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 'rapaljer'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679, >>Next

 Graphs/51314: f(x)=x^2+6x+5 What is the y- intercept of this function? My ans is (5,0) and what is the zero's of this parabola? My ans is (0,-1),(0,-5) am I correct? 1 solutions Answer 34246 by rapaljer(4667)   on 2006-09-09 08:50:25 (Show Source): You can put this solution on YOUR website!You are correct!! Here is the graph: R^2 at SCC
 Geometric_formulas/51300: I have tried this one and cannot figure it out. I have tried versions of the Pythagorean Theorem. Please Help! Two posts, one 12 meters high and the other 21 meters high, are 30 meters apart. A single wire runs from the top of the first post to the ground and from the ground to the top of the second post. The wire is attached to the ground at a distance of x units from the first post. What is a function representation that states the total length of the wire?1 solutions Answer 34245 by rapaljer(4667)   on 2006-09-09 08:26:52 (Show Source): You can put this solution on YOUR website!You have two right triangles, in which the two poles are the vertical legs of the triangles, and the length of the wire is the sum of the two hypotenuses (or would that be hypotenii???). Since the distance between the poles is 30 meters, let x= distance from first pole to the point where the wire touches the ground, and 30-x = distance from this point on the ground to the base of the second pole. By Theorem of Pythagoras, the length of the wire from the top of the first pole to the ground is , and the distance from the top of the second pole to the ground is . The total length of the wire, is the sum of these radicals It doesn't simplify much: R^2 at SCC
Quadratic_Equations/51308: This question is from textbook
I am using the quadratic formula on 3x^2 = 11x + 4; 3x^2 - 11x + 4 = 0; 3x^2 - 11x - 4 = -2; I have to convert the 5.5 to a fraction, but I am confused. The answer is 1/3,-4 or the other way around (I think). I need an assist please.
1 solutions

Answer 34238 by rapaljer(4667)   on 2006-09-09 01:22:20 (Show Source):
You can put this solution on YOUR website!
I'm confused too!! You have three different quadratic equations, and I don't see how any of them relate to changing 5.5 to a fraction.

However, the first equation is
, which becomes
, which factors into

or
or .

This works very well by factoring, so you don't need the quadratic formula, unless you specifically wanted to do it by quadratic formula. In this case, algebra.com has a "pluggable solver" that looks like this:
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=169 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -0.333333333333333. Here's your graph:

R^2 at SCC

 Coordinate-system/51267: This question is from textbook Beginning Algebra For this question, we must find the revenue from the sale of x items given by R=50x. Does this ask to graph the equation only or do I need to solve this for x. And if so, how do I do it?1 solutions Answer 34237 by rapaljer(4667)   on 2006-09-09 01:04:33 (Show Source): You can put this solution on YOUR website!You can't solve for x unless they give you the value of R. If you are to graph it, then it is a VERY steep graph with the y intercept (actually the R intercept) of 0, and a slope of 50 over 1. Like this: Look closely at this graph. The graph is so steep you can hardly see it!! R^2 at SCC
 Linear_Equations_And_Systems_Word_Problems/51302: "To which form can a rotional number always be changed?" Thank you.1 solutions Answer 34236 by rapaljer(4667)   on 2006-09-09 00:55:50 (Show Source): You can put this solution on YOUR website!A rational number can always be changed to either a repeating or a terminal decimal. R^2 at SCC
 Linear-systems/51233: Exercise 2.2 #19 on page 97 Solve the system for p and q in terms of x and y. Explain how you could check your solution and perform the check. x=2+p-2q y=3-p+3q I've been all over the chapter and couldn't find anything remotely helpful for this. Please help!!!1 solutions Answer 34176 by rapaljer(4667)   on 2006-09-08 08:05:43 (Show Source): You can put this solution on YOUR website!It may be helpful to find a way to eliminate the p, and then eliminate the q, and write two equations, one for p and one for q. First, if you add the two equations together, you can eliminate the p, and get x=2+p-2q y=3-p+3q x+y = 5 + q, so q = x+y-5 Second, to eliminate the q, multiply both sides of the first equation by 3, and the second equation by 2: 3(x)=3(2+p-2q) 2(y)=2(3-p+3q) 3x= 6 +3p-6q 2y = 6-2p+6q 3x+2y = 12 +p, so p=3x+2y - 12 There you have it: p=3x+2y-12 q=x+y-5 I have no idea how to check this, unless you solve for x and y to see if you come back with the same equations that you started with. It looks like Linear Algebra to me. Hey, I gotta go to work this morning!! R^2 at SCC
 Linear_Algebra/51240: Find the two solutions to this equation. ax^2+8ax=01 solutions Answer 34174 by rapaljer(4667)   on 2006-09-08 07:40:50 (Show Source): You can put this solution on YOUR website!Factor the common factor of ax: ax(x+8) = 0 ax = 0 or x+8 = 0 x=0 or x=-8 R^2 at SCC
 Exponential-and-logarithmic-functions/51141: i dont realli no how 2 word this...but wats it mean if theres an exponent before a sq. root (not after)...u multiply the sq. root by the exponent? 1 solutions Answer 34168 by rapaljer(4667)   on 2006-09-08 01:16:55 (Show Source): You can put this solution on YOUR website!You are probably talking about a cube root, fourth root, etc. For example, is a cube root. It means "what number can you raise to the third power and get 27?" Of course, the answer is 3, because . As another example, is a fourth root. It means "what number can you raise to the fourth power and get 16?" Of course, the answer is 2, because . I have a complete explanation of this as a Lesson Plan in algebra.com under "Square-cubic-other-roots." Also, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then go to Basic Algebra, the look for "Samples from Basic Algebra: One Step at a Time", then Chapter 5, which is a complete explanation of radicals. R^2 at SCC
 Polynomials-and-rational-expressions/51144: is -x^2 positive while -(x)^2 is negitive or are they both negitive1 solutions Answer 34167 by rapaljer(4667)   on 2006-09-08 01:09:31 (Show Source): You can put this solution on YOUR website!They are both negative! R^2 at SCC
 Functions/51184: If f(x) = 7x^5 - 3, then f ^-1(x) = a. [(x + 7)/5]1/3 b. [(x + 3)/5]1/7 c. [(x + 5)/7]1/3 d. [(x + 7)/3]1/5 e. [(x + 3)/7]1/5 f. [(x + 5)/3]1/7 g. none of these1 solutions Answer 34166 by rapaljer(4667)   on 2006-09-08 01:05:49 (Show Source): You can put this solution on YOUR website!The way to find an inverse function, you begin with an xy equation:. There are two steps: 1. Interchange the x and y; and 2. Solve for y. Given: Step 1: Step 2: Solve for y. Add +3 to each side: Divide by 7: Take the 5th root of each side or raise both sides of the equation to the power It looks like e) is the correct answer! R^2 at SCC
 Graphs/51186: Determine whether the relation is a function. If it is a function, state its domain and range. {(–8, 7), (–5, –4), (–3, 3), (–3, 6)} a. Domain: {7, –4, 3, 6}; Range: {–8, –5, –3} b. Domain: {–8, –5, –3}; Range: {7, –4,3, 6} c. Domain: {–8, –5, –3}; Range: 11 d. The relation is not a function.1 solutions Answer 34164 by rapaljer(4667)   on 2006-09-08 00:55:56 (Show Source): You can put this solution on YOUR website!Given: {(–8, 7), (–5, –4), (–3, 3), (–3, 6)} First, the Domain is the set of all x values, which are the first numbers in each pair: {-8,-5,-3}. Second, the Range is the set of all y values, which are the second numbers in each pair: {7,-4,3,6} Third, it is NOT a function, since two points have the same x coordinate: (-3,3) and (-3,6). Now, a. Domain: {7, –4, 3, 6}; Range: {–8, –5, –3} Domain and range are backwards. False b. Domain: {–8, –5, –3}; Range: {7, –4,3, 6} Both are correct!! True c. Domain: {–8, –5, –3}; Range: 11 Domain is correct, but range is wrong. False d. The relation is not a function. This is true. R^2 at SCC
 Graphs/51199: Find two quadrants in which there are no points on the graph of xy = 12. a. I & II b. I & III c. I & IV d. II & III e. II & IV f. III & IV g. Al of these have points in at least three quadrants.1 solutions Answer 34162 by rapaljer(4667)   on 2006-09-08 00:46:24 (Show Source): You can put this solution on YOUR website!Since you have a product of x times y equal to a positive number, this means that either x and y are both positive (Quadrant I) or they are both negative (Quadrant III). Therefore all the points are in Q I and III, so there are NO points in Q II and IV. Final answer is e). R^2 at SCC
 Graphs/51201: Determine if the point (–5, 3) lies in the viewing window defined by Xmin = –3, Xmax = 12, Ymin = –6, Ymax = 15. a. Yes b. No1 solutions Answer 34161 by rapaljer(4667)   on 2006-09-08 00:43:35 (Show Source): You can put this solution on YOUR website!No! The x value is -5, which is NOT between -3 and 12. The value of y is 3, which is between -6 and 15, but the x value is not, so it will not be in the viewing window. R^2 at SCC
 Quadratic_Equations/51207: This question is from textbook Beginning Algebra I'm lost here, can someone help? Find the axis of symmetry. y=x^2+6x+51 solutions Answer 34160 by rapaljer(4667)   on 2006-09-08 00:41:16 (Show Source): You can put this solution on YOUR website!This is a parabola that opens upward, and the axis of symmetry for such a graph in the form of will always be . In the case of , the axis of symmetry will be The graph looks like this, using a graphing calculator, or this fantastic "algebra.com" calculator: R^2 at SCC
 Inequalities/51226: 5/2x-3 = 3/x-5 no idea how to work it out1 solutions Answer 34159 by rapaljer(4667)   on 2006-09-08 00:34:21 (Show Source): You can put this solution on YOUR website!Anytime you have a fraction equal to a fraction, like this:, remember that means that means that Now, 5x-25 =6x - 9 Subtract 5x from each side to get all the x terms on the right side: 5x-5x -25= 6x-5x-9 -25 = x-9 Next, add +9 to each side: -25+9 = x-9+9 -16=x Check by substituting back into the original equation: It checks!! R^2 at SCC
 Polynomials-and-rational-expressions/51222: This question is from textbook algebra beggining and intermediate Hi- im just strted school after a long time time and i dint know hoo to do this please help1 solutions Answer 34157 by rapaljer(4667)   on 2006-09-08 00:26:38 (Show Source): You can put this solution on YOUR website!You need to state the problem. Most of the tutors are not going to have a copy of your book. R^2 at SCC
 logarithm/50915: Hi, I have a multiple choice question and i'm stuck between the two answers. I have ln (x\square root of yz) = either lnx - 1\2 (ln y - ln z) or ln x - 1\2 (ln y + ln z). I have got as far as ln x - square root ln y SOMETHING ln z I am just not sure whether the SOMETHING should be plus or minus sign. thanks for your help.1 solutions Answer 33936 by rapaljer(4667)   on 2006-09-06 01:17:29 (Show Source): You can put this solution on YOUR website!The ln of a product is the SUM of the logs, so use the positive. The negative is still outside the parentheses. I have ln (x/square root of yz) = ln x - 1/2 (ln y + ln z). R^2 at SCC
 logarithm/50916: Hi, the following question has me a little stumped... it is solve for x e^2in(2x) does this then become e^(2x)squared?? not quite sure what to do with this question. thanks.1 solutions Answer 33935 by rapaljer(4667)   on 2006-09-06 01:13:17 (Show Source): You can put this solution on YOUR website!Could this be ? if so, then do this by the laws of logarithms: R^2 at SCC
 Linear-systems/50913: Hi, I have to determine the linear function f(t) with slope -1 and f(2)= -1. I have done slope -1 and (2, -1). form f(x) =ax+b a= -1 f(x) = -1 Since f(2)=1 f(2)= -1(2)+b 2=-2+b 2+2=b 4=b f(t) = -1t+4 Is this even remotely on the right track?? thanks for your time!1 solutions Answer 33933 by rapaljer(4667)   on 2006-09-06 01:05:41 (Show Source): You can put this solution on YOUR website!You are almost right. You made a couple of very small errors, which I have corrected below for you. I have done slope -1 and (2, -1). form f(x) =ax+b a= -1 f(x) = -1 Since f(2)=-1 f(2)= -1(2)+b -1=-2+b -1+2=b 1=b f(t) = -1t+1 Now, check it! The slope is indeed -1. f(2)= -1(2) + 1 = -2 +1 = -1, as it should be. R^2 at SCC
 Linear-equations/50686: How do you use a graphing calculator to graph the following equation: x2-11x+18. I am assuming by X2 it means x to the second power.1 solutions Answer 33756 by rapaljer(4667)   on 2006-09-04 08:04:16 (Show Source): You can put this solution on YOUR website!Notice that there are five buttons across the top of the calculator. The first one is "y=" and the last one is "GRAPH". Start with the "y=" button. This opens up a whole screen full of y1=, y2=, y3=, etc. Next, you need to find the x-variable button, which is the second button down in the second column. This button actually says something that looks like "x,t,0,n". Press this button to get "x". To get the "squared" you can either press the x^2 button in the first column, or you can press the "^2" buttons. Then finish typing in the equation with a "minus 11 x + 18". After you get that all typed in, press the last button across the top that says "GRAPH", and it should graph a parabola. See my handout on my website, since you may want to adjust the window to see it better. R^2 at SCC
 Linear-equations/50687: I have a TI84 plus graphing calculator> Could someone please explain to me how to use it in regards to graphing linear equations Thanks1 solutions Answer 33741 by rapaljer(4667)   on 2006-09-04 01:25:32 (Show Source): You can put this solution on YOUR website!You need to see my handout on the TI 84 graphing calculator. It's on my website, which you can find by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for the page on "Calculator Handouts and Websites". My handout was so large I had to place it in three sections, and you will need the second of these three for graphing. It's really too much to do right here. Let me know if you need help with this. I won't have access to my office Email until Tuesday. R^2 at SCC
 expressions/50554: f(x) = (1 + x)/x g(x) = 1/(1 - x) h(x) = 1/(1 + x) If so, (g o h)(x) = a. x b. 2 - x c. -x d. x/(2x + 1) e. (1 - x)/(2 - x) f. (1 + x)/x g. (2 - x)/(1 - x) h. (1 - x)/x i. 2 + x j. none of these1 solutions Answer 33740 by rapaljer(4667)   on 2006-09-04 01:19:33 (Show Source): You can put this solution on YOUR website!g(x) = 1/(1 - x) h(x) = 1/(1 + x) (g o h)(x) = g[ f(x) ] g[ f(x) ] = This looks a LOT worse than it really is!! It's a complex fraction, and I have a LOT of these worked out on my Math in Living Color pages of my website! I'm more comfortable in that format, and they are in "Living Color"! Multiply both numerator and denominator by the LCD which is (1+x). g[ f(x) ] = g[ f(x) ] = g[ f(x) ] = g[ f(x) ] = , which is the f) answer. R^2 at SCC
 Miscellaneous_Word_Problems/50667: The sum of two numbers is 130. One number is 46 times more than 1/2 the other number. What are the numbers? Boy do I hate word problems. I can never seem to make sense out of them. Matt1 solutions Answer 33739 by rapaljer(4667)   on 2006-09-04 01:03:47 (Show Source): You can put this solution on YOUR website!Let x = first number and y = second number Now, you need to write two equations since there are two unknowns. The sum of two numbers is 130. x+y = 130 One number is 46 times more than 1/2 the other number. x= 1/2*y+46 If you don't like this equation because of the fraction, just multiply both sides by 2: 2x = y + 92 or 2x-y = 92 There, now it's not a word problem any more. It's solving two equations with two unknowns!! x+ y = 130 2x -y = 92 Just add the two equations together: 3x= 222 x=74 Now, x + y = 130 so, 74 + y = 130 y=56 Check in the second equation: x=1/2*y +46 74=1/2*56 + 46 74=28 + 46 It checks!! R^2 at SCC
 Equations/50655: 1/(2*x-6)+2/(3*x-9)=7/(x^2-3*x) I LOVE this site~!! Thanks for the help:) Chris1 solutions Answer 33738 by rapaljer(4667)   on 2006-09-04 00:55:46 (Show Source): You can put this solution on YOUR website!This is a fractional equation. Start by factoring the denominators so you can find the LCD for the problem. The LCD = 6x(x-3), so multiply both sides of the equation by the LCD. It's ugly at first, but in the first step all the fractions divide out! After all the denominator factors divide out, this is what is left: One more step: Check each denominator, and make sure that x= 6 doesn't make any denominators zero. Also, you can check the answer by substituting x= 6 into the original equation (if you want to go to some trouble). R^2 at SCC
 Graphs/50652: Dear Tutor, Please help me with this problem..thanks! Why is 2y+7x=-3 considered a line? We were asked in multiple choice form, and I figured this equation was a line by process of elimination but I would like to know why. Thank You, student in need1 solutions Answer 33737 by rapaljer(4667)   on 2006-09-04 00:44:11 (Show Source): You can put this solution on YOUR website!Any equation that is in the form of a number times x plus or minus a number times y equal to a number term will ALWAYS be a straight line. This form Ax+By=C is called the standard form of a line. Also, any equation in the form of y = mx + b (called the slope-intercept form of a line) is also a straight line. It's when you get x^2 or y^2 or division by x or y, like y = 12/x, etc. Then this is NOT a straight line. R^2 at SCC
 logarithm/50654: Hi, I have a question that is assume log4=.6021 determine log1\16. I know I can do this on the calculator and find log 1/16 is -1.2041, but that gives me no understanding of the problem. Is there a way to do working out to come to the solution??? thanks very much.1 solutions Answer 33736 by rapaljer(4667)   on 2006-09-04 00:38:52 (Show Source): You can put this solution on YOUR website!Given log 4 = .6021, notice that 1/16 is actually . So, log 1/16 = log 4^-2 = -2* log 4 =-2(.6021) =-1.2042 R^2 at SCC
 Equations/50656: 8*k^2+5*k=2*k^2+4 Thanks for the help, Chris1 solutions Answer 33735 by rapaljer(4667)   on 2006-09-04 00:31:56 (Show Source): You can put this solution on YOUR website!Set the equation equal to zero: 8k^2+5k=2k^2+4 8k^2 -2k^2 + 5k -4 = 2k^2 + 4 - 2k^2- 4 6k^2 + 5k - 4 = 0 Factoring this trinomial is the hard part!! Try this combination: 6k^2 + 5k - 4 = 0 (3k + 4 )(2k - 1)= 0 3k = -4 or 2k = 1 k= -4/3 or k = 1/2 R^2 at SCC
 Equations/50657: x^3-x^2+4*x-4=0 thanks a million:)1 solutions Answer 33734 by rapaljer(4667)   on 2006-09-04 00:24:16 (Show Source): You can put this solution on YOUR website!This is factoring by grouping. Group the first two and last two terms together. Notice that there is a common factor of (x-1): or Are you solving with complex numbers or real numbers only? If real numbers only, then the only answer you have to worry about is x=1. End of problem, since real numbers squared cannot equal a negative. However, if complex numbers are allowed, then gives two solutions: , , in addition to . R^2 at SCC
 Equations/50682: solve: x^3-x^2+4*x-4=0 thanks, chris1 solutions Answer 33730 by rapaljer(4667)   on 2006-09-03 22:30:54 (Show Source): You can put this solution on YOUR website!This is factoring by grouping. Group the first two and last two terms together. Notice that there is a common factor of (x-1): or Are you solving with complex numbers or real numbers only? If real numbers only, then the only answer you have to worry about is x=1. End of problem, since real numbers squared cannot equal a negative. However, if complex numbers are allowed, then gives two solutions: , , in addition to . R^2 at SCC
 Linear-equations/50675: This question is from textbook Beginning Algebra Find the slope and the y-intercept. y = 4x – 3 Please help1 solutions Answer 33729 by rapaljer(4667)   on 2006-09-03 22:23:55 (Show Source): You can put this solution on YOUR website!In the equation y=mx+b, the coefficient of x is the slope and the constant term or the number term is the y-intercept. m=slope, b= y-intercept. y = 4x -3 slope m= 4 y-intercept = b = -3 R^2 at SCC