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Equations/269876: The table shows the current heights and average growth rates of two different species of trees. How long will it take for the two trees to be the same height?
Tree Species | Current Height | Annual Growth
A 38 Inches 4 inches
B 45.5 Inches 2.5 Inches
Define Variables, Write an equation.
I would very much appreciate everyone's help!
1 solutions
Answer 197712 by drk(1908)   on 2010-02-15 15:51:17 (Show Source):
You can put this solution on YOUR website!The equation we need is
step 1 - subtract 38 to get
step 2 - subtract 2.5x to get
step 3 - divide by 1.5 to get
in 5 years they will be the same height
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Quadratic-relations-and-conic-sections/269877: If a right circular cone intersects a plane that passes through one of its nappes, but the plane is neither parallel to the edge of the cone nor perpendicular to the cone's axis, the resulting curve will be a(n)
1 solutions
Answer 197711 by drk(1908) on 2010-02-15 15:49:11 (Show Source):
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Probability-and-statistics/269858: An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same colour is 0.44. Calculate the number of blue balls in the second urn.
1 solutions
Answer 197706 by drk(1908) on 2010-02-15 15:32:26 (Show Source):
You can put this solution on YOUR website!Probability same color means 2 red or 2 blue
P(red from both) = (4/10) * 16/(16+b)
P(blue from both) = (6/10) * b/(16+b)
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The sum of these = .44 so we can say
(i) 
combining like terms, we get
(ii) 
cross multiply to get
(iii) 
distribute to get
(iv) 
subtract 64 and then subtract 4.4b to get
(v) 
divide to get
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Polynomials-and-rational-expressions/269865: I need help on finding the potential rational zeros of the polynomial function
f(x) = -4x^4 + 3x^2 - 4x + 6
1 solutions
Answer 197699 by drk(1908) on 2010-02-15 15:07:14 (Show Source):
You can put this solution on YOUR website!First we apply P - N - I to help us view sign changes and possible combinations.
P . . . . N . . . . I
3 . . . . 1 . . . .0
1 . . . . 1 . . . .2
So we know that there must be 1 real negative root.
-----------
next we apply P / Q as
P: +-1, +-2, +-3, +-6
Q: +-1, +-2, +-4
we take all possible fractions and get:
P/Q = +-1, +-1/2 +-1/4, +-2, +-3, +-3/2, +-3/4, +-6
This is our list of potential rational zeros
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Exponents/269864: I need help with an exponential function using data from a table.
x values are 1,3,5
y values are 48,108,243
the questions are
a. What is the growth factor?
b. What is the percent of growth?
c. Find the formula?
d. What is the initial value?
I know that the growth factor is 2.25 but I don't know where to go from there.
You help would be greatly appreciatied.
1 solutions
Answer 197698 by drk(1908) on 2010-02-15 15:01:40 (Show Source):
You can put this solution on YOUR website!x values are 1,3,5
y values are 48,108,243
the questions are
a. What is the growth factor?
answer:
the growth factor is
or r = 1.5
---
b. What is the percent of growth?
answer:
The percent of growth is
(1.5-1) x 100% = .5 x 100% = 50%
---
c. Find the formula?
answer:
---
d. What is the initial value?
answer:
initial value is 48.
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Rational-functions/269853: Hi. I am having trouble with the following problem. I understand everything except for the x-intercept part. I would greatly appreciate your help,
Thanks in advance.
Find an equation of a rational function f that satisfies the conditions:
vertical asymptotes: x = - 2, x = 0
horizontal asymptote: y = 0
x-intercept: 5; f (6) = 1
1 solutions
Answer 197693 by drk(1908) on 2010-02-15 14:50:44 (Show Source):
You can put this solution on YOUR website!Find an equation of a rational function f that satisfies the conditions:
vertical asymptotes: x = - 2, x = 0
we can write a general form as
(i) 
---
horizontal asymptote: y = 0
This means as x approaches infinity, then the function approaches zero. This happens when the degree of the numerator is less than the degree of the denominator
we keep our function at
(ii)
---
x-intercept: 5
If y = 0 , then x = 5.
From (ii) we get
(iii) 
cross multiply to get
5a+b = 0
solving for a , we get
(iv) 
---
f (6) = 1
means that if x = 6, then y = 1.
From (i) and (iv) we get
(vi) 
cross multiplying we get
(vii) 
multiply by common denominator of 5, we get
(viii) 
solving for b, we get
(ix) 
This means that
and our equation is
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Mixture_Word_Problems/269837: linda's cell phone bill is bill is $30 per month plus 5 cents for every minute over 300 minutes. last month she paid $31 for her cell phone usage. how many minutes did she use?
1 solutions
Answer 197691 by drk(1908) on 2010-02-15 14:32:08 (Show Source):
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Travel_Word_Problems/269831: A freight train and an express train leave towns 390km apart, traveling toward one another. The freight train travels 30km per hr slower than the express train. They pass one another 3 hr later. What are their speeds?
1 solutions
Answer 197684 by drk(1908) on 2010-02-15 14:04:55 (Show Source):
You can put this solution on YOUR website!This is an RTD problem. Here is a table based on the given information
trains . . . . . . . . .rate . . . . . . . . .time . . . . . . . . .distance
freight. . . . . . . . r - 30 . . . . . . . . .3 . . . . . . . . . . 3r - 90
express. . . . . . . .r . . . . . . . . . . . . 3 . . . . . . . . . . . 3r
totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .390
Look at the last column, we get
simplify to get
add 90 to get
divide to get
express: 
freight: 
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Rectangles/269821: What are the dimensions of a rectangle whose perimeter is 48 meters and whose area is 135 square meters?
1 solutions
Answer 197676 by drk(1908) on 2010-02-15 13:34:52 (Show Source):
You can put this solution on YOUR website!(i) P = 2L + 2W
we know that P = 48, so we get
(ii) 48 = 2L + 2W
dividing by 2 we get
(iii) 24 = L + W
solving for L, we get
(iv) L = 24 - W
--------
(v) A = LW
We know that A = 135, so we get
(vi) 135 = LW
substituting (iv) into (vi) we get
(vii) 135 = (24-W)(W)
expanding we get
(viii) 135 = -W^2 + 24W
setting = 0 we get
(ix) W^2 - 24W + 135 = 0
factoring, we get
(x) (W-15)(W-9) = 0
and then
W = 15
or
W = 9
----
answer: W = 9, L = 15 ; W = 15, L = 9
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Miscellaneous_Word_Problems/269822: Please help me solve the following word problem: A picture frame measures 12 centimeters by 20 centimeters. 48 cm^2 of the picture shows inside the frame. Find the length and width of the inside of the frame.
1 solutions
Answer 197673 by drk(1908) on 2010-02-15 13:30:01 (Show Source):
You can put this solution on YOUR website!Assume that the 48 cm^2 is centered in the picture. We get
(i) 
foil the left to get
(ii) 
set = 0 and in descending order, we get
(iii) 
factoring, we get
(iv) 
solving for x, we get
x = 4
or
x = 12
the dimensions of the inside of the frame are: 4 x 12
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Quadratic_Equations/269820: Please help me solve this problem by completing the square:  .
1 solutions
Answer 197670 by drk(1908) on 2010-02-15 13:21:15 (Show Source):
You can put this solution on YOUR website!step 1 - factor out 2 from the first and second term to get
the blanks are waiting for certain numbers.
step 2 - take (1/2) of the middl term and square it. Put that number in the first blank.
step 3 - squaring it gives us 25/16, but we multiply this by 2 since there are 2 groups of these. We get 50/16. Now put this number into the other blank space to get
step 4 - rewrite the trinomial as a binomial squared and simplify the right side to get
step 5 - divide by 2 and reduce to get
step 6 - take a square root to get
step 7 - add 5/4 to get
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Travel_Word_Problems/269818: luke road his bike on a trail that formed a right triangle. One leg of the right triangle was 5 kilometers longer than the other leg. they hypotenuse of the right triangle was 25 kilometers long. How far did he ride all together?
1 solutions
Answer 197669 by drk(1908) on 2010-02-15 13:14:37 (Show Source):
You can put this solution on YOUR website!The three sides are: x, x+5, 25. By Pythagorean theorem we get
(i) 
expanding, we get
(ii) 
combine like terms to get
(iii) 
set = 0 to get
(iv) 
factor to get
(v) 
So,
x = 15
or
x = -20
----
The three sides are: 15, 20, and 25
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Problems-with-consecutive-odd-even-integers/269817: solve by quadratic equation. Find 3 positive consecutive integers such that the sum of their squares is 245
1 solutions
Answer 197668 by drk(1908) on 2010-02-15 13:11:21 (Show Source):
You can put this solution on YOUR website!Let x, x+1 and x + 2 be 3 positive consecutive integers.
we get
(i) 
expanding, we get
(ii) 
combine like terms to get
(iii) 
set = 0 to get
(iv) 
factoring, we get
(v) 
and solving for x, we get
x = -10
or
x = 8.
The three numbers are 8, 9, and 10.
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Geometry_Word_Problems/269816: What could represent a cross section of a ball rolling along a flat surface?
a.circle with a tangent line
b.a circle with a secant line
c. a circle with a chord
d. an intercepted arc
1 solutions
Answer 197666 by drk(1908) on 2010-02-15 13:07:09 (Show Source):
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Linear-equations/269813: bob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out are many are quarters and how many are dimes.
1 solutions
Answer 197665 by drk(1908) on 2010-02-15 13:06:03 (Show Source):
You can put this solution on YOUR website!(i) 
(ii) 
step 1 - multiply (i) by -10 to get
(iii) 
step 2 - add (ii) and (iii) to get
(Iv) 
step 3 - divide by 15 to get
This means
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Numbers_Word_Problems/269624: The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.
1 solutions
Answer 197602 by drk(1908) on 2010-02-14 20:38:31 (Show Source):
You can put this solution on YOUR website!we have
(i) 
simplify the left side to get
(ii) 
cross multiply to get
(iii) 
set = 0 to get
(iv) 
factoring, we get
(v) 
So, x = -7 or x = 6
If x = -7 then x + 1 = -6 and we get -1/7 - (-1/6) = -1/7 + 1/6 = 1/42
If x = 6 then x + 1 = 7 and we get 1/6 - 1/7 = 1/42
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Miscellaneous_Word_Problems/269619: a cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool an the area of the walk is 700 square feet. How wide will the walk be?
1 solutions
Answer 197598 by drk(1908) on 2010-02-14 20:31:25 (Show Source):
You can put this solution on YOUR website!The pool covers 800 square feet.
The new cement walk plus pool will have dimensions
(i) 
the area of the walkway - area of pool = 700, or
(ii) 
distributing the left we get
(iii) 
simplify the left to get
(iv) 
subtract 700 and set = 0 to get
(v) 
solving for x by the quadratic, we get
x = -35 or x = 5.
SInce we can use x = -35, we have
x = 5
walkway = 5 feet wide
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Linear-equations/269620: input output change in output
x y=2x-6
-2 2(-2)-6=-10 2
-1 ? -8=?
0 ? ? ? ?
1 ? ? ? ?
2 ? ? ? ?
question is complete this table?
1 solutions
Answer 197595 by drk(1908) on 2010-02-14 20:15:26 (Show Source):
You can put this solution on YOUR website!here is the completed table:
input . . . . . . . . output . . . . . . . . . . . . . . . . change in output
x . . . . . . . . . . . y = 2x - 6 . . . . . . . . . . . . . . . .y = ?
-2 . . . . . . . . . . 2(-2) - 6 =-10 . . . . . . . . . . . . . .
-1 . . . . . . . . . . .2(-1) - 6 = -8 . . . . . . . . . . .(+2)
0 . . . . . . . . . . . 2(0) - 6 = -6 . . . . . . . . . . . .(+2)
1 . . . . . . . . . . . .2(1) - 6 = -4. . . . . . . . . . . . (+2)
2 . . . . . . . . . . . .2(2) - 6 = -2. . . . . . . . . . . . (+2)
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Inequalities/269622: 2(x-1)+3=x-3(x+1)what is x?
1 solutions
Answer 197593 by drk(1908) on 2010-02-14 20:08:51 (Show Source):
You can put this solution on YOUR website!here is the original problem
(i) 
step 1 - distribute to get
(ii) 
step 2 - simplify the left and right to get
(iii) 
step 3 - add 2x to both sides to get
(iv) 
step 4 - subtract 1 to get
(v) 
divide by 4 to get
(vi) 
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percentage/269621: results of surveying 200 high school seniors to find out how many hours they worked per week at a job. pie charts: 42 (15 hours or less) 82(more than 15 hours) 76 (Didn't work0
a. find the ratio of students who work more than 15 hours a week to total students
answers: 82/200=41/100
b. find the ratio of students who don't have a job to students who work more that 15 hours a week. answers: 76/200= 38=41
c. find the ratio of students with jobs to total students.
d. find the ratio of students with jobs to students without jobs.
I do not know how to solve problems c and d please help me.
1 solutions
Answer 197590 by drk(1908) on 2010-02-14 20:06:15 (Show Source):
You can put this solution on YOUR website!200 total students
students with jobs = 42 + 82 = 124
students without jobs = 76
----
c. find the ratio of students with jobs to total students.
answer
124/200 = 62/100 = 31/50
-----
d. find the ratio of students with jobs to students without jobs.
124/76 = 31/19
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Percentage-and-ratio-word-problems/269557: Where Sondra lives, there is a 3% state sales tax, a 1½% county sales tax, and a 1% municipal sales tax. How much tax would Sondra pay if she bought a $340 bicycle?
PLEASE PLEASE HELP! I'M STUCK ON THIS PROBLEM
1 solutions
Answer 197588 by drk(1908) on 2010-02-14 20:03:03 (Show Source):
You can put this solution on YOUR website!She buys the bike for $340
3% state sales tax = 340 * .03 = 10.20
1½% county sales tax = .015 * 340 = 5.10
1% municipal sales tax = .01 * 340 = 3.40
Bike + all taxes = 340 + 10.20 + 5.10 + 3.40 = $358.70
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