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Angles/714949: I want to know what property(addition, subtraction, substitution, transitive, partition) is used, if x=2 and y=5, then xy=10
1 solutions
Answer 439084 by jim_thompson5910(28598)   on 2013-02-15 18:07:28 (Show Source):
You can put this solution on YOUR website!x*y = x*y ... reflexive property (any number is ALWAYS equal to itself)
x*y = 2*5 ... substitution property (ie you're replacing x with 2 and y with 5 on the right side)
x*y = 10 ... multiplication
So it sounds like the answer is substitution
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Parallelograms/714951: If someone draws a parallelogram and measures 120 degrees what is the measure of the three angles
1 solutions
Answer 439080 by jim_thompson5910(28598) on 2013-02-15 17:59:00 (Show Source):
You can put this solution on YOUR website!The adjacent angle is supplementary to the given angle. So the adjacent angle is 180 - 120 = 60 degrees
The angle opposite the 120 degree angle is also 120 degrees.
The angle opposite the 60 degree angle is also 60 degrees.
So the four angles are: 120, 60, 120, 60
Which means that the given angle is 120, while the other 3 angles are 60, 120, 60
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Sequences-and-series/714941: study the sequence,and find the pattern.then answer the question below. 1,2,4,7,11,16,22
1 solutions
Answer 439058 by jim_thompson5910(28598) on 2013-02-15 17:10:24 (Show Source):
You can put this solution on YOUR website!from 1 to 2 you add 1
from 2 to 4, you add 2
from 4 to 7, you add 3
from 7 to 11, you add 4
from 11 to 16, you add 5
from 16 to 22, you add 6
The values you add to jump from term to term are: 1,2,3,4,5,6
So the term would be 22+7 = 29 and the next term would be 29+8 = 37 and so on...
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Average/714927: For each of the described lines write an equation in point slope form
a) passing through (3,2) with the slope 1/5
b) passing through (-12,1) with the slope -2
Can you please help me? Thanks so much in advance
1 solutions
Answer 439042 by jim_thompson5910(28598) on 2013-02-15 15:59:37 (Show Source):
You can put this solution on YOUR website!a)
 Plug in the given slope
 Plug in the given point the line goes through
and you're done with part a)
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a)
 Plug in the given slope
 Plug in the given point the line goes through
 Simplify
and you're done with part b)
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Linear-systems/714887: What is the equation of line as a solution for the given pair (2,10) and (1,5)
1 solutions
Answer 439039 by jim_thompson5910(28598) on 2013-02-15 15:43:51 (Show Source):
You can put this solution on YOUR website!
First let's find the slope of the line through the points ) and )
Note: ) is the first point . So this means that  and  .
Also, ) is the second point . So this means that  and  .
 Start with the slope formula.
 Plug in , , , and
 Subtract  from  to get 
 Subtract  from  to get 
 Reduce
So the slope of the line that goes through the points and is
Now let's use the point slope formula:
 Start with the point slope formula
 Plug in , , and
 Distribute
 Multiply
 Add 10 to both sides.
 Combine like terms.
 Remove the trailing zero
So the equation that goes through the points and is
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test/714899: Graph equation and solve for y
y=-2x+1
1 solutions
Answer 439038 by jim_thompson5910(28598) on 2013-02-15 15:42:44 (Show Source):
You can put this solution on YOUR website!Looking at  we can see that the equation is in slope-intercept form  where the slope is  and the y-intercept is 
Since this tells us that the y-intercept is ) .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is  , this means:
which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1
So starting at , go down 2 units
and to the right 1 unit to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
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test/714926: Write a quadratic equation that opens up and has an axis of symmetry at x=0. Thank You.
1 solutions
Answer 439036 by jim_thompson5910(28598) on 2013-02-15 15:40:31 (Show Source):
You can put this solution on YOUR website!Anything of the form  , where  is a positive number and  is any real number, fits this the criteria you set.
So say a = 3 and b = 5 which gives us 
The equation has an axis of symmetry at x=0.
This is because the axis of symmetry formula is x = -b/2a, but notice how b = 0. So x = -b/2a = 0/2(3) = 0/6 = 0, which shows that x = 0 is the axis of symmetry.
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Polynomials-and-rational-expressions/714872: Factor the trinomial completely
12x^3-15x^2-18x
1 solutions
Answer 439032 by jim_thompson5910(28598) on 2013-02-15 15:35:39 (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
---------------------------------------------------------------
Looking at the expression , we can see that the first coefficient is  , the second coefficient is , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-24) = -24
2*(-12) = -24
3*(-8) = -24
4*(-6) = -24
(-1)*(24) = -24
(-2)*(12) = -24
(-3)*(8) = -24
(-4)*(6) = -24
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -24 | 1+(-24)=-23 | | 2 | -12 | 2+(-12)=-10 | | 3 | -8 | 3+(-8)=-5 | | 4 | -6 | 4+(-6)=-2 | | -1 | 24 | -1+24=23 | | -2 | 12 | -2+12=10 | | -3 | 8 | -3+8=5 | | -4 | 6 | -4+6=2 |
From the table, we can see that the two numbers  and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
--------------------------------------------------
So then factors further to 
===============================================================
Answer:
So completely factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
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Quadratic_Equations/714922: Please help me solve this question! I have to have it solved by tomorrow for school or i will receive a failing grade for not completing it and getting the right answer. Thanks in advance for your help.
Find the zeros of the problem: x^3 - 10x^2 + 25x = 0
I came out with the solution (0,5,5) but i think it might actually be (0,5,D.R.)
*(D.R. meaning double root)(^ meaning to the __ power)
1 solutions
Answer 439031 by jim_thompson5910(28598) on 2013-02-15 15:34:23 (Show Source):
You can put this solution on YOUR website!x^3 - 10x^2 + 25x = 0
x(x^2 - 10x + 25) = 0
x(x - 5)(x - 5) = 0
x = 0 or x-5 = 0 or x-5 = 0
x = 0 or x = 5 or x = 5
So the solutions are x = 0 or x = 5 or x = 5
You can say that the unique roots are 0 and 5, where 0 is a single root and 5 is a double root.
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Equations/714751: 7(p+3)-3p=5+6(p+5)-4p
1 solutions
Answer 438963 by jim_thompson5910(28598) on 2013-02-15 01:10:10 (Show Source):
You can put this solution on YOUR website! Start with the given equation.
 Distribute.
 Combine like terms on the left side.
 Combine like terms on the right side.
 Subtract  from both sides.
 Subtract  from both sides.
 Combine like terms on the left side.
 Combine like terms on the right side.
 Divide both sides by to isolate  .
 Reduce.
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Answer:
So the solution is
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Probability-and-statistics/714753: According to a recent study, 1 in every 6 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled 25 women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that more than 22 of the women sampled have not been the victim of domestic abuse.
Would like to see the formula that gives the answer 0.188687
1 solutions
Answer 438959 by jim_thompson5910(28598) on 2013-02-15 00:47:24 (Show Source):
You can put this solution on YOUR website!Let X = number of women who have not been the victim of domestic abuse
So each trial has a probability of 1 - 1/6 = 5/6 = 0.83333333333333
So
p = 0.83333333333333
n = 25
Now compute the following probabilities P(X = 23), P(X = 24), P(X = 25)
P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)
P(X = 23) = (25 C 23)*(0.83333333333333)^(23)*(1-0.83333333333333)^(25-23)
P(X = 23) = (25 C 23)*(0.83333333333333)^(23)*(0.16666666666667)^(25-23)
P(X = 23) = (300)*(0.83333333333333)^(23)*(0.16666666666667)^2
P(X = 23) = (300)*(0.015094938254969)*(0.0277777777777789)
P(X = 23) = 0.125791152124747
P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)
P(X = 24) = (25 C 24)*(0.83333333333333)^(24)*(1-0.83333333333333)^(25-24)
P(X = 24) = (25 C 24)*(0.83333333333333)^(24)*(0.16666666666667)^(25-24)
P(X = 24) = (25)*(0.83333333333333)^(24)*(0.16666666666667)^1
P(X = 24) = (25)*(0.0125791152124741)*(0.16666666666667)
P(X = 24) = 0.0524129800519766
P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)
P(X = 25) = (25 C 25)*(0.83333333333333)^(25)*(1-0.83333333333333)^(25-25)
P(X = 25) = (25 C 25)*(0.83333333333333)^(25)*(0.16666666666667)^(25-25)
P(X = 25) = (1)*(0.83333333333333)^(25)*(0.16666666666667)^0
P(X = 25) = (1)*(0.0104825960103951)*(1)
P(X = 25) = 0.0104825960103951
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To summarize, we found the following
P(X = 23)= 0.125791152124747
P(X = 24)= 0.0524129800519766
P(X = 25)= 0.0104825960103951
Now add up the individual probabilities to find P(X > 22)
P(X > 22) = P(X = 23)+P(X = 24)+P(X = 25)
P(X > 22) = 0.125791152124747+0.0524129800519766+0.0104825960103951
P(X > 22) = 0.18868672818711
So the probability that more than 22 of the women sampled have not been the victim of domestic abuse is roughly 0.18868672818711
If you want to round to 6 decimal places, you would get 0.188687
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Linear_Equations_And_Systems_Word_Problems/714737: Highway bridges often have expansion joints- small gaps between the bridge sections-that allow for the expansion of the bridge when the weather gets hot. Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F and that gap increases to 1 inch when the temperature is 50°F . Assume that there is a linear relationship between the width of the gap and the temperature.
1. Write an equation that expresses the width of the gap (W) as a function of the temperature (T).
I need HELP!!! Please I BEG OF U PLEASE HELP!!!
1 solutions
Answer 438953 by jim_thompson5910(28598) on 2013-02-14 23:47:41 (Show Source):
You can put this solution on YOUR website!Let x = gap width in inches and y = temperature in Fahrenheit
"Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75°F" means x = 1/2 and y = 75
"and that gap increases to 1 inch when the temperature is 50°F " means x = 1 and y = 50
Let's find the slope of the line through these two points
Slope:
m = (y2 - y1)/(x2 - x1)
m = (50 - 75)/(1 - 1/2)
m = (-25)/(1/2)
m = -50
So the slope is m = -50
Now use this to find the equation
y = mx + b
y = -50x + b ... plug in the slope we just found
50 = -50(1) + b ... plug in x = 1 and y = 50
50 = -50 + b
50 + 50 = b
100 = b
b = 100
So the equation is y = -50x + 100
Replace x with W since x = gap and y with T because y = temp to get
T = -50W + 100
Now solve for W (because we want an equation that expresses the width of the gap (W) as a function of the temperature (T))
So the final answer is
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Expressions-with-variables/714344: My question is: Use substitution to solve this- y=2x-5 & 3y-x=5
i tried adding them together then dividing it by 2, but it came out wrong.
1 solutions
Answer 438778 by jim_thompson5910(28598) on 2013-02-13 20:49:43 (Show Source):
You can put this solution on YOUR website!3y-x=5
3(2x-5)-x=5 ... plug in y = 2x-5 (ie replace y with 2x-5, we can do this because y and 2x-5 are the same)
6x - 15 - x = 5
5x - 15 = 5
I'll let you finish. You need to solve that equation for x. Once you have x, you can use that value of x, along with y = 2x - 5, to find y.
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Subset/714308: I am having trouble with subsets can you help me and tell me if i am on the right track?: list all the subsets of Q={2,4,6,8,10,12}
here is what I have so far:
{2} {2,4}
{4} {2,6}
{6} {2,8}
{8} {2,10}
{10} {2,12}
{12}
1 solutions
Answer 438769 by jim_thompson5910(28598) on 2013-02-13 20:32:17 (Show Source):
You can put this solution on YOUR website!List all the subsets that have 0 elements, 1 element, 2 elements, 3 elements, etc until you reach 6 like so
List of Subsets with Six Elements: Empty Set {}
List of Subsets with One Element: {2}, {4}, {6}, {8}, {10}, {12}
List of Subsets with Two Elements: {2, 4}, {2, 6}, {2, 8}, {2, 10}, {2, 12}, {4, 6}, {4, 8}, {4, 10}, {4, 12}, {6, 8}, {6, 10}, {6, 12}, {8, 10}, {8, 12}, {10, 12}
List of Subsets with Three Elements: {2, 4, 6}, {2, 4, 8}, {2, 4, 10}, {2, 4, 12}, {2, 6, 8}, {2, 6, 10}, {2, 6, 12}, {2, 8, 10}, {2, 8, 12}, {2, 10, 12}, {4, 6, 8}, {4, 6, 10}, {4, 6, 12}, {4, 8, 10}, {4, 8, 12}, {4, 10, 12}, {6, 8, 10}, {6, 8, 12}, {6, 10, 12}, {8, 10, 12}
List of Subsets with Four Elements: {2, 4, 6, 8}, {2, 4, 6, 10}, {2, 4, 6, 12}, {2, 4, 8, 10}, {2, 4, 8, 12}, {2, 4, 10, 12}, {2, 6, 8, 10}, {2, 6, 8, 12}, {2, 6, 10, 12}, {2, 8, 10, 12}, {4, 6, 8, 10}, {4, 6, 8, 12}, {4, 6, 10, 12}, {4, 8, 10, 12}, {6, 8, 10, 12}
List of Subsets with Five Elements: {2, 4, 6, 8, 10}, {2, 4, 6, 8, 12}, {2, 4, 6, 10, 12}, {2, 4, 8, 10, 12}, {2, 6, 8, 10, 12}, {4, 6, 8, 10, 12}
List of Subsets with Six Elements: {2, 4, 6, 8, 10, 12}
If you count up the individual sets, you'll find that there are 64 different sets. You can also use the formula 2^n to get 2^6 = 64
So again, there are 64 different possible subsets of {2, 4, 6, 8, 10, 12}
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test/714312: Basic factoring of x^2+2x-48
1 solutions
Answer 438766 by jim_thompson5910(28598) on 2013-02-13 20:25:08 (Show Source):
You can put this solution on YOUR website!
Looking at the expression  , we can see that the first coefficient is , the second coefficient is , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-48) = -48
2*(-24) = -48
3*(-16) = -48
4*(-12) = -48
6*(-8) = -48
(-1)*(48) = -48
(-2)*(24) = -48
(-3)*(16) = -48
(-4)*(12) = -48
(-6)*(8) = -48
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -48 | 1+(-48)=-47 | | 2 | -24 | 2+(-24)=-22 | | 3 | -16 | 3+(-16)=-13 | | 4 | -12 | 4+(-12)=-8 | | 6 | -8 | 6+(-8)=-2 | | -1 | 48 | -1+48=47 | | -2 | 24 | -2+24=22 | | -3 | 16 | -3+16=13 | | -4 | 12 | -4+12=8 | | -6 | 8 | -6+8=2 |
From the table, we can see that the two numbers and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF from the first group.
 Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
===============================================================
Answer:
So factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
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Polynomials-and-rational-expressions/714299: I've been trying to factor this all night but cannot figure it out. Please help...16z^2-54z+35 I've tried AC=560, factors 40 and 14 but that doesn't account for the -54, it's positive 54.
1 solutions
Answer 438750 by jim_thompson5910(28598) on 2013-02-13 19:50:55 (Show Source):
You can put this solution on YOUR website!
Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
-1,-2,-4,-5,-7,-8,-10,-14,-16,-20,-28,-35,-40,-56,-70,-80,-112,-140,-280,-560
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*560 = 560
2*280 = 560
4*140 = 560
5*112 = 560
7*80 = 560
8*70 = 560
10*56 = 560
14*40 = 560
16*35 = 560
20*28 = 560
(-1)*(-560) = 560
(-2)*(-280) = 560
(-4)*(-140) = 560
(-5)*(-112) = 560
(-7)*(-80) = 560
(-8)*(-70) = 560
(-10)*(-56) = 560
(-14)*(-40) = 560
(-16)*(-35) = 560
(-20)*(-28) = 560
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | 560 | 1+560=561 | | 2 | 280 | 2+280=282 | | 4 | 140 | 4+140=144 | | 5 | 112 | 5+112=117 | | 7 | 80 | 7+80=87 | | 8 | 70 | 8+70=78 | | 10 | 56 | 10+56=66 | | 14 | 40 | 14+40=54 | | 16 | 35 | 16+35=51 | | 20 | 28 | 20+28=48 | | -1 | -560 | -1+(-560)=-561 | | -2 | -280 | -2+(-280)=-282 | | -4 | -140 | -4+(-140)=-144 | | -5 | -112 | -5+(-112)=-117 | | -7 | -80 | -7+(-80)=-87 | | -8 | -70 | -8+(-70)=-78 | | -10 | -56 | -10+(-56)=-66 | | -14 | -40 | -14+(-40)=-54 | | -16 | -35 | -16+(-35)=-51 | | -20 | -28 | -20+(-28)=-48 |
From the table, we can see that the two numbers  and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
===============================================================
Answer:
So factors to .
In other words,  .
Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
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Rational-functions/714238: Hello, I am working with functions just substituting and solving problems. The given is f(x)=5x^2+4x-3 and what I am trying to solve is f(x+1) put into the equation. I understand that to substitute the problem would be f(x+1)=5(x+1)^2+4(x+1)-3 I am just unsure of how to solve. If you could help that would be great.
1 solutions
Answer 438736 by jim_thompson5910(28598) on 2013-02-13 18:06:36 (Show Source):
You can put this solution on YOUR website!f(x)=5x^2+4x-3
f(x+1)=5(x+1)^2+4(x+1)-3 ... so far, so good
Now you expand, distribute, and combine like terms to simplify
f(x+1)=5(x+1)(x+1)+4(x+1)-3
f(x+1)=5(x^2+2x+1)+4(x+1)-3
f(x+1)=5x^2+10x+5+4x+4-3
f(x+1)=5x^2+14x+6
So the answer is f(x+1)=5x^2+14x+6
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