Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'PRMath'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149, >>Next

 Numbers_Word_Problems/758275: The ratio of cars to vans at an auto dealership is 8 to 1. If the total number of both cars and vans at the dealership is 189, find the number of cars and the number of vans. 1 solutions Answer 461381 by PRMath(124)   on 2013-06-15 10:31:02 (Show Source): You can put this solution on YOUR website!When you have a ratio problem, you can always think of it like this: The ratio of cars to vans is 8 to 1. Just think of that as 8x to 1x. If the TOTAL number of cars and vans is 189, just take the info above and set up the equation like this: 8x + 1x = 189 (equation) 9x = 189 (add the like terms together) x = 21 (divide both sides by 9 to isolate the x) Now you know that x equals 1. Plug that into your ratios like this: CARS 8x 8(21) = 168 VANS 1x 1(21) = 21 That means there are 168 cars and 21 vans. You can check that like this: 168 cars + 21 vans = 189 cars and vans total. I hope this helps. :-)
 Expressions-with-variables/696940: find the value of p if 2(p + 4)= 7p + 21 solutions Answer 429504 by PRMath(124)   on 2012-12-26 17:16:31 (Show Source): You can put this solution on YOUR website!2(p + 4) = 7p + 2 <---- original problem 2p + 8 = 7p + 2 <---- distributed the 2 to "p" and to "4" -7p ..... -7p <---- subtracted 7p from both sides of the equation ____________________ -5p + 8 = 2 ..... -8 .... -8 <---- subtracted 8 from both sides of the equation ____________________ -5p = -6 = <----divide both sides by -5 to isolate the 'p' p = Does this work? We can plug in the answer into "p" in the original problem. 2(p + 4) = 7p + 2 2() = 7 + 2 + 8 = + 2 + = + = Now we can see that yes, the solution works. :-)
 Polynomials-and-rational-expressions/311500: Divide (42b^3+23b^2+32b+41) divided by (6b+5) not sure which is the ans. if at all correct.. i am so confused 7b^2-2b-7-6/6b+5 or 7b^2-2b+7+6/6b+51 solutions Answer 222814 by PRMath(124)   on 2010-06-05 09:17:21 (Show Source): You can put this solution on YOUR website!ivide (42b^3+23b^2+32b+41) divided by (6b+5) not sure which is the ans. if at all correct.. i am so confused 7b^2-2b-7-6/6b+5 or 7b^2-2b+7+6/6b+5 These are confusing but don't panic. These are not impossible. Here is your problem: My problem in showing this to you is going to be how to make this show up in typing! Arrgghh. I'm going to use this as my dividing sign: ] I will also draw a line above that symbol, so I can TRY to make this division look normal! It will look like this: .________________________ ] So here goes: ......._________________________ ] ......... ________________________ ................... ................... _____________________________________ .............................. ............................. ____________________________________________ ..................................... Therefore... our answer is: I'm sure this looks weird to you. If I could scan a copy of my work to you, it would be easier for you to see! I'm sorry it doesn't show up well here but maybe you can see thru how awful this looks and it will make sense to you. Good luck and I hope this was helpful. :-)
 Geometry_Word_Problems/310984: Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.1 solutions Answer 222415 by PRMath(124)   on 2010-06-03 12:02:02 (Show Source): You can put this solution on YOUR website!Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width. Ok... you have to first tell yourself that a perimeter is the sum of the measurements of all four sides of the rectangle. In other words, you add all four sides and voila, you have the perimeter. In a rectangle, tho, you have TWO lengths and TWO widths. The equation to find the perimeter, then,if we use "L" for Length and "W" for Width is: L + L + W + W = Perimeter Now this problem tells us that the perimeter is 112 cm. At first then, we can set up this equation: L + L + W + W = 112. We don't know, tho, the lengths and the widths - or do we? WELL.. the problem says this: the length is 4 cm less than four times the width. All you have to do is write that information in an equation form. Break down what you are given and see what you come up with: The Length: L is: = 4 cm less than 4 times the width: 4w - 4 <---See how this is 4 cm less than four times the width? Our equation then is: L = 4w - 4 and you can PLUG this info into the equation we started with, like this: L + L + W + W = 112 4w - 4 + 4w - 4 + W + W = 112 (see where I replaced "L" with 4w - 4? Now combine like terms, by adding the "Ws" and the numbers: 10W - 8 = 112 (now add 8 to both sides to start to isolate the w) 10W = 112 + 8 10w = 120 (now divide both sides by 10 to further isolate the w) w = 12 SO --- now we know that w = 12. We can just plug this info into what we were told about the length, which was: the length is 4 cm less than four times the width OR as we wrote it: L = 4w - 4 SO let's use that equation and plug in our info: L = 4w - 4 L = 4(12) - 4 (See where we plugged "12" in where the "w" was?) L = 48 - 4 L = 44 Now we know that the width is 12 and the length is 44. Does that work out in what we know to be the perimeter of the shape? We were told the perimeter was 112 cms, so, let's test our numbers out: L + L + W + W = 112 44 + 44 + 12 + 12 = 112 YAY! It works out! Sooooo our length is 44 cm and our width is 12 cm. I hope this was helpful. :-)
 Graphs/310642: 4+6x>4x-181 solutions Answer 222133 by PRMath(124)   on 2010-06-02 10:42:51 (Show Source): You can put this solution on YOUR website!4+6x>4x-18 Solve this like you would solve the problem if there were an equal sign in the problem. Put your "Xs" on one side of the equation and your numbers on the other side...... 4 + 6x > 4x - 18 (original equation) 4 + 6x - 4x > 18 (subtract 4x from both sides of the equation) 4 + 2x > 18 (6x - 4x = 2x) 2x > 18 - 4 (subtract 4 from both sides of the equation) 2x > 14 (18 - 4 = 14) x > 7 (divide both sides by 2 to isolate the 'x') If you graph this, you draw a number line with a circle around the 7 (you don't fill in the circle) and thennnn you draw an arrow from that circle that goes to the right. I hope this is helpful. :-)
 Expressions-with-variables/310639: 1 solutions Answer 222132 by PRMath(124)   on 2010-06-02 10:25:43 (Show Source): You can put this solution on YOUR website!Evaluate the variable expression when .a=-1/4, b=7/8, and c=1/8 8a + (7b -c) Just "plug" in the info you are given, like this: a = b = c = 8a + (7b - c) (original equation) 8 + ( - ) (see where the fractions are substituted in for the variables?) + (If you multiply 8 times you will get and... If you multiply 7 times you will get ) (If you subtract: you get: ) (Reduce the fractions: and ) (if you take -2 + 6 you will get 4) I hope this helps you. :-)
 Polynomials-and-rational-expressions/310385: Hi,I am having a hard time with this equation and would like some help./1 solutions Answer 221919 by PRMath(124)   on 2010-06-01 15:30:06 (Show Source): You can put this solution on YOUR website!/ Factoring is tricky but don't let it intimidate you. Just do this: Now can you see that these highlighted terms cancel each other? BUT when I say: "cancel" I'm not meaning that you can just just wipe out the (x + 4) in the numerator. Why? Well, when we "cancel" terms, we aren't just DELETING them! Think of this: = 1, right? Similarly, = 1, right? SO when we cancel out the (x + 4) above, we are really saying that equals 1. Therefore, this: is really: Does that make sense? I hope so. If you need more help with canceling and factoring, check out my YouTube videos. Just do a search on YouTube for PRMathChicago and when you find my name, you'll see some vids that my help you because they explain this in more detail. Good luck. :-)
 Polynomials-and-rational-expressions/310389: hi,I would like help with this equation, /1 solutions Answer 221910 by PRMath(124)   on 2010-06-01 15:13:45 (Show Source): You can put this solution on YOUR website! First you have to factor the numerator and the denominator, like this: Now look at this: See how those two highlighted terms can cancel each other out? Then you are left with your answer, which is: I hope this is helpful but for more examples of this type of problem, check out my YouTube videos. Just do a search on YouTube for PRMathChicago. When you find my name, there are a few videos there that show and explain this type of work in more detail. Good luck! :-)
 Linear-equations/310384: Please show me how to find the x-intercept and y-intercept of the line 2x+3y=-18 1 solutions Answer 221904 by PRMath(124)   on 2010-06-01 14:59:21 (Show Source): You can put this solution on YOUR website!x-intercept and y-intercept of the line 2x+3y=-18 Here are two facts to keep in mind: When you want to find the X intercept SOLVE for X by making y = 0 When you want to find the Y intercept SOLVE for Y by making x = 0. It's that simple. Just plug in 0... like this: Let's find the X intercept first. We'll SOLVE FOR X by making y = 0. 2x+3y=-18 (original equation) 2x + 3(0) = -18 (plug in 0 for the y variable) 2x = -18 (3 times 0 equals 0, so we just wipe it out of the equation). x = -9 (Divide both sides by 2 to isolate the x. So, -18 divided by 2 is -9) Now we know, when y =0, then x = -9. So our X intercept is: (-9, 0) Now let's find the Y intercept. We'll SOLVE FOR Y by making x = 0. 2x+3y=-18 (original equation) 2(0) + 3y = -18 (plug in 0 for the X variable) 3y = -18 (2 times 0 equals 0, so we just wipe it out of the equation). y = -6 (Divide both sides by 3 to isolate the y. So.. -18 divided by 3 is -6) Now we know, when x = 0, then y = -6. So our Y intercept is: (0, -6) That's all there is to it. I hope this was helpful. :-)
 Evaluation_Word_Problems/307871: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? I know the answer is 13 but I don't even know where to begin. It doesn't make any sense.1 solutions Answer 220193 by PRMath(124)   on 2010-05-24 08:40:18 (Show Source): You can put this solution on YOUR website!Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color? I know the answer is 13 but I don't even know where to begin. It doesn't make any sense. This isn't so much a problem of a math equation, but instead of logic. I hope I explain this well for you. Think of this.............. You have 8 red jellybeans, 4 green and 4 blue. If you held these beans in a bag and took out just 8 jellybeans, it is entirely possible that you could pull out 8 RED ones. (It would be pretty unlikely you would pull 8 red ones out, but it is definitely possible!) Sooooo... ok... now you have pulled out 8 red jellybeans. Keep the number 8 in your mind. Now there are 4 green and 4 blue left, right? If you took FOUR more beans out of the bag, it is entirely possible that you could pull out 4 green ones. This is unlikely to happen but again, it is definitely possible! So now you have 8 red ones and four green ones. That's 12 beans in all and you STILL don't have one of every color. What's left in the bag? You have 4 blue left. If you pull out ONE more bean, you will then have one jelly bean of each color. You had 12 beans and now this final bean means you have a total of 13 jellybeans. THAT'S why it takes 13 beans to be ABSOLUTELY sure you have one of each color. I hope this makes sense for you. :-)
 Linear-equations/306247: Which answer choice is the set of all solutions to the inequality |x + 3| > -2? A. There are no solutions. B. x < -5 or x > -1 C. x > -5 and x < -1 D. All real numbers. 1 solutions Answer 219217 by PRMath(124)   on 2010-05-19 10:02:43 (Show Source): You can put this solution on YOUR website!Which answer choice is the set of all solutions to the inequality |x + 3| > -2? A. There are no solutions. B. x < -5 or x > -1 C. x > -5 and x < -1 D. All real numbers. With all respect to the person who has already answered this problem, I am sorry to say that I think that person is wrong. The answer to this problem is A: There is NO solutions. Why? The absolute-value principle reminds us that absolute value is always non negative. Therefore,your equation of: |x + 3| > -2 has no solution, which is "A" in your choices. I hope this helps you. :-)
 Linear-equations/306237: Solve the formula for v: g = f – v1 solutions Answer 219188 by PRMath(124)   on 2010-05-19 09:01:36 (Show Source): You can put this solution on YOUR website!Solve the formula for v: g = f – v This is very similar to your other problem, so let's solve it by asking the question of: How can we isolate the "v"? Well, what is going on with the "v"? You can see that an "f" is added to the "v" so how about we do the OPPOSITE of adding an "f"? Let's SUBTRACT "f" from the equation and of course, we have to do this on both sides of the equation. Therefore, we have: g = f - v (Original equation) g - f = f - f - v (Subtract "f" from both sides of the equation). g - f = -v You are still not done. Why? Well, the "v" is still not isolated! There is a negative sign in front of the "v", which means that there is a -1 next to the "v". You see, in front of any variable, there is always a "1" next to the variable and in this case, that 1 happens to be a NEGATIVE 1. How do we isolate the "v"? How can we get rid of that negative 1? How about if we DIVIDE by -1? AND of course, we have to do this on both sides of the equation: g - f = -1v = See how the -1 cancels out? So now you have: v = which is also: v = -g + f
 Linear-equations/306238: Solve the formula for f: g = f – v1 solutions Answer 219184 by PRMath(124)   on 2010-05-19 08:46:35 (Show Source): You can put this solution on YOUR website!Solve the formula for f: g = f – v When solving for a variable, ask yourself: How can I isolate the variable? In this problem, you ask: How can I isolate the "f"? Well... what is going on near the "f"? You can see that there is a "v" that is subtracted from the "f". So... to isolate the "f", let's get rid of that "v". How? Well, you are subtracting "v" so let's do the opposite: Let's ADD "v" to the equation and if we do it on the right side, we must also do it on the left. Therefore, you have this: g= f - v (Original equation) g + v = f - v + v (Add "v" to both sides of the equation) g + v = f (-v + v = 0, (so to speak) and so, our "f" is now isolated). THEREFORE: f = g + v I hope this helps. :-)
 Linear-systems/295732: what is the slope of the line y=9?1 solutions Answer 213156 by PRMath(124)   on 2010-04-23 13:47:10 (Show Source): You can put this solution on YOUR website!You were already given an answer to this problem, but I think the tutor accidentally hit the number 9 on his puter, instead of "0". Let's review: The previous tutor said that if you put y = 9 into the y = mx + b format, you'd get: y = 0x + 9. AND since "m" represents the slope, you can see that the slope in this case, is a 0. (The previous tutor said the slope was 9 -- and that's a typing mistake, I'm certain). Let's discuss slopes in general: When x equals a number, it is a VERTICAL line and the slope is UNDEFINED. When y equals a number, then you have a HORIZONTAL line and the slope is 0. I tell students that the way to remember that horizontal lines have a slope of zero is to think that the word "HORIZONTAL" has two letter Os in it. I say that those Os are actually zeros, reminding you that horizontal lines have 0 as a slope. :-) Ok, corny but it works. Good luck with your math and I hope this helps you. :-)
 Inequalities/295714: do you change the sign when dividing by an negative or du you do it before1 solutions Answer 213151 by PRMath(124)   on 2010-04-23 13:40:50 (Show Source): You can put this solution on YOUR website!Do you change the sign when dividing by an negative or do you do it before? This is a confusing question, because I'm not sure the type of problem you are referring to, given that there are many instances where you divide by a negative. For example, consider these rules: A positive divided by a negative is a negative. A negative divided by a negative is a positive. In those cases, you are changing the sign. If you are talking about inequalities, then you "flip" the sign when you divide by a negative. For example, you could solve for "X" in the problem below, and you'd have to flip the sign because you are dividing by a negative. See the following: -2x < 6 x > -3 (see how the sign flipped when we divided by -2? And see how the answer became -3 because we divided a positive by a negative?) Here's another example: -3y > -9 y < 3 (Again, the sign flipped because we divided by a negative. BUT, -9 divided by -3 gives a +3, so the answer was positive, which is also a changed sign). If you give a sample question, you may get a little more help. I hope this helps you tho. :-)
 Finance/295468: I have one more that I don't get at all either. thx lauren Solving for the specified variable PV = nRT; T1 solutions Answer 212962 by PRMath(124)   on 2010-04-22 20:50:41 (Show Source): You can put this solution on YOUR website!PV = nRT; T Hi Lauren... When you solve for any variable, always think of "undoing" whatever operation is going on, so that you can get the variable all by itself. What do I mean? Well, if you are multiplying, for example, how to you "undo" that? You can divide. In another example, if you are adding, you can "undo" the adding by subtracting. Do you get the idea? Soooo in your equation, you have PV = nRT and you have to solve for T. SO to get "T" all by itself, ask yourself, what is going on in the equation between "T" and nR? As you can see, the variables nRT are being MULTIPLIED together. How can we "undo" multiplication? We can DIVIDE. We can DIVIDE nR away from T, BUT if we do it on one side of the equation, we have to do it on the other so PV must be divided by nR, also. SO.... let's just DIVIDE nR on both sides of the equation, like this: PV = nRT (original equation) = Now nR is divided from both sides of the equation. Ok... can you see what I have highlighted? These highlighted terms can cancel each other out, like this: = Then what do you have left? You have: = T That's all there is to it. Just identify what is going on with your variables, and try to "undo" whatever operation is performed, so that you can work to get your variable by itself.
 Surface-area/294934: How do you find the surface area of a cylinder1 solutions Answer 212696 by PRMath(124)   on 2010-04-21 21:10:07 (Show Source): You can put this solution on YOUR website!Think of a cylinder like a can of pop, k? At the top of the can, there is a circle. At the bottom of the can, there is a circle. Now if you cut off the top and you cut off the bottom and sort of spread out the can (uncurled it), you'd have a rectangle. Now picture this: The height of the rectangle is the height of the can. Can you picture that? The top of the rectangle is REALLY the the circumference of the circle. How so? Think about it -- it was a circle until you uncurled it. So the measure of the circumference of the can will not change simply because you uncurled it, right? Sooooo to get the total surface area of the cylinder, you use this equation: FIRST find the "lateral area" (the rectangle) which is: r is the radius h is the height NEXT find the areas of two bases (the top and bottom of the can). The area formula for ONE circle is: Area = r is the radius. HOWEVER -- there are TWO circles (the TOP and the BOTTOM of the can) soooo, we have to find the TWO bases so our formula for the TWO bases is: IF we add the lateral area plus the base areas, we'll know the total surface area. Our final equation is: Total Area of a Cylinder = + Just put in the correct numbers for the radius and height and do the math and voila - you'll have the total surface area. If you need more help, just get a specific question (such as the measurements of a sample problem) and post it here. I'm sure someone can give you more info if you need it. I hope this helps. :-)
 Linear-systems/295019: Find the intercepts for the equations. -4x + y = -41 solutions Answer 212686 by PRMath(124)   on 2010-04-21 20:38:45 (Show Source): You can put this solution on YOUR website!When you want to find the "X" intercept, then solve for "X" by making Y = 0 When you want to find the "Y" intercept, then solve for "Y" by making X = 0. Now that you know those two facts above, let's solve for the "X" intercept first. The "X" intercept means we solve for "X" by making Y = 0. Here's your equation: -4x + y = -4 Now let's plug in 0 for the Y variable and solve for "X" -4x + 0 = -4 -4x = -4 (Now let's divide by -4 to isolate the "X") = x = 1 SO X = 1 when Y = 0. Our ordered pair would be: (1, 0) Now let's do the "Y" Intercept. The "Y" intercept means we solve for "Y" by making "X" = 0 -4x + y = -4 Now let's plug in 0 for the X variable and solve for "Y" -4(0) + y = -4 See where the 0 is in place of the "X" variable? 0 + y = -4 If you multiply -4 times 0, you will get 0. y = -4 SO... Y = -4 when X = 0. Our ordered pair will be: (0, -4) I hope this helps you. :-)
 Square-cubic-other-roots/287577: What is the square root of 5 on the outside of the check mark and 18 inside the check mark?1 solutions Answer 208372 by PRMath(124)   on 2010-04-01 09:09:03 (Show Source): You can put this solution on YOUR website!What is the square root of 5 on the outside of the check mark and 18 inside the check mark? (I love the description of the square root sign as a check mark. That was a great description and let me know immediately what the problem should look like). :-) Excellent. :-) So ok... here is your problem: Think of the various ways you can reach 18 through multiplication. There is: Let's look at that choice. In that situation, you can take the square root of 9, right? In other words, you know what this is: . This answer to is 3. Keep that in your mind now and look at your problem this way: <----This can be rewritten as: Now... let's take the square root of 9, which is 3, k? We can "pull" that 3 out of the square root sign and we'll leave the 2 on the inside of the square root sign -- inside the check mark, like this: BUT don't forget the 3 that you got from the . You have to multiply that 3 times the 5 that was already sitting outside the sign. soooo we write the problem as: So... here it is so you can see it all together: I hope this helps. :-)
 Quadratic_Equations/287323: 1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle? 2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg?1 solutions Answer 208254 by PRMath(124)   on 2010-03-31 14:37:30 (Show Source): You can put this solution on YOUR website!1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle? One leg of the right triangle is unknown: We'll call it "x" The other leg is 2 feet longer than the other leg: 2 + x The hypotenuse is 10 feet long. You know ("c" is the hypotenuse). Now let's fill in the blank. Now let's fill in what we know. One leg is "x" The other leg: 2 + x The hypot. is: 10 (FOILED the above) (subtracted 100 from both sides of the equation) (combined like terms) (factored out a 2 from everything) (divided 2 from both sides of the equation) = 0 x = -8 or x = 6 (disregard the -8 because a side cannot equal -8) Does this work? If one side is 6 and the other is 2 more than 6 (or 8) and the hypotenuse is 10, then we have: } YAY it works. 2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg? One leg is 5 units: 5 The hypotenuse is 1 longer than the other leg: X+ 1 The other leg is: X Put it all together: Does x = 12 work? One leg is 5 The other is 12 the hypotenuse is one more than 12: this is 13 YAY this works, too. I hope this helps you.
 Exponents/287253: Simpify. Write the answer with positive exponents... 4^(5)*4^(7)1 solutions Answer 208239 by PRMath(124)   on 2010-03-31 13:17:22 (Show Source): You can put this solution on YOUR website! When you are multiplying with exponents, if the bases are the same, then you ADD the exponents. In this case, you have the same base, which is 4. Therefore, you just add the exponent 5 with the exponent 7. You get this: = I hope this helps. :-)
 Coordinate-system/286855: Divide y2 + 13y + 22 by y + 2.1 solutions Answer 208024 by PRMath(124)   on 2010-03-30 12:16:05 (Show Source): You can put this solution on YOUR website! Ok, first you have to factor the numerator, which will be: Now you have this for your problem: See what I have highlighted? These can cancel each other out, like this: When you cancel those terms, you get the answer: If you search for PRMathChicago on YouTube, you'll see more examples of rational expressions like this. Maybe something there will help you. I hope this helps. :-)
 Linear_Equations_And_Systems_Word_Problems/286828: Find the slope of the line... x=41 solutions Answer 208011 by PRMath(124)   on 2010-03-30 11:14:42 (Show Source): You can put this solution on YOUR website!x = 4 is a VERTICAL line. All vertical lines have an UNDEFINED slope. If it had been y = 4, then you would have had a horizontal line, and horizontal lines have a slope of ZERO. I hope this helps.