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# Recent problems solved by 'richwmiller'

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 Circles/290259: Two circles with exactly three common tangents1 solutions Answer 210064 by richwmiller(9135)   on 2010-04-09 12:02:10 (Show Source): You can put this solution on YOUR website!Do you have a question about the circles? Otherwise I would like to order a dozen.
 Graphs/290283: I am getting ready to take the praxis I math test, and I am strugging with questions about graphing inequalities like this one: y=x^-2x. would you explain how to graph this one and if you have another example too please. My email: pierceluisa@yahoo.com thank you Luisa Pierce 1 solutions Answer 210062 by richwmiller(9135)   on 2010-04-09 11:59:57 (Show Source): You can put this solution on YOUR website!We have a problem with your problem. It is not an inequality. Inequalities use > and < But one way to graph an inequality is to change from < and > to equal and graph it and then decide if the line of the equation is included or not above or below or inside or outside
 test/290285: Two numbers are in the ratio of 3:7. Find the numbers if their sum is 90.1 solutions Answer 210060 by richwmiller(9135)   on 2010-04-09 11:56:26 (Show Source): You can put this solution on YOUR website!3x+7x=90 10x=90 x=9 3*9=27 7*9=63 check 27/63=3/7 ok
 Sequences-and-series/290287: 1)Frances has paints in 4 different colors, She is going to paint the inside of a box with one color and the outside of the box with another color, in how many ways can she paint the box? I GOT 30 WAYS, but I'm not sure! 1 solutions Answer 210059 by richwmiller(9135)   on 2010-04-09 11:54:24 (Show Source): You can put this solution on YOUR website!4*3 She can choose 4 different colors outside and the inside can't be one of them so she has 3 choices inside 12 choices total How did you get 30?
 Problems-with-consecutive-odd-even-integers/290286: the sum f two even integers is 194. what are they? use the variable n for the value of the smaller integers1 solutions Answer 210055 by richwmiller(9135)   on 2010-04-09 11:48:54 (Show Source): You can put this solution on YOUR website!At first you might think that there is not enough info. n+n+2=194 2n=192 n=96 96+98=194 ok
 logarithm/290256: Express this equation in logarithmic form. b^x = N 1 solutions Answer 210054 by richwmiller(9135)   on 2010-04-09 11:31:50 (Show Source): You can put this solution on YOUR website!One way is x = (log(N))/(log(b)) in natural log
 Graphs/290279: Hi. I need help with writing the following equation in y=mx+b form, with slope -1/2 and y-intercept 11. Thanks.1 solutions Answer 210051 by richwmiller(9135)   on 2010-04-09 11:24:10 (Show Source): You can put this solution on YOUR website!slope is m y intercept is b m=-1/2 b=11 y=mx+b Just plug them in
 Quadratic_Equations/289684: I do not understand how to figure the solution to the equation: x^2 + x + sqrt x^2 +x -2 = 0. I was hoping you would be able to help me understand this a little more.1 solutions Answer 210050 by richwmiller(9135)   on 2010-04-09 11:22:06 (Show Source): You can put this solution on YOUR website!please use parentheses . what goes with sqrt?
 Miscellaneous_Word_Problems/290233: The number of positive integers k for which the equation kx − 12 = 3k has an integer solution for x is A.3 B. 4 C. 5 D. 6 E. 7 1 solutions Answer 210046 by richwmiller(9135)   on 2010-04-09 11:14:47 (Show Source): You can put this solution on YOUR website!k (x-3) = 12 k=12/(x-3) 6 integer solutions for k>0 1, 2,3 4, 6,12 All the positive factors of 12 x=15,9,7,6,5,4
 Quadratic-relations-and-conic-sections/290241: Graph 4x squared plus 25y squared equals one hundred on a graphing calculator. I dentify the conic section. Then, describe the center and intercepts.1 solutions Answer 210045 by richwmiller(9135)   on 2010-04-09 10:48:18 (Show Source): You can put this solution on YOUR website!4x^2+25y^2=100 That is an ellipse center at the origin 0,0 x=0 y=-2 and +2 x=+5 and -5 y=0
 Angles/290254: In trinagle ABC, angles A & B have the same measure, while the measure of C is 75 degrees larger than each of A & B. What are the measures of the 3 angles?1 solutions Answer 210044 by richwmiller(9135)   on 2010-04-09 10:41:49 (Show Source): You can put this solution on YOUR website!a=b c=75+a a+b+c=180 35, 35, 110
 Conjunction/290268: deductive reasoning argument: All cats have fur. Frisky is a cat. Therefore, by deductive reasoning, I can conclude,....1 solutions Answer 210043 by richwmiller(9135)   on 2010-04-09 10:38:41 (Show Source): You can put this solution on YOUR website!Frisky is an annoying cat with fur balls everywhere. Oops, I meant Frisky has fur.
 Radicals/290267: what is the solution for square root of 2/3 times square root 5/6 1 solutions Answer 210042 by richwmiller(9135)   on 2010-04-09 10:36:16 (Show Source): You can put this solution on YOUR website! sqrt(2/3)*sqrt(5/6)=sqrt(2/3*5/6)=
 Pythagorean-theorem/290266: Find the length of side a in the right triangle, if b = 4 and c=5. a =1 solutions Answer 210041 by richwmiller(9135)   on 2010-04-09 10:31:27 (Show Source): You can put this solution on YOUR website!3,4, 5 is a classic right triangle. You should know it and 5,12,13 otherwise x^2+4^2=5^2 x^2+16=25 x^2=9 x=3 reject neg root
 Travel_Word_Problems/290262: trains a and b are traveling in the same direction on parallel tracks. Train A is traveling at 60 MPH and train B is traveling at 80 MPH. Train A passes a staion at 4:10PM. If train B passes that same station at 4:22PM, at what time will train B catch up with Train A? Exact time am or pm1 solutions Answer 210040 by richwmiller(9135)   on 2010-04-09 10:28:43 (Show Source): You can put this solution on YOUR website!60*1/5=12 miles 80=60=20 20*x=12 x=12/20=6/10 6/10*60=36 minutes 4:22+0:36=4:58 pm or this way 60*(t+1/5)=80*t 60t+12=80t 12=20t 12/20=t 6/10=t 6/10*60=36 minutes=t 4:22+0;36=4:58 pm
 Probability-and-statistics/290261: Mark has 10 red marbles and 15 blue in a bag. He reaches into choses one without looking and sets it aside. He draws another. what is the probabiliy that he draws 2 blue marbles. What is the %?1 solutions Answer 210039 by richwmiller(9135)   on 2010-04-09 10:22:44 (Show Source): You can put this solution on YOUR website!25 marbles to start 15 blue to start 15/25*14/24 3/5*7/12=21/60=35%
 Miscellaneous_Word_Problems/290257: Can use some help with a word problem. This is what it is: A biologist recorded 2 snakes on 9 acres in one area and 9 snakes on 12 acres in another are. Let s be the number of snake and a be the number of acres. Find a linear equation that you could use to calculate for any number of acres. I tried to put the numbers in the formula of y=mx+b (2,9)and (9,12). I solved for m and got -3/7, but I know I am doing something wrong because we have choices as: a)s=7a b)3s=-2a+9 c)3s-7a-57 d)3s-7a I do not know what I am doing wrong because my final answer was y=6/7+b. 1 solutions Answer 210035 by richwmiller(9135)   on 2010-04-09 10:14:10 (Show Source): You can put this solution on YOUR website!First you have the x and y backwards. x (a) is acres and y (s) is snakes (9,2) and (12, 9) so s=ma+b But first we have to find the slope (y-y)/(x-x)=m or in this case (s-s)/(a-a)=m (9-2)/(12-9)=7/3=m 7/3=m s=(7/3)*a+b now plug in either point 2=(7/3)*9+b 2=63/3+b 2=21+b -19=b s=7a/3-19 3s=7a-57 The closest answer is c 3s-7a-57 I think you copied - for = Double check your answer options Perhaps you copied them wrong.
Quadratic_Equations/290255: Dear tutor, I am in Iraq about to fail my math class. Can you please assist with these problems?
Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x = 1 is the day tickets go on sale).
tickets = -0.2^2 + 12x + 11
In this equation, does the graph of the equation open up or down?
Describe what happens to the tickets sales as time passes?
Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.
After how many days will the peak or low occur?

1 solutions

Answer 210030 by richwmiller(9135)   on 2010-04-09 09:56:34 (Show Source):
You can put this solution on YOUR website!
You forgot the x^2 in the first term which caused this equation to be a straight line rather than a parabola.

t= -0.2x^2 + 12x + 11
opens down - Notice the x^2 term is minus
This is a parabola like the St Louis Arch .
It rises then peaks and falls
The graph below doesn't show the arch because the numbers shown are too small
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=152.8 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:

The solutions tells when t is zero.
The peak will be -b/2a=-12/-2*.2=120/4=30
-b/2a is the x of the vertex and the axis of symmetry.
The peak occurs on the 30th day.
The last day is 60.9 or on the 61st day
And apparently some tickets were sold the day before tickets were sold.

 Sequences-and-series/289472: Which sequence follows the rule 6n-2, where n represents the position in the sequence? a. 6, 12, 18, 24 b. 4, 10, 16, 22 c. 4, 12, 16, 24 d. 4, 12, 18, 22 1 solutions Answer 210026 by richwmiller(9135)   on 2010-04-09 09:29:26 (Show Source): You can put this solution on YOUR website!plug in 1 then 2 then 3 then 4 and solve them. 6*1-2=6-2 6*2-2=12-2 6*3-2=18-2 6*4-2=24-2
 Problems-with-consecutive-odd-even-integers/290166: The sum of two numbers is 32; the larger number is 12 greater than twice the smaller. What are the 2 numbers?1 solutions Answer 210016 by richwmiller(9135)   on 2010-04-09 07:21:54 (Show Source): You can put this solution on YOUR website!10 and 22 don't work because the 22 is not 12 greater than twice the smaller it is only 12 greater than the smaller. 32-12=20 20/3=smaller and 40/3+12= larger 6 2/3 12 4/3=13 1/3+12=25 /13 25 1/3+6 2/3=32 check 25 1/3-12=13 1/3 13 1/3 is twice 6 2/3 ok Answer 25 1/3 6 2/3 which is equal to maththerapy's answer since 20/3=6 2/3 76/3=25 1/3
 Word_Problems_With_Coins/290168: Ann, Ben, and Carol have some money. If Ann gives Ben 30 cents, then Ben will have twice as much as Ann. If Ben givens Carol 30 cents, then Carol will have as much as Ben. If Carol gives Ann 15 cents, they will both have the same amount of money. How much money to they each have?1 solutions Answer 210014 by richwmiller(9135)   on 2010-04-09 06:55:42 (Show Source): You can put this solution on YOUR website!2*(a-30)=(b+30) b-30=(c+30) c-15=a+15 a = 180, b = 270, c = 210
 Pythagorean-theorem/290201: A portable ladder is needed to climb onto a rooftop 24 feet high. How long should the ladder be? How far should its base set away from the building wall? Explain your answer and show your calculation.1 solutions Answer 210013 by richwmiller(9135)   on 2010-04-09 06:38:29 (Show Source): You can put this solution on YOUR website!24^2+b^2=c^2 if c=25 ladder then b =7 ft away from bldg. if c=26 then b=10
 Polynomials-and-rational-expressions/290199: Find the Horizontal Asymptote. I tried doing this problem: If the numerator and denominator of the equation had the same highest degree, then I would just divide the coefficients. What if the equation was bottom "heavy" or the denominator has a higher degree than the numerator? I got confused from here. Please help! Thank you!1 solutions Answer 210012 by richwmiller(9135)   on 2010-04-09 06:25:26 (Show Source): You can put this solution on YOUR website! The degree on the denominator (namely, 3) was bigger than the degree on the numerator (namely, 2), and the horizontal asymptote was y = 0 (the x-axis). This property is always true: If the degree on x in the denominator is larger than the degree on x in the numerator, then the denominator, being "stronger", pulls the fraction down to the x-axis when x gets big. That is, if the polynomial in the denominator has a bigger leading exponent than the polynomial in the numerator, then the graph trails along the x-axis at the far right and the far left of the graph.
 Pythagorean-theorem/290182: how do u do perimeters and diagonals1 solutions Answer 210011 by richwmiller(9135)   on 2010-04-09 06:03:26 (Show Source): You can put this solution on YOUR website!a) carefully b) very well What do you want to do with them?
 Mixture_Word_Problems/290207: How many ounces of a 20% acid solution must be mixed with 30 ounces of a 60% solution to obtain a 50% solution?1 solutions Answer 210010 by richwmiller(9135)   on 2010-04-09 05:58:39 (Show Source): You can put this solution on YOUR website!.2x+30*.6=(30+x)*.5 x=10 oz.
 Miscellaneous_Word_Problems/290210: In an archery competition, Galen hits the bullseye three times as often as Jason. Jason hits it four times fewer than Kevin and Eddy hits it one less than twice the number of times that Kevin does. Nathalie hits the bullseye as many times as Jason and Galen combined. If Kevin hits the bullseye 9 times, how many times was the bullseye hit? (A)24 (B) 42 (C) 54 (D) 60 (E) 66 1 solutions Answer 210009 by richwmiller(9135)   on 2010-04-09 05:56:05 (Show Source): You can put this solution on YOUR website!g=3j j=-4+k e=2k-1 n=j+g k=9 g = 15, j = 5, k = 9, n = 20, s = 17 total 66
 Numbers_Word_Problems/290204: It takes Carolyn 4 hour to type a final exam. It takes Elise 3 hour to do the same job. How long would it take them, working together, to do the typing?1 solutions Answer 210008 by richwmiller(9135)   on 2010-04-09 05:51:14 (Show Source): You can put this solution on YOUR website!x/4+x/3=1 3x+4x=12 7x=12 x=12/7 1 5/7 hours together check 12/7/4=3/7 12/7/3=4/7 Carolyn does 3/7 and Elise does 4/7 of the work.
 Coordinate-system/290214: How far from the origin is the line 3x + 4y = 100? (a)20 (b) 21 (c) 22 (d) 23 (e) None of the above 1 solutions Answer 210007 by richwmiller(9135)   on 2010-04-09 05:47:02 (Show Source): You can put this solution on YOUR website!4 steps a)find the slope of he given line. b)find a line perpendicular c)Find a point with the new slope (intersection of two lines) d) Find distance between two points. e) answer question a)3x+4y=100 -a/b=-3/4 so we want 4/3 b)y=mx+b 0=0+b b=0 c)y=4x/3 4y=100-3x y=-3x/4+100 y=4x/3 4x/3=-3x/4+100 14x=-9x+1200 25x=1200 x=1200/25=48 x=48 y=4x/3 y=16*3*4*x/3 y=64 d)64^2+48^2=d^2 d=80 e)Answer none of the above
 Linear_Equations_And_Systems_Word_Problems/290176: A shopkeeper has two types of coffee beans on hand. One type sells for \$3.20 per lb, the other for \$7.80 per lb. How many pounds of the \$3.20 per lb coffee beans must be used in the mixture to produce 80 lbs of a blend that sells for \$5.04 per lb? Round your answer to 2 decimal places. 1 solutions Answer 209989 by richwmiller(9135)   on 2010-04-08 22:59:34 (Show Source): You can put this solution on YOUR website!(3.2*x)+(7.8*y)=(80)*5.04 x+y=80 x=48 y=32
 Mixture_Word_Problems/290177: I have 2 problems, hear they are. A gallon of vinegar is labelled 5% acidity. How many fluid Ounces of pure acid must be added to get 6% acidity? 1 solutions Answer 209988 by richwmiller(9135)   on 2010-04-08 22:51:12 (Show Source): You can put this solution on YOUR website!Guess what? This website has rules. "Hear" are some of them. One problem at a time. No similar problems. Limit 4 problems daily. (128*.05)+x=.06*(x+128) x=1.3617