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Recent problems solved by 'drk'

drk answered: 1901 problems
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Evaluation_Word_Problems/267510: p=1/3mt for m
1 solutions

Answer 196286 by drk(1908) on 2010-02-09 09:49:30 (Show Source):

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step 1 - multiply by 3 to get
3p = mt
step 2 - divide by t to get
(3p)/t = m

Evaluation_Word_Problems/267511: A=P+PRT for T
1 solutions

Answer 196285 by drk(1908) on 2010-02-09 09:48:25 (Show Source):

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step 1 - subtract P to get
A - P = PRT
step 2 - divide by PR to get
(A - P) / PR = T

Numeric_Fractions/267496: Please help me Simplify.
(1 - 16x^(2)) / (16x^(2)+8x+1)
1 solutions

Answer 196284 by drk(1908) on 2010-02-09 09:47:38 (Show Source):

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%281+-+16x%5E2%29

factoring we get
%281-4x%29%281%2B4x%29

cancel the 4x + 1 to get
%281-4x%29%2F%284x%2B1%29

Probability-and-statistics/267508: A bag contains 6 red marbles,9 blue marbles,and 5 green marbles.you withdraw one marble,replace it'and then withdraw another marble.what is the probability that you do not pick two green marbles?
1 solutions

Answer 196283 by drk(1908) on 2010-02-09 09:44:17 (Show Source):

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There are 15 non green marbles.
P(non green) = 15/20
P(non green and then non green) = (15/20)*(15/20) = 225/400 = 9/16

Inverses/267506: What is the best metric unit to measure the distance between Los Angeles and New York City?
1 solutions

Answer 196281 by drk(1908) on 2010-02-09 09:42:33 (Show Source):

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The best metric unit is kilometers

Square-cubic-other-roots/267505: what is the square root of 150?
1 solutions

Answer 196280 by drk(1908) on 2010-02-09 09:41:46 (Show Source):

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If we prime factorize 150 we get 2 x 3 x 5^2
taking out a 5, we get
5*sqrt(6) ~ 12.247

Linear-equations/267501: Can you please explain how you find the rise, run and slope. I have to write the equation of each line in the standard form Ax+By=C, A>0.
1 solutions

Answer 196279 by drk(1908) on 2010-02-09 09:35:52 (Show Source):

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here is the original equation
Ax%2BBy=C

step 1 - subtract Ax to get
By+=+-Ax+%2B+C

divide by B to get
y+=+%28-A%2FB%29x+%2B+%28C%2FB%29

slope = -A/B
y - intercept = (C/B)
rise = -A and run = B

expressions/267485: Evaluate 5r - 3s when r = 3 and s = 5.
1 solutions

Answer 196277 by drk(1908) on 2010-02-09 09:23:23 (Show Source):

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5*3 - 3*5
15 - 15
0

Exponents/267388: what are six ways to solve 125^(-4/3)?
1 solutions

Answer 196256 by drk(1908) on 2010-02-08 21:48:15 (Show Source):

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I think I have all 6 ways:
(1)
125%5E%28-4%2F3%29%7D%7D%0D%0A%7B%7B%7B5%5E-4%7D%7D%0D%0A%7B%7B%7B1%2F5%5E4

---
(2)

125%5E%28-4%2F3%29%7D%7D%0D%0A%7B%7B%7B%281%2F125%29%5E%284%2F3%29

---
(3)

125%5E%28-4%2F3%29%7D%7D%0D%0A%7B%7B%7B%285%5E3%29%5E%28-4%2F3%29

---
(4)

---
(5)

---
(6)

125%5E%28-4%2F3%29%7D%7D%0D%0A%7B%7B%7B%28125%5E%28-4%29%29%5E%281%2F3%29

%28%285%5E3%29%5E%28-4%29%29%5E%281%2F3%29

Money_Word_Problems/267392: I have a total of $6000 invested in two simple interest accounts. The annual simple interest rate on one account is 9%. The annual simple interest rate on the second account is 6%. How much is invested in each account if both accounts earn the same amount of interest?
1 solutions

Answer 196253 by drk(1908) on 2010-02-08 21:37:59 (Show Source):

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This is an I = PRT problem. we have the formula
I = PRT and another I = PRT.
From above, we get
I = x(.09)(1)
and
I = (6000-x)(.06)(1)
since interest is equal set them equal to get
.09x = 360 - .06x
adding .06x we get
.15x = 360
dividing, we get
x = 2400 at 9%
6000-x = 3600 at 6%.

Rectangles/267389: find the area of a rectangle that measures 2 2/3 inches by 36 1/2 inches
1 solutions

Answer 196252 by drk(1908) on 2010-02-08 21:34:40 (Show Source):

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step 1 - turn your numbers into improper fractions to get
(8/3) and (73/2)
step 2 - area = length x width so we get
a = (8/3)*(73/2) = 292/3 = 97 1/3 square inches

Numbers_Word_Problems/267390: unit digit of a sum
11^11 + 14^14 + 16^16 whats the unit digit of this sum
1 solutions

Answer 196250 by drk(1908) on 2010-02-08 21:32:15 (Show Source):

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Look for patterns:
11^1 = 11
11^2 = 121
11^3 = 1331
I see the pattern of ending in 1.
---
14^1 = 14
14^2 = 196
14^3 = 2744
when the power is odd it ends in 4, and when it is even it ends in 6.
---
16^1 = 16
16^2 = 256
16^3 = 4096
The units digit is always 8.
---
we get 1 + 6 + 6 = 13
The final units digit will be 3.

Quadratic-relations-and-conic-sections/267384: Find the vertex. Is the vertex a maximum or minimum point? Graph the parabola.
a(x) = x^2 -4x +4
1 solutions

Answer 196249 by drk(1908) on 2010-02-08 21:29:00 (Show Source):

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Factoring the original equation, we get
(x-2)*(x-2)
However, that can be expressed as
(x-2)^2
SInce there is no number after the squared binomial, the vertex form of this is
y = (x-2)^2 + 0
The vertex is "opposite of the inside number, outside number"
so the vertex is (2,0)
The vertex shows us a minimum
Here is the graph
+graph%28+300%2C+200%2C+-5%2C+5%2C+-10%2C+10%2C+%28x-2%29%5E2%29+

+graph%28+300%2C+200%2C+-5%2C+5%2C+-10%2C+10%2C+%28x-2%29%5E2%29+

test/267380: Given y=x/(x^2+1), use the algebraic tests to determine symmetry with respect to both axes and the origin.
1 solutions

Answer 196248 by drk(1908) on 2010-02-08 21:27:06 (Show Source):

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To be symmetric to the x axis replace y with -y. we get
-y=x/(x^2+1)
which is
y=-x/(x^2+1)
or
f(x) - - - > -f(x)
therefore, not symmetric to the x axis
-----
To be symmetric to the y axis replace x with -x. we get
y = -x/(x^2+1)
or
f(x) - - -> -f(x)
therefore, not symmetric to the x axis
-----
To be symmetric to the origin replace x with -x AND y with -y. we get
-y=-x/(x^2+1)
which is
y=x/(x^2+1)
f(x) - - - -> f(x)
Therefore, symmetric to origin.
-----
here is the graph.
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F%28x%5E2%2B1%29%29+

+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F%28x%5E2%2B1%29%29+

Problems-with-consecutive-odd-even-integers/267375: Find two consecutive integers whose product is 6 less than the square of the larger number.
1 solutions

Answer 196247 by drk(1908) on 2010-02-08 21:21:29 (Show Source):

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%28x%29%28x%2B1%29+=+%28x%2B1%29%5E2+-+6

step 1 -expand both sides to get
x%5E2+%2B+x+=+x%5E2+%2B+2x+%2B+1+-+6

step 2 - combine like terms on the right to get
x%5E2+%2B+x+=+x%5E2+%2B+2x+-+5

step 3 - set = 0 as
0+=+x-5

step 4 - solve for x to get
x+=+5

----
we get
x = 5
x + 1 = 6

logarithm/267340: log%282%2C%2848x%5E3%29%29-log%282%2C%2812x%5E2%29%29=8

solve equation for x and round to nearest two decimal places.
1 solutions

Answer 196246 by drk(1908) on 2010-02-08 21:18:40 (Show Source):

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we start with
log%282%2C%2848x%5E3%29%29-log%282%2C%2812x%5E2%29%29=8

step 1 - subtraction of logs means divide the terms as
log%282%2C%2848x%5E3%29%2F%2812x%5E2%29%29=8

step 2 reduce the fraction to get
log%282%2C%284x%29%29=8

step 3 - rewrite using exponents as
2%5E8+=+4x

step 4 - divide to get
x+=+64

Quadratic-relations-and-conic-sections/267239: Identify the conic x^2-4y^2-4x-8y-4=0 and find its center and foci
1 solutions

Answer 196225 by drk(1908) on 2010-02-08 20:16:51 (Show Source):

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This conic is a hyperbola. The adjusted equation after completing the square is
%28x-2%29%5E2+-+4%28y%2B2%29%5E2+=+4+%2B4%2B4

%28x-2%29%5E2+-+4%28y%2B2%29%5E2+=+4+%2B4%2B4

%28x-2%29%5E2%2F12+-+%28y%2B2%29%5E2%2F3+=+1

The center is (2, -2)
The foci are sqrt(12+3) = sqrt(15)
The coordinates of the foci are
(2 +- sqrt(15), -2)

Miscellaneous_Word_Problems/267237: A group of 64 people attend a ball game. There were 3 times as many childre as there were adults in the group. Write a system of equations that you could use to set up this problem where a is the number of adults and c is the number of children in the group.
Solve the system of equations for c, the number of children in the group.
1 solutions

Answer 196179 by drk(1908) on 2010-02-08 17:19:20 (Show Source):

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(i) a+%2B+c+=+64

(ii)

by substitution, we get
(iii) 3a+%2B+a+=+64

we get
(iv) 4a+=+64%7D%7D+dividing%2C+we+get%0D%0A%28v%29+%7B%7B%7Ba+=+16

Pythagorean-theorem/267232: The diagonal of a computer monitor is measured to be 17 inches. If the width of the monitor is 12 inches, find the height of the monitor to the nearest inch. what is the height ? i have to show all work... thanks for helping
1 solutions

Answer 196178 by drk(1908) on 2010-02-08 17:12:14 (Show Source):

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What we have is Pythagorean theorem or
a%5E2+%2B+b%5E2+=+c%5E2

from above, we have
12%5E2+%2B+b%5E2+=+17%5E2

squaring 12 and 17 we get
144+%2B+b%5E2+=+289

subtracting 144 we get
b%5E2+=+145

by square roots we get
b+=+12.04

this rounds to 12 inches

Inequalities/267234: how to use formula A=s^2 for square 11 in length/11 in width
1 solutions

Answer 196177 by drk(1908) on 2010-02-08 17:08:22 (Show Source):

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Area = side x side
our side = 11
so we get
a = 11 x 11 = 121 square inches

Polynomials-and-rational-expressions/267203: I am trying to help my child with her homework. So, if you can explain it to me, maybe I can explain it to her.....without GIVING her the answer!
Find all of the zeros of the function:
h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156

h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156

I know how to figure out how many positive and negative zeros, but I don't understand how to figure out how many imaginary zeros. Then I don't know how to find all of the zeros.
1 solutions

Answer 196176 by drk(1908) on 2010-02-08 17:07:13 (Show Source):

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h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156

first we use a technique called P-N-I This gives us the positive negative and imaginary zero combinations
P . . . N . . . I
3 . . . 1 . . . 0
1 . . . .1 . . . 2
So, I see that we must have 1 negative root somewhere.
Next I apply synthetic division to get roots.
-1 // 1 . . . . -15 . . . . 70 . . . . -70 . . . . -156
. . . . . . . . . . .-1 . . . . 16 . . . . .-86 . . . . 156
. . . . .1 . . . . .-16 . . . 86 . . . . .-156 . . . .0
and then
6// 1 . . . . -16 . . . . 86 . . . . -156
. . . . . . . . . . 6 . . . . -60 . . . .156
. . . . .1 . . . -10 . . . 26 . . . . .0
So we know that -1 and 6 are roots.
Now we can factor x^2 - 10x + 26 using the quadratic as
x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A26+%29%29%2F%282%29+

x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A26+%29%29%2F%282%29+

and then

x+=+%2810+%2B-+sqrt%28-4%29%29%2F%282%29+

which gives us imaginary answers of
x+=+%285+%2B-+i%29+

-----
So, in total we have the following roots:
-6, 6, and 5 +-i

Linear_Equations_And_Systems_Word_Problems/267202: Ina Crespo rowed 7.5 miles down the Habashabee River in 1.5 hrs, but the return trip took her 2.5 hrs. Find the rate Ina rows in still water and the rate of the current
1 solutions

Answer 196162 by drk(1908) on 2010-02-08 16:19:18 (Show Source):

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This is an RTD problem. Here is a table based on the given information
rowing . . . . . . . rate . . . . . . . . . time . . . . . . . . . . distance
upriver. . . . . . . .r -c. . . . . . . . . . 2.5. . . . . . . . . . . . 7.5
downriver. . . . . .r + c. . . . . . . . . .1.5 . . . . . . . . . . . 7.5
total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
rate x time = distance. The distance are equal, so the rate x time parts are also equal. We get
2.5%28r-c%29+=+7.5

and

we get

adding down, we get
2r+=+8

and then

Now,

Graphs/267197: The top part says -
Graph each inequality in a coordinate plane.
5. x < y
I have no idea how to solve this as it gives me no numbers. She only have us examples such as 5x-4y>10.
1 solutions

Answer 196159 by drk(1908) on 2010-02-08 16:13:31 (Show Source):

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Maybe think about this as
y > x + 0
now the slope = 1
and the y intercept is 0.
put a dot at (0,0) now move 1 unit up and 1 unit to the right and place a second dot.
connect the dots with a dashed line.
shade up (away) from you.
looks like this
+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+y%3Ex%29+

+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+y%3Ex%29+

Parallelograms/267199: what is the perimeter of a parallelogram where one side is 12m and the other is 8m?
1 solutions

Answer 196158 by drk(1908) on 2010-02-08 16:10:50 (Show Source):

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Perimeter means add all sides. IN our case that would be 12 + 8 + 12 + 8 = 40m

Equations/267198: how would i find out the answer too the problem 16=4w+2w-2
1 solutions

Answer 196157 by drk(1908) on 2010-02-08 16:10:03 (Show Source):

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here is the original question
16=4w%2B2w-2

step 1 - combine like terms on the right to get
16+=+6w+-+2

step 2 - add 2 to get
18+=+6w

step 3 - divide by 6 to get
w+=+3

Circles/267155: what is the area of an ellipse with the major axis 20m and the minor axis 10m?
1 solutions

Answer 196156 by drk(1908) on 2010-02-08 16:07:18 (Show Source):

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The formula for area of ellipse is
A+=+pi%2A%28%28a%2Bb%29%2F2%29%5E2

where a and b are major and minor axis
* Note if a = r and b = r as in a circle, then the area would be pir^2
---
1/2 major = 10
1/2 minor = 5
so,
A+=+pi%2A%28%2810%2B5%29%2F2%29%5E2

or
56.25*pi meters squared.

Graphs/267126: Taking an on-line class and cannot find any examples of this in my book and I am at a loss. I can sketch graphs like 3x-2y =6, but I don't know how to solve and sketch greater than, less than, and greater than/less than equal to problems. Thank you.
Sketch the graph of 9 + 2y >= 5. (9 + 2 y greather than/equal to 5)

1 solutions

Answer 196105 by drk(1908) on 2010-02-08 12:50:57 (Show Source):

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Here are the general steps:
(1) solve for y.
* remember the negative 1 rule - if you multiply or divide by a negative, you reverse the inequality sign.
(2) if you see y > or y >= then shade up or away from you.
(3) if you see y < or y <= then shade down or toward you.
(4) If you see =, then draw a sold line
(5) if you do not see = , then draw a dashed (dotted) line.
That should help.
----
Sketch the graph of 9x + 2y >= 5. (9x + 2 y greater than/equal to 5)
step 1 - solve for y as
y >= (-9/2)x + (5/2)
step 2 - slope = (-9/2), y intercept = (5/2). Plot y intercept and then create a second dot with the slope.
step 3 - draw solid line because =.
step 4 - shade up and away because of >.
looks like this
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+y+%3E=+%28-9%2F2%29x+%2B+%285%2F2%29%29

+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+y+%3E=+%28-9%2F2%29x+%2B+%285%2F2%29%29

Matrices-and-determiminant/267123: find the determinant of this matrix
[A -2 O]
[4 A -4]
1 solutions

Answer 196102 by drk(1908) on 2010-02-08 12:43:21 (Show Source):

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This is a 2 x 3 matrix. You cannot find determinants of non-square matricies.

Matrices-and-determiminant/267121: determine whether the given systems are solvable
1. x+2y+3z =1
-x+y =-2
2x-3x+z =0
2. x+2y+3z =-1
4x+5y+6z =0
7x+8y+9z =1
1 solutions

Answer 196100 by drk(1908) on 2010-02-08 12:42:12 (Show Source):

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(1) is solvable
(2) not solvable - line 2 and three will cancel each other out

Miscellaneous_Word_Problems/267120: Bob gave 4/5 of his pencils to Barb, then gave 2/3 of the remaining pencils to Bonnie. Bob ended up with 10 pencils left, how many did he start with?
1 solutions

Answer 196095 by drk(1908) on 2010-02-08 12:19:31 (Show Source):

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bob gave (4/5) P
bob left (1/5) p
---
bob gave (2/3)(1/5)p
bob left (1/3)(1/5)p = 10
---
(1/3)(1/5)p = 10
becomes
(1/15)p = 10
multiply by 15 to get
p = 150
---

Pythagorean-theorem/267117: The shortest side of a triangle is one half the length of the middle side, plus 2 cm. The longest side of the triangle is one and one-half times the length of the middle side, less 2 cm. The perimeter of the triangle is 60 cm. How long are each of the sides?
1 solutions

Answer 196094 by drk(1908) on 2010-02-08 12:16:55 (Show Source):

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S = (1/2)m + 2
m = m
L = (3/2)m - 2
P = 60
----
P = short + middle + long
60 = (1/2)m + 2 + m +(3/2)m - 2
combine like terms to get
60 = 3m
divide to get
m = 20
s = 12
L = 28

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