# See tutors' answers!

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 'funmath'

funmath answered: 2925 problems
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, >>Next

 Polynomials-and-rational-expressions/61089: This question is from textbook Please help stuck with this one for hours.I need to know if I am performing this operation correctly. Thank you very much. Find all real or imaginary solution to the equation. 6x=-(19x+25)/(x+1) (6x)(x+1)=-19x-25 6x^2+6x+19x+25=-19x-25+19x+25 6x^2+25x+25=0 My answers is -5/3 and -5/21 solutions Answer 42016 by funmath(2925)   on 2006-11-13 07:11:26 (Show Source): You can put this solution on YOUR website! Find all real or imaginary solution to the equation. 6x=-(19x+25)/(x+1) (6x)(x+1)=-19x-25 6x^2+6x+19x+25=-19x-25+19x+25 6x^2+25x+25=0 : 6x^2+10x+15x+25=0 (6x^2+10x)+(15x+25)=0 2x(3x+5)+5(3x+5)=0 (2x+5)(3x+5)=0 2x+5=0 and 3x+5=0 2x=-5 and 3x=-5 x=-5/2 and x=-5/3 You're right!!! Keep up the good work! Happy Calculating!!!
 Trigonometry-basics/61090: To Whom May It Concern, I have the question but I am not very able to do it. A church spire 82 metres high casts a shadow 62 metres long. Find the angle of elevation of the sun at that moment. Please help. Thanks a lot. CH Lam1 solutions Answer 42015 by funmath(2925)   on 2006-11-13 07:00:17 (Show Source): You can put this solution on YOUR website!Hi CH lam, A church spire 82 metres high casts a shadow 62 metres long. Find the angle of elevation of the sun at that moment. : Draw a right triangle, the spire (I'm not sure what that is, I am assuming that it goes all the way down to the ground) is the side going up and down opposite the angle with the ground, the shadow is the side ajacent to the angle. : Opposite side=82m ajacent side=62m angle of elevation=x : tan(x)=opposite/ajacent x=tan^(-1)(41/31)<--inverse tan or arctan x=52.907 degrees Happy Calculating!!!
 Trigonometry-basics/61091: To whom may it concern, I have problem to solve this question below. A ladder 6.54 metres long leans against a wall, touching a window sill, and makes an angle of 62° with the ground. Find the height of the window sill above the ground. How far is the foot of the ladder from the foot of the wall ? Please help and thanks in advanced. CH Lam1 solutions Answer 42013 by funmath(2925)   on 2006-11-13 06:48:40 (Show Source): You can put this solution on YOUR website!Hi CH Lam, A ladder 6.54 metres long leans against a wall, touching a window sill, and makes an angle of 62° with the ground. Find the height of the window sill above the ground. How far is the foot of the ladder from the foot of the wall ? : Draw a right triangle, the ladder is the hypotenuse, the wall is the side opposite the angle with the ground, the distance frome the wall is the side adjacent to the angle with the ground. : angle with the ground=62 height of the wall=o distance from the wall=a The ladder is the hypotenuse=6.54 m : sin(x)=opposite/hypotenuse The wall is about 5.774 m : cos(x)=adjacent/hypotenuse The distance from the wall is 3.07 m. : Happy Calculating!!!
 Linear-systems/61093: This question is from textbook Intermediate Algebra The current in ther lazy river moves at a rate of 4mph. Monica'sdinghy motors 6mi upstream in the same time it take to motor 12mi downstream. What is the speed of the dinghy?1 solutions Answer 42012 by funmath(2925)   on 2006-11-13 06:32:26 (Show Source): You can put this solution on YOUR website!The current in ther lazy river moves at a rate of 4mph. Monica'sdinghy motors 6mi upstream in the same time it take to motor 12mi downstream. What is the speed of the dinghy? The distance formula is d=rt. d=distance, r=rate, and t=time. Solve the formula for t. ---> distance up stream=6 rate upstream is the rate of the boat (r)- rate of the current(4):r-4 distance downstream=12 rate downstream is the rate of the boat (r)+ rate of the current(4): r+4 The time is the same for both, so set the distance formula solved for time equal to each other. The dingy was moving at 12 mph. : Happy Calculating!!!
 Trigonometry-basics/61066: What is the advantage of helping students with their homework? What's in it for you guys? Are you simply pure philanthopic beings with the sole desire to help humanity, or is there a catch? I know I am being cynical, but there is no such thing as a free lunch.1 solutions Answer 41987 by funmath(2925)   on 2006-11-12 21:17:36 (Show Source): You can put this solution on YOUR website!I can't speak for everyone. I can speak for myself. I think someone is making money, because students keep telling me they are sending someone donations. Some tutors have a side paid online tutoring businesses, I've seen them advertise. I personally don't make any money from this. I taught high school math for 5 years. Now, I am a math instructional assistant for a community college full time. We don't have good online software for tutoring math, so I tell my students that I monitor this site from time to time if they need help from home or work. I monitor the site while I'm in my office and have no students and when I've got nothing to do at home. I really like helping students acheive their goals. That's why I do what I do for a living. But this site gives me no monitary gain, I just like helping people with math. It's nice to be good at something and help others. I've been professionally tutoring for my college for 5 years, it's a lot more personally rewarding to personally tutor people than to teach a whole class. Besides, math is fun!!!
 Linear-systems/61042: Instructions: solve each system by the eliminsation method. What is the solution for x-y=4 x-y=-31 solutions Answer 41984 by funmath(2925)   on 2006-11-12 21:00:55 (Show Source): You can put this solution on YOUR website!Instructions: solve each system by the eliminsation method. What is the solution for x-y=4 x-y=-3 Don't freak out, but this one has no solution. If you try to eliminate either variable both go and you get 0=7 or 0=-7. Graphically, these lines are parallel and will never intersect. Multiply the top equation by -1 and add them together. -1(x-y)=-1(4)--->-x+y=-4 : -x+y=-4 x-y=-3 _______ 0+0=-7 0=-7 No solution. Happy Calculating!!!
 Percentage-and-ratio-word-problems/61065: if sally can paint a house in 4 hrs, and john can paint the asame house in 6 hrs, how long will it take for both of them to apint the house together?1 solutions Answer 41981 by funmath(2925)   on 2006-11-12 20:53:34 (Show Source): You can put this solution on YOUR website!if sally can paint a house in 4 hrs, and john can paint the asame house in 6 hrs, how long will it take for both of them to apint the house together? Let sally's rate be x/4 Let john's be x/6 : x=2.4 hrs or x=2hr+.4(60)min=2hrs and 24 min Happy Calculating!!!
 Miscellaneous_Word_Problems/61063: An airplane covered 25 miles of its route while decreasing its altitude by 19,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.]1 solutions Answer 41977 by funmath(2925)   on 2006-11-12 20:39:30 (Show Source): You can put this solution on YOUR website!An airplane covered 25 miles of its route while decreasing its altitude by 19,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. [Hint: 1 mi = 5280 feet.] The plane covered horizontally. Slope=rise/run or vertical/horizontal slope=-19,000/132,000=-.14393939...=-.14 Happy Calculating!!!
 Linear-equations/61062: Find the slope and the y-intercept. y = –9x + 81 solutions Answer 41971 by funmath(2925)   on 2006-11-12 20:26:10 (Show Source): You can put this solution on YOUR website!Find the slope and the y-intercept. y = –9x + 8 The slope intercept form of a line is , m=slope, and (0,b) is the y-intercept. the slope m=-9 the y-intercept is (0,b)=(0,8), some books and teachers let you say 8. Happy Calculating!!!
 Probability-and-statistics/61048: on a true/false test a student has no idea what the answers are to 3 of the questions so he guesses. What is the probability that he will guess correctly on all 3 questions? at least 2 times?1 solutions Answer 41969 by funmath(2925)   on 2006-11-12 20:22:00 (Show Source): You can put this solution on YOUR website!on a true/false test a student has no idea what the answers are to 3 of the questions so he guesses. What is the probability that he will guess correctly on all 3 questions? at least 2 times? There's 1 write answer out of two choices for each question. Therefore there's a probability of guessing all three questions right. Percetagewise that's 12.5%. Note that that's the same probability of getting them all wrong (think about it.). At least two right is 2 out of three and 3 out of three There are three ways to get 2 right (wrr),(rwr),(wrr) and one way to get them all right (rrr) ++ ways to get 2 right ways to get 3 right ways to get 2 or 3 right. Note that this is the same probability of getting less than 2 right. (think about it.) You can use binomial probability for this, but it would only be easier to do for a problem this small if you have a capable calculator. If you have a TI-83 or 84. Just hit, binomialpdf(3,.5,2)+binomialpdf(3,.5,3)=.5 or 1/2. : The formula for binomial probability is: P(x)=probability of x n=number of trials x=number of successes p=probabillty of success q=1-p=probabilty of failure For the probability of 2 correct answers: n=3, x=2, p=1/2=.5, q=1-1/2=.5 For the probabilty of 3 correct answers: n=3, x=3, p=.5, q=.5 Happy Calculating!!!
 Linear-equations/61031: Find the slope of any line parallel to the line through points (19, 11) and (9, 9).1 solutions Answer 41959 by funmath(2925)   on 2006-11-12 18:42:34 (Show Source): You can put this solution on YOUR website!Find the slope of any line parallel to the line through points (19, 11) and (9, 9). The slope through these two points can be found with the slope formula: , m=slope (x1,y1)=(19,11) and (x2,y2)=(9,9) Parallel lines have the same slopes, so any line parallel to the line made by these two points also has a slope of Happy Calculating!!!
 Linear-equations/61032: Find the slope of any line perpendicular to the line through points (8, 17) and (9, 9).1 solutions Answer 41958 by funmath(2925)   on 2006-11-12 18:37:17 (Show Source): You can put this solution on YOUR website!Find the slope of any line perpendicular to the line through points (8, 17) and (9, 9). The slope between these two points can be found with the slope formual: , m=slope, (x1,y1) and (x2,y2) are the given points. (x1,y1)=(8,17) and (x2,y2)=(9,9) Perpendicular lines have slopes that are negative reciprocals of each other. (That mean that they're opposite signs and upsidedown.) The slope of any perpendicular line through the line created by those two points is: Happy Calculating!!!
 Linear-systems/61036: Rewrite the equation 2x – 3y = –6 as a function of x1 solutions Answer 41956 by funmath(2925)   on 2006-11-12 18:30:22 (Show Source): You can put this solution on YOUR website!Rewrite the equation 2x – 3y = –6 as a function of x Solve for y. -2x+2x-3y=-2x-6 0-3y=-2x-6 -3y=-2x-6 Some books want you to also replace y with f(x) Happy Calculating!!!
 Linear-systems/61035: Given f(x) = x2 – 3x + 9, find f(0).1 solutions Answer 41954 by funmath(2925)   on 2006-11-12 18:27:03 (Show Source): You can put this solution on YOUR website!Given f(x) = x^2 – 3x + 9, find f(0). Substitute 0 in where the x's are and simplify: This is a special point called the y-intercept of the graph of the equation. Happy Calculating!!!
 Linear-equations/61033: Write the equation of the line that passes through point (–4, 19) with a slope of –6.1 solutions Answer 41953 by funmath(2925)   on 2006-11-12 18:23:36 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through point (–4, 19) with a slope of –6. There are a couple of ways to do this, but whenever I'm given a slope and a point, I like to use the point slope formula , m=slope, (x1,y1)=given point. m=-6, (x1,y1)=(-4,19) <--This is the slope intercept form of a line. Happy Calculating!!!
 Equations/61023: f(x)= x^-2x+8\x+41 solutions Answer 41952 by funmath(2925)   on 2006-11-12 18:16:12 (Show Source): You can put this solution on YOUR website!f(x)=(x^2-2x+8)/(x+4) You didn't give us instructions. x cannot = -4 has to be stipulated, because the original function is undefined when it's denominator equals 0 The domain therefore is {x|x cannot=-4}<--set builder notation There is a vertical asymptote at x=-4 The degree of the numerator is higher than the denominator, so there is no horizontal asymptote. The degree of the numerator is exactly 1 more than the denominator, so there is a slant asymtote you can get through long division of y=x-6. If you plot a few points on both sides of x=-4 you get this graph. If you had something else in mind, let me know. Happy Calculating!!!
 Functions/61022: I can't seem to find the function rule for this set of data: x y -2 -2 0 1 2 4 4 71 solutions Answer 41950 by funmath(2925)   on 2006-11-12 17:43:31 (Show Source): You can put this solution on YOUR website!I can't seem to find the function rule for this set of data: x y -2 -2 0 1 2 4 4 7 If you plot the points and connect them you will see that they make a perfect line like this. You were given the y-intercept (0,1), all we need is a slope and we can form the function. The slope formula , m is the slope, (x1,y1) and (x2,y2) are two points on the line. (x1,y1)=(-2,-2) and (x2,y2)=(0,1) The slope intercept form of a line is , m=slope, and (0,b)=y-intercept. Your m=3/2 and (0,b)=(0,1) y=(3/2)x+1 You can replace the y with f(x) if you need function notation. f(x)=(3/2)x+1 Happy Calculating!!!
 Rational-functions/61021: Graph f(x)= 4x+8/x^2-2x-15 Indicate all intercepts and asymptotes. I am almost positive all my calculations are correct but my graph doesn't seem to be coming out right. Thanks in adavnce!!!!1 solutions Answer 41947 by funmath(2925)   on 2006-11-12 17:20:04 (Show Source): You can put this solution on YOUR website!Graph Indicate all intercepts and asymptotes. The horizontal asymptote is y=0, because the degree of the numerator is less the the degree of the denominator. : The vertical asymptotes are when the denominator=0: (x-5)(x+3)=0 x=5 and x=-3 are vertical asymptotes. : The x-intercept happens when the numerator =0. 4x+8=0 4x=-8 4x/4=-8/4 x=-2 The x-intercept is (-2,0) : The y-intercept happens when x=0. The y-intercept (0,-8/15) : Happy Calculating!!!
 Polynomials-and-rational-expressions/60886: Could someone help me? Solve the following equations. Leave radicals in radical form(do not calculate there approximate values). a. 4x^2+3x-10=0 b. 2x^2=3x c. x^3-4x^2-x+4=0 d. x^4-10x^2+9=0 e. x^3-3x^2+x-3=0 f. 3x^2-5x+1=0 I also need to know how to put radicals signs on here. Thank you for your help!!1 solutions Answer 41944 by funmath(2925)   on 2006-11-12 17:05:52 (Show Source): You can put this solution on YOUR website! Solve the following equations. Leave radicals in radical form(do not calculate there approximate values). a. Replace the middle term with two numbers that multiply to give you 4x^2*-10=-40x^2, but add to give you 3x. 8x*-5x=-40x^2, 8x+-5x=3x. : Factor by grouping, group the first two terms and the last two. Factor the GCF out of each parentheses Factor out x+2 Set each parentheses equal to 0 and solve for x. 4x-5=0 and x+2=0 4x=5 and x=-2 4x/4=5/4 and x=-2 x=5/4 and x=-2 : b. 2x^2=3x Set equal to 0 Factor out the GCF. x(2x-3)=0 x=0 and 2x-3=0 x=0 and 2x=3 x=0 and 2x/2=3/2 x=0 and x=3/2 : c. x^3-4x^2-x+4=0 Factor by grouping x^2-1 is the difference of squares (x+1)(x-1)(x-4)=0 x+1=0 and x-1=0 and x-4=0 x=-1 and x=1 and x=4 : d. x^4-10x^2+9=0 (x+3)(x-3)(x+1)(x-1)=0 x+3=0 and x-3=0 and x+1=0 and x-1=0 x=-3 and x=3 and x=-1 and x=1 : e. x^3-3x^2+x-3=0 (x^2+1 is prime, so if you need only real numbers you can ignore it, otherwise it's solution is +/-i) x-3=0 x=3 : f. 3x^2-5x+1=0 a=3 b=-5 and c=1 The quadratic formula is : An abreviation for radical is "sqrt(whatever you want)" like the square root of x+5 is sqrt(x+5) : Happy Calculating!!!
 Linear-systems/61008: how can i solve the system by graphing. 2x + y = 4 x + y = 3 1 solutions Answer 41940 by funmath(2925)   on 2006-11-12 16:33:01 (Show Source): You can put this solution on YOUR website!how can i solve the system by graphing. E1: 2x + y = 4 E2: x + y = 3 : For E1: let x=0 and solve for y. 2(0)+y=4 0+y=4 y=4 Plot (0,4) Now let y=0 and solve for x. 2x+0=4 2x=4 2x/2=4/2 x=2 Plot (2,0) Connect the points and you have a line. For E2: let x=0 and solve for y. 0+y=3 y=3 Plot(0,3) Let y=0 and solve for x. x+0=3 x=3 Plot (3,0) Connect the points and you have another line: They connect at (1,2)<--this is the solution of the system. Happy Calculating!!!
 Linear-equations/61013: how do i write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line. 1 solutions Answer 41938 by funmath(2925)   on 2006-11-12 16:24:17 (Show Source): You can put this solution on YOUR website!how do i write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line. The slope intercept form of a line is , m=slope, and (0,b)=y-intercept. Your m=4 and b=-5 To graph the line put a point on the y axis at -5. From that point use the slope=rise/run=4/1. Go up 4 and right 1 plot another point. (This should be (1,-1) if you did it right.) Connect the points and you have a line. Happy Calculating!!!
 Polynomials-and-rational-expressions/61003: This question is from textbook Can somebody please help me! Find all real solutions to (a) x^2 + x + SQRT(x^2 + x) - 2 = 0 I have been working on this problems for a couple of days and I can't seem to understand, or even know what to do. I know I need to use the substitution methods but the radical in the equation is confusing me. 1 solutions Answer 41937 by funmath(2925)   on 2006-11-12 16:14:56 (Show Source): You can put this solution on YOUR website!Find all real solutions to (a) Use the substitution method. Let Factor (P+2)(P-1)=0 P+2=0 and P-1=0 P=-2 and P=1 But we want to know what x is, so let and and and and You have to use the quadratic equation to solve these: when a=1, b=1, c=-4 You have to check these to see if they are valid or extraneous. I checked these by plugging them into my calculator and the were both extraneous. when a=1, b=1, and c=-1 You have to check these to see if they are valid or extraneous. I checked these with my calculator and they were both valid. If you have a TI-83 or 84, I can give you instructions on checking for extraneous solutions if you ask. Happy Calculating!!!
 Polynomials-and-rational-expressions/61000: I received help yesterday(11/11) on these problems and think I understand. I have submitted my attempts at some to see if I have the right idea and a few that still escape me. Some seem pretty straight forward now but others elude me. Thanks again for such timely help. For the following, letf(x)=x+5; let g(x)=x^2^-2; let h(x)=-3x for h{f(4)} I set 4=x, the value of f(4) then being 9; the expression h(9) would then be -27???right??? for g(x+3), I set (x)=x+3 and then the value of g(x+3) being x^3^+3x^2^-2x-6??? I lost it on the following and need help: 1. Same parameters (f-g)(x) 2. h(2x^2^+4x) The last problem has nothing to do with the parameters above. It has just given me fits. 3. 5x^3/2^-25=0 Thanks in advance for your help and this great program.1 solutions Answer 41934 by funmath(2925)   on 2006-11-12 15:40:59 (Show Source): You can put this solution on YOUR website!For the following, letf(x)=x+5; let g(x)=x^2-2; let h(x)=-3x for h(f(4)) I set 4=x, the value of f(4) then being 9; the expression h(9) would then be -27???right???RIGHT!!!! : for g(x+3), I set (x)=x+3 and then the value of g(x+3) g(x+3)=(x+3)^2-2 g(x+3)=(x+3)(x+3)-2 g(x+3)=x^2+3x+3x+9-2 g(x+3)=x^2+6x+7 : 1. Same parameters (f-g)(x) (f-g)(x)=(x+5)-(x^2-2) (f-g)(x)=x+5-x^2+2 (f-g)(x)=-x^2+x+7 : 2. h(2x^2+4x)=-3(2x^2+4x) h(2x^2+4x)=-6x^2-12x : I had trouble interpretting this one. From what I can tell you are putting ^ before AND after your exponents. (You only need it before, and if you have a fractional exponent, put it in parentheses.) If this isn't what you meant, let me know. 3. 5x^(3/2)-25=0 5x^(3/2)-25+25=0+25 5x^(3/2)=25 : Check by substitution to see if it's true. 0=0 we're right!!! Happy Calculating!!!
 Linear-equations/60993: given a line containing (1,3),(2,4),(3,5)determine the slope-intercept from of the equation and give one additional point on this line and grapg the function.1 solutions Answer 41924 by funmath(2925)   on 2006-11-12 14:53:12 (Show Source): You can put this solution on YOUR website!given a line containing (1,3),(2,4),(3,5)determine the slope-intercept from of the equation and give one additional point on this line and graph the function. We need a slope and a point to make the equation of a line. We don't have the slope, but we can find it using the slope formula:, m=slope, (x1,y1) and (x2,y2) are given points. Let (x1,y1)=(1,3) and (x2,y2)=(2,4) (I checked all the points, you can use any of them to get m=1) We can now use the point slope equation to get the equation:, m=slope, and (x1,y1) is a given point. m=1 and (x1,y1)=(1,3) y-3=1(x-1) y-3=x-1 y-3+3=x-1+3 y=x+2 <--this is slope intercept form , m=slope and b=y-intercept. : You can find another point by letting x= a number, like 0 and solve for y. y=0+2 y=2 Plot all these points and connect them and you should have this line: Happy Calculating!!!
 Trigonometry-basics/61002: Hi, I am trying to help my daughter with her math homework and we are both feeling overwhelmed. There are some concepts that her teacher hasn't covered yet in class...I am trying to help her without her textbook being at home. My question is: Find the numerical value of the expression sin 30degrees + cos 60degrees. The answer choices are: 1. 1 2. 1/4 3. square root of 3 4. square root of 3 + 1/2 I am not trying to cheat, but just am trying to help her get the answer and learn how to do this... Thanks! The answers that we were coming up with were .5 or 180! so not sure what to do!1 solutions Answer 41923 by funmath(2925)   on 2006-11-12 14:35:00 (Show Source): You can put this solution on YOUR website!Find the numerical value of the expression sin 30degrees + cos 60degrees. The answer choices are: 1. 2. 1/4 3. square root of 3 4. square root of 3 + 1/2 There are two special right triangles that you have to memorize the values of. One is the 30, 60, 90 degree triangle. Draw the triangle, label the side opposite the 30 degree angle 1, the side opposite the 60 degree angle is , and the side opposite the 90 degree angle (the hypotenuse) is 2. sin(30)=opposite/hypotenuse=1/2 cos(60)=adjacent/hypotenuse=1/2 sin(30)+cos(60)=1/2+1/2=2/2=1 The other special right triangle you have to memroize is the 45,45,90 triangle. On that one the hypotenuse is , and the other two sides are 1. Happy Calculating!!!
 Exponents/60975: This question is from textbook Intermediate Algebra Help please - I need this layed out so I can do it for my final submission - Thank you. (4x^3y)1/2 (in superscript) over (9xy) 1/2 superscript The question is - perform the operation. Write the answers without negative exponents. Assume that all variables represent positive numbers. THANK YOU1 solutions Answer 41921 by funmath(2925)   on 2006-11-12 14:24:18 (Show Source): You can put this solution on YOUR website! Happy Calculating!!!
 Functions/60995: given that. f: 3x^2-4x+1 g: 2x-1 calculate fg(10)1 solutions Answer 41919 by funmath(2925)   on 2006-11-12 13:57:10 (Show Source): You can put this solution on YOUR website!given that. f: 3x^2-4x+1 g: 2x-1 calculate fg(10) This means evaluate the function of f times the function of g when x=10. : fg(x)=(3x^2-4x+1)(2x-1) fg(10)=(3(10)^2-4(10)+1)(2(10)-1) fg(10)=(3(100)-40+1)(20-1) fg(10)=(300-40+1)(19) fg(10)=(261)(19) fg(10)=4959 : You could have also just found f(10) and g(10) and multiplied them if you're intimidated by the size of the equation. f(10)=261 g(10)=19 fg(10)=261*19=4959 Happy Calculating!!!
 Square-cubic-other-roots/60914: I can only solve part of this equation and then I get stuck. Can someone show me the next steps I need to take and explain how they are done? I have done the equation as far as I can: SQRT(2X-1)+SQRT(X-4)= 4 <----original equation SQRT(2X-1)=4-SQRT(X-4) (SQRT<2X-1>)^2 = (4-SQRT)^2 2X-1 = (4-SQRT)(4-SQRT) <------I am lost as to how to solve finish this side of the equation. Thanks!1 solutions Answer 41868 by funmath(2925)   on 2006-11-11 16:09:08 (Show Source): You can put this solution on YOUR website! <----original equation (x-5)(x-85)=0 x-5=0 and x-85=0 x=5 and x=85 Check for extraneous solutions: Let x=5 4=4 x=5 is a valid solution. let x=85 x=85 is an extraneous solution, it's not valid. Therefore the solution is: Happy Calculating!!!
 Polynomials-and-rational-expressions/60916: Please can someone walk me through factoring this polynomial? Factor completely 64x^3-27 Thank you 1 solutions Answer 41867 by funmath(2925)   on 2006-11-11 15:34:21 (Show Source): You can put this solution on YOUR website!The formula you need to remember is: Factor completely Use the formula letting a=4x and b=3 Happy Calculating!!!
 Linear_Equations_And_Systems_Word_Problems/60915: This question is from textbook The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation. (b) Graph the cost equation. (c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation. (d) How many items must be produced for the revenue to equal the cost (the break-even point)?1 solutions Answer 41866 by funmath(2925)   on 2006-11-11 15:27:41 (Show Source): You can put this solution on YOUR website!The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). (a) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation. b=40, m=10 (b) Graph the cost equation. (c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation. (d) How many items must be produced for the revenue to equal the cost (the break-even point)? The lines intersect at (1,50), therefore the number of items that must be produced to break even is x=1. You could have found this algebraically by letting C=R 10x+40=50x 10x-10x+40=50x-10x 40=40x 40/40=40x/40 1=x Happy Calculating!!!
 Quadratic_Equations/60913: Please, please help with this question. I do not know where to go. When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground?1 solutions Answer 41865 by funmath(2925)   on 2006-11-11 15:15:04 (Show Source): You can put this solution on YOUR website!When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground? Use the quadratic formula: a=16, b=-96, c=23 and and and x=.25 s and x=5.75 s One the way up, the ball hits 103 ft in .25 s, on the way back down it hits it again in 5.75 s. Since this came out to rational answers this could have been factored. When the numbers are more difficult to deal with the quadratic formula is easier to use than factoring. Here's what it looks like factored. 4t-1=0 and 4t-23=0 4t=1 and 4t=23 t=1/4 s and t=23/4 s Happy Calculating!!!