. Thanks for your time1 solutions Answer 67962 by Earlsdon(6294)   on 2007-08-19 19:09:03 (Show Source): You can put this solution on YOUR website!Is the point (-120, -99) on the graph of ? If the given point is on the line then the x- and y-coordinates of the point will satisfy the equation. To find out if this is true, you will substitute the x- and y-coordinates of the point (-120, -99) into the equation. Evaluate this. The answer is yes.
 Linear-equations/93335: I am having trouble with another question for a homework assignment: For the line 7x-4y =14, determine X intercept, Y intercept, and slope. Thank you so much1 solutions Answer 67961 by Earlsdon(6294)   on 2007-08-19 19:00:41 (Show Source): You can put this solution on YOUR website!First, it would be helpful if you wrote your equation in the slope-intercept form: where m is the slope and b is the y-intercept. here, you can see that the slope and the y-intercept, The x-intercept occurs when y = 0. Add to both sides. Multiply both sides by This is the x-intercept.
 Functions/93317: i have a math packet and i only have 2 questions left. The directions say EXACTLY this: "Write the equation in function form" and the question is this: -4x + 6y = 24 I've checked a lot of help sites and asked a ton of people but i still can't find the answer. Can you tell me how to solve the problem?1 solutions Answer 67931 by Earlsdon(6294)   on 2007-08-19 15:05:28 (Show Source): You can put this solution on YOUR website!Write, in function form: First, you need to identify which of the two variables is the "independent" variable. Usually, x is the independent variable, so we'll first write the equation in terms of x, which means that we'll need to solve for y. Add 4x to both sides. Divide both sides by 6. Now, to write this in function form, we replace the y with f(x), which is read as f of x or function of x. The nice thing about an equation written in function form is that it easy to identify the independent variable. That's the variable inside the parentheses of the f(x).
 Surface-area/93315: Can you please help me with this problem? The exterior of a spherical water tank is to be painted. The radius of the tank is 15 feet. How many square feet will need to be painted? I got 2826ft^ the first time but I don't know if I used the correct formula. Thank you in advance!!!1 solutions Answer 67929 by Earlsdon(6294)   on 2007-08-19 14:47:32 (Show Source): You can put this solution on YOUR website!Well, let's see if you got it! The surface area (S) of a sphere is given by: where r is the radius of the sphere. In this problem, r = 15 ft, and we can use as an approximation. sq.ft. So you are right on!
 Problems-with-consecutive-odd-even-integers/93272: What are 3 consecutive odd intergers that equal 201?1 solutions Answer 67902 by Earlsdon(6294)   on 2007-08-19 12:03:55 (Show Source): You can put this solution on YOUR website!Try this: Let x be the first odd integer, then x+2 is the next consecutive odd integer and x+4 is the third consecutive odd integer. The sum of these is 201. x+(x+2)+(x+4) = 201 Combine like-terms. 3x+6 = 201 Subtract 6 from both sides. 3x = 195 Divide both sides by 3. x = 65 This is the first odd integer. x+2 = 67 This the next consecutive odd integer. x+4 = 69 This is the third consecutive odd integer. Check: 65+67+69 = 201
 Equations/93267: The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs.1 solutions Answer 67901 by Earlsdon(6294)   on 2007-08-19 11:23:11 (Show Source): You can put this solution on YOUR website!Starting with the perimeter: where s = the length of one of the equal sides and b = the length of the base and P = 29 cm. But s = 4b-8 s is "8 cm less than 4 times the length of the base" Substituting 4b-8 for s in the formula for the perimeter: Simplify. Add 16 to both sides. Divide both sides by 9. This is the length of the base, but you need the length of s, so... cm. Check:
 Polynomials-and-rational-expressions/93265: I am having problems solving this equation could someone please help me. I have a few other problems like this one and am unable to solve them as well. I think if shown how to solve this one i may be able solve the others. - Please help me.1 solutions Answer 67899 by Earlsdon(6294)   on 2007-08-19 11:04:58 (Show Source): You can put this solution on YOUR website!Subtract: You'll notice that these two fractions have a common denominator, so you can subtract the numerators and put the result over the common denominator. Now you need to simplify this. Factor a 2 from the numerator and factor the trinomial in the denominator. Cancel the indicated factors.
 Expressions-with-variables/93240: The number of gallons in q quarts1 solutions Answer 67876 by Earlsdon(6294)   on 2007-08-18 21:49:17 (Show Source): You can put this solution on YOUR website!Think of the word "quart" as an abreviation of "quarter of a gallon" So there are four quarts in one gallon, therefore there are 0.25 gallons in one quart.
 Linear_Algebra/93239: I am so lost, if anyone could please answer this one I'd really appreciate it: What is the domain of g(x) when 1 solutions Answer 67874 by Earlsdon(6294)   on 2007-08-18 21:45:42 (Show Source): You can put this solution on YOUR website!What is the domain of g(x) when: You'll recall, no doubt, that the domain of a function is the set of all possible values of the independent variable, which is x in this case. First, we need to examine the denominator of the given function (2x-5) and ask..."what value of x will cause this to become zero?" You can find out by setting the denominator equal to zero and solving for x. Add 5 to both sides. Divide both sides by 2. So, when the denominator of the function becomes zero, and, as you know, mathematics does not allow division by zero. It undefined. Therefore, we must exclude from the domain. All other real values of x, however, are legal, so we can write the domain as: You would read this as..."all the real numbers not incuding 5/2"
 Bodies-in-space/93229: jimmy works on a farm. one of his jobs is to fill up the liquid fertilizer tanks when the farmer is spreading the fertilizer. each tank is a cylinder with a diameter of 6 ft. and a height of 4ft. if there seven tanks and 1 cubic foot=7.5 gallons of liquid. how many gallons of fertilizer will all the tanks hold?1 solutions Answer 67870 by Earlsdon(6294)   on 2007-08-18 21:31:42 (Show Source): You can put this solution on YOUR website!First, find the volume of one cylindrical tank: where: r = radius of the circular base and h = the height of the tank. Radius = half the diameter. r = D/2 = 6/2 = 3 ft. h = 4 ft. Use as an approximation. The volume of one tank is: cu.ft. Multiply this by 7 to find the volume of 7 tanks. cu.ft. If 1 cu.ft = 7.5 gallons of liquid fertilizer, then: 791.28 cu.ft. = (7.5gal/cu.ft)(791.28cu.ft.) gallons. This equals 5934.6 gallons. So, the 7 tanks will hold 5934.6 gallons of liquid fertilizer.
 Linear_Algebra/93236: I am so confused, can you please help me with this question: 1 solutions Answer 67868 by Earlsdon(6294)   on 2007-08-18 21:11:20 (Show Source): You can put this solution on YOUR website!If: and Find: First find by substituting 2 for x in the function Evaluate this. Now substitute -5 for x in the function So,
 Triangles/93150: This question is from textbook Problem: One leg of a right triangle has a length of 3m. The other sides have lengths that are consecutive integers. Find these lenths. The other leg is ____ m The length of the hypotenuses is ____m I get the consecutive inegers n, n+1 and if I use the formula a^2 + b^2 = c^2 - I don't know what to plug in for c. I've been shown several ways, and now I'm just confused. Thanks!!! 1 solutions Answer 67784 by Earlsdon(6294)   on 2007-08-17 18:36:00 (Show Source): You can put this solution on YOUR website!Well, on this problem you do have to make at least one assumption: The given side of 3 meters is (or is not) the hypotenuse. If you assume that it is the hypotenuse, it is therefore the longest of the three sides of the right triangle. Since the other two sides are consective integers and each is less then 3, they can only be 1 and 2 mters in length. Well, as soon as you apply the Pythagorean theorem, you soon see that this cannot be so, because does not equal . So the 3-meter side is one of the legs, right? Now you have a choice: Is it the shorter leg or the longer leg (not the hypotenuse)? Let's try the shorter leg. So the hypotenuse, being the longest side must be n+1 and the other leg must be n. Applying the Pythagorean theorem: Subtract from both sides. and... So, the hypotenuse is 5 meters,and the other leg is 4 meters. If you were familiar with Pythagorean triplets, you could easily have guessed this result.