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Recent problems solved by 'oberobic'
oberobic answered: 2303 problems
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1 solutions
Answer 350500 by oberobic(2304)   on 2011-11-14 18:26:57 (Show Source):
You can put this solution on YOUR website!The sum of the interior angles of a polygon is (n-2)*180, where n = number of sides.
.
(n-2)*180 = 2340
.
(n-2) = 2340/180 = 13
.
n - 2 = 13
.
n = 15
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Equations/531541: Four times a number minus twice another number is -16. The sum of the two numbers is -1.
1 solutions
Answer 350497 by oberobic(2304) on 2011-11-14 18:16:27 (Show Source):
You can put this solution on YOUR website!x + y = -1
so
x = -y-1
.
4x -2y = -16
.
substitute
.
4(-y -1) -2y = -16
.
-4y -4 -2y = -16
.
-6y = -12
.
y = 2
.
x + y = -1
.
x + 2 = -1
.
x = -3
.
Answer: x = -3, y = 2
.
Done.
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Mixture_Word_Problems/531551: The manager of a food store wants to create a blend of herbs that she can sell for $1 per once. She decides to make 8 ounces of a blend of oregano and sage. What will be the ratio of oregano to sage in the mixture?
1 solutions
Answer 350492 by oberobic(2304) on 2011-11-14 18:11:41 (Show Source):
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Graphs/531520: how do you solve 10a-37=6a+51
1 solutions
Answer 350481 by oberobic(2304) on 2011-11-14 17:55:36 (Show Source):
You can put this solution on YOUR website!You have to remember to do the same thing to both sides of the equation, whatever that might be.
.
10a-37=6a+51
.
Subtract 6a from both sides. That will cancel the 6a on the right side, so that all 'a' terms are on the left side.
.
4a -37 = 51
.
Add 37 to both sides. That will cancel the -37 on the left.
.
4a = 88
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Divide both sides by 4. That will eliminate the coefficient on 'a'.
.
a = 22
.
Always check the solution to make sure it is the correct answer.
Substitute 22 for 'a' and check the values.
.
10*22 -37 = 220 -37 = 183
6*22 + 51 = 132 + 51 = 183
183 = 183
Correct.
.
Answer: a = 22
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P.S. In the old days, teachers talked about "moving" factors from one side of the equation to the other. After years of confusion and frustration, I ran into a math teacher who explained that you have to do the same time to both sides. You cannot just "move" anything from one side to the other.
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Rational-functions/531502: graph y=(x+5)^2+5
1 solutions
Answer 350475 by oberobic(2304) on 2011-11-14 17:42:21 (Show Source):
You can put this solution on YOUR website!y = (x+5)^2 + 5
y = x^2 +10x +25 +5
y = x^2 +10x +30
.
You know this is a parabola. So find several values of x to calculate values of y.
.
The axis of symmetry is where x = -b/2a.
-10/2 = -5
.
The vertex is where the parabola ends. It occurs on the axis of symmetry.
y = (-5)^2 +10(-5) + 30
y = 25 -50 + 30
y = 5
.
Pick several points to either side of the vertex.
x = -4, y = 6
x = -6, y = 6
x = 0, y = 30
x = -10, y = 30
x = 5, y = 105
x = -15, y = 105
.
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Equations/531510: The perimeter of a rectangle is 50 centimeters. The length of the rectangle is one more than 3 times the width of the rectangle. What are the dimensions of the rectangle?
1 solutions
Answer 350472 by oberobic(2304) on 2011-11-14 17:29:24 (Show Source):
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Angles/531446: An angle has a degree measure such that its complement is 1/4 its supplement. Determine this angle's complement.
1 solutions
Answer 350455 by oberobic(2304) on 2011-11-14 15:59:36 (Show Source):
You can put this solution on YOUR website!Angle 'x' has a complement: 90-x.
Angle 'x' has a supplement: 180-x.
Angle 'x's' complement is 1/4 its supplement.
.
90-x = 1/4(180-x)
.
Multiply both sides by 4 to eliminate fraction.
.
4(90-x) = 180-x
.
Use distribute property to remove parentheses
.
360 -4x = 180 -x
.
Add 'x' to both sides and subtract 360 from both sides.
.
-3x = -180
.
Divide both sides by -3.
.
x = 60
.
Check this answer to see if it is correct.
The complement = 90-60 = 30.
The supplement = 180-60 = 120.
Is the complement 1/4 of the supplement?
Yes.
.
Answer: The angle is 60 degrees.
.
Done.
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Polynomials-and-rational-expressions/531099: I still need some assistance with these problems, the ones I think I have right I wrote down so someone could check it over for me. I would greatly appreciate any help on those problems and the ones I have not been able to figure out. Thanks so much in advance!
1. Divide and simplify 3x-27/14 divide by x-9/6x
2. Find all numbers for which the rational expression is undefined. q^3-2q/q^2-16
3. Multiply (5x+4)(7x^2+9x+4)
*is the answer (5x)(7x^2)+(5x)(9x)+(5x)(4)+(4)(7x^2)+(4)(9x)+(4)(4)
35x^3+45x^2+20x+28x^2+36x+16
answer**35x^3+73x^2+56x+16
4. Factor completely 3x^5-27x^4+9x^3
*is this answer 3x^3(x-3)(x-3)?
5. Subtract. Simplify, if possible. (4-v/v-7)-(6v-5/7-v)
*is the answer 9-7v/2v-14?
6. Perform the indicated operations and simplify (y-6/y-8) – (y+1/y+8 )+(y-40/y^2-64)
*is the answer y-47/(y+8)(y-8)?
7. Simplify by taking roots of the numerator and the denominator 3^sqrt
8x^14/y^3
8. Multiply and simplify. (4b^2/4b^2-24b+36)(4b-12/2b)
9. Solve. 2/v=6/v-1/3
10. Add. Simplify if possible. (3w/w^2-25) + (w/w-5)
*is the answer 4w/w^3-30?
1 solutions
Answer 350344 by oberobic(2304) on 2011-11-13 22:07:22 (Show Source):
You can put this solution on YOUR website!Please ask 1 question at a time.
.
1. Divide and simplify 3x-27/14 divide by x-9/6x
.
x=9/14
.
2. Find all numbers for which the rational expression is undefined. q^3-2q/q^2-16
.
If the expression is  then will be undefined for q = -4 or +4 because that will result in division by 0.
.
3. Multiply (5x+4)(7x^2+9x+4)
.
35*x^3+73*x^2+56*x+16
.
4. Factor completely 3x^5-27x^4+9x^3
.
3*x^3*(x^2-9*x+3)
.
5. Subtract. Simplify, if possible. (4-v/v-7)-(6v-5/7-v)
.
(-5*v-23/7)
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Quadratic_Equations/531111: The problem is 5x^2=-12x-5
Don't I set this to "0"?
I moved the -12x-5 over to the left (the other side of the =) to read:
5x^2+12x+5=0
Is this the final answer? I get confused on if I need to do anymore or if this should be the end of the problem.
Your help is greatly appreciated.
Cheers!
Angela
1 solutions
Answer 350343 by oberobic(2304) on 2011-11-13 21:47:02 (Show Source):
You can put this solution on YOUR website!Hint: You cannot "move" anything when dealing with equations. You must do the same thing to both sides of the equation. The notion of "moving" obscures that you are doing something to both sides.
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5x^2 = -12x + 5
.
Add 12x to both sides.
.
5x^2 +12x = (-12x+12x) + 5
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Subtract 5 from both sides.
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5x^2 +12x -5 = 0
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| 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=244 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 0.362049935181331, -2.76204993518133.
Here's your graph:
 |
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Equations/531113: Caroline's score is 5 less than twice Aikos score. It is also 45 points greater than Aiko's score. What score did the two girls receive?
1 solutions
Answer 350341 by oberobic(2304) on 2011-11-13 21:38:49 (Show Source):
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test/531086: 6x+6y=-6
5x+y=-13
1 solutions
Answer 350340 by oberobic(2304) on 2011-11-13 21:37:18 (Show Source):
You can put this solution on YOUR website!6x +6y = -6
5x + y = -13
.
divide the first equation by 6 and then subtract the second from it
.
x + y = -1
5x +y = -13
------------ subtract
-4x = 12
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x = -3
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substitute to find y
.
-3 +y = -1
y = 2
.
check these values using the second equation
5(-3) + 2 = -13
correct
.
Answer: x = -3, y = 2
.
Done.
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Sequences-and-series/531095: name two integers whose product is -18 and whose difference between the greatest and least is 9
1 solutions
Answer 350333 by oberobic(2304) on 2011-11-13 21:19:25 (Show Source):
You can put this solution on YOUR website!x and y are two integers.
.
x*y = -18
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x-y = 9
x = y+9
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(y+9)*y = -18
y^2 +9y + 18 = 0
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(y+3)(y+6) = 0
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y = -3 or -6, which means x = 6 or 3, respectively
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The ordered pairs would be: (6,-3) or (3,-6)
.
Done.
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Word_Problems_With_Coins/531081: You have 100 coins in nickels,dimes, and quarters. The value of the coins is $21.25. You have 3 more nickels than dimes. What are the three equations that you would use to solve this problem?
1 solutions
Answer 350329 by oberobic(2304) on 2011-11-13 21:05:20 (Show Source):
You can put this solution on YOUR website!n + d + q = 100
.
5n +10d +25q = 2125
.
n = d+3
.
d+3 +d +q = 100
2d + q = 97
.
5(d+3) + 10d + 25q = 2125
5d +15 +10d + 25q = 2125
15d +25q = 2110
.
2d + q = 97
15d +25q = 2110
.
50d + 25q = 2425
15d + 25q = 2110
------------------ subtract
35d = 315
.
d = 115/35
d = 9 dimes
.
n = d+3 = 12 nickels
.
q = 100 -9 -12
q = 79 quarters
.
Check the values to determine if the answer is correct.
12(5) + 10(9) + 25(79) = 2125 ??
Yes.
.
Answer: 12 nickels, 9 dimes, and 79 quarters
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Mixture_Word_Problems/531060: A Chemist has a mixture that is 10% iodine and another that is 50% iodine. How much of each solution should the druggist use to get 100 ml of a solution that is 20% iodine
1 solutions
Answer 350324 by oberobic(2304) on 2011-11-13 20:19:59 (Show Source):
You can put this solution on YOUR website!The chemist needs 100 ml of a 20% solution.
.2*100 ml = 20 ml of pure iodine in the 100 ml solution.
.
The chemist has 10% solution and 50% solution.
.
x = 10% solution
y = 50% solution
.
x + y = 100 ml
x = 100-y ml
.
.1x + .5y = .2*100
.
multiply by 10 to eliminate the decimals
.
1*x + 5*y = 2*100
.
substitute
.
(100-y) + 5y = 200
100 + 4y = 200
4y = 100
y = 25 ml of 50% iodine
.
x = 100-25
x = 75 ml of 10% iodine
.
Check the amount of pure stuff to be sure this is the answer.
.5*25 = 12.5 ml
.1*75 = 7.5 ml
12.5 + 7.5 = 20 ml, which is the amount we need.
Correct.
.
Done.
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Finance/531061: If you add pure alcohol to a 15% solution, what percent alcohol are you adding, and how do you represent the percentage in decimal form?
1 solutions
Answer 350321 by oberobic(2304) on 2011-11-13 20:10:44 (Show Source):
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Money_Word_Problems/531054: A chlds bank contains $6.30 in dimes and quarters. There are twice as many dimes as quarters. How many of each kind of coin are in the bank?
1 solutions
Answer 350317 by oberobic(2304) on 2011-11-13 20:06:32 (Show Source):
You can put this solution on YOUR website!With coin problems you need to keep track of the count of the coins and the value.
d = number of dimes
10d = value of the dimes in cents
q = number of quarters
25q = value of the quarters in cents
.
10d + 25q = 630 cents
.
d = 2q
.
substitute
.
10(2q) + 25q = 630
20q + 25q = 630
45q = 630
q = 14
.
d = 2q
d = 2*14 = 28
.
Check the values to be sure this answer is right.
25(14) = 350 cents
10(28) = 280 cents
total = 630 cents
Correct.
.
Answer: The child has 14 quarters and 28 dimes.
.
Done.
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Mixture_Word_Problems/531021: I'm trying to figure out the formula for this word problem. If I can figure out the formula for mixtures I should be able to do the entire worksheet.
Sample Problem: A Chemist has a solution that is 12% acid and another solution that is 42% acid. She wants 10L of solution that is 30% acid. How much of each solution should she mix?
1 solutions
Answer 350306 by oberobic(2304) on 2011-11-13 19:43:26 (Show Source):
You can put this solution on YOUR website!With solution problems you need to determine how much 'pure' stuff you have or need.
.
The chemist needs 10 liters of a 30% acid. .3*10 = 3 liters of 'pure' acid in a solvent (likely water).
.
She has 12% acid and 42% acid to mix together.
.
x = liters of 12% acid
y = liters of 42% acid
x+y =10
so
x = 10-y
or
y = 10 - x
.
.12*x + .42*y = .3*10
.
multiply by 100 to eliminate decimals
.
12x + 42y = 30*10
.
substitute for x
.
12(10-y) + 42y = 300
120 -12y + 42y = 300
30y = 180
y = 6
.
Answer: Mix 6 liters of 42% acid and 4 liters of 12% acid.
.
Check the amount of pure acid to be sure this answer is correct.
.42*6 = 2.52
.12*4 = 0.48
2.52 + .48 = 3.0
Correct.
.
Done.
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