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 Graphs/729208: y=-4x+2 I don't know how to graph this1 solutions Answer 445767 by jim_thompson5910(28595)   on 2013-03-21 19:54:32 (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 -4 and the run is 1. This means that to go from point to point, we can go down 4 and over 1 So starting at , go down 4 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
 Rational-functions/729178: Find the slope and the equation of the line passing through (-5,4) and (-5,1) Thanks so much!1 solutions Answer 445766 by jim_thompson5910(28595)   on 2013-03-21 19:54:02 (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 Remember, you cannot divide by zero. So this means that the slope is undefined. Since the slope is undefined, this means that the equation of the line through the points and is .
 Rational-functions/729184: Find the equation of the line that has a slope of 2 and passes through the point (1,4). THANK YOU! :)1 solutions Answer 445765 by jim_thompson5910(28595)   on 2013-03-21 19:52:17 (Show Source): You can put this solution on YOUR website!y = mx + b y = 2x + b 4 = 2(1) + b 4 = 2 + b 4 - 2 = b 2 = b b = 2 So the answer is y = 2x + 2
Polynomials-and-rational-expressions/729201: Factor by grouping. (If the expression is nonfactorable enter PRIME.)
50x2 – 50x – 12
1 solutions

Answer 445764 by jim_thompson5910(28595)   on 2013-03-21 19:51:15 (Show Source):
You can put this solution on YOUR website!

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 :
1,2,3,5,6,10,15,25,30,50,75,150
-1,-2,-3,-5,-6,-10,-15,-25,-30,-50,-75,-150

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-150) = -150
2*(-75) = -150
3*(-50) = -150
5*(-30) = -150
6*(-25) = -150
10*(-15) = -150
(-1)*(150) = -150
(-2)*(75) = -150
(-3)*(50) = -150
(-5)*(30) = -150
(-6)*(25) = -150
(-10)*(15) = -150

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-1501+(-150)=-149
2-752+(-75)=-73
3-503+(-50)=-47
5-305+(-30)=-25
6-256+(-25)=-19
10-1510+(-15)=-5
-1150-1+150=149
-275-2+75=73
-350-3+50=47
-530-5+30=25
-625-6+25=19
-1015-10+15=5

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

===============================================================

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).

Polynomials-and-rational-expressions/729202: Factor by grouping. (If the expression is nonfactorable enter PRIME.)
4a2 + 7ab - 2b2
1 solutions

Answer 445763 by jim_thompson5910(28595)   on 2013-03-21 19:48:45 (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 coefficient is .

Now multiply the first coefficient by the last coefficient 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 :
1,2,4,8
-1,-2,-4,-8

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-8) = -8
2*(-4) = -8
(-1)*(8) = -8
(-2)*(4) = -8

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-81+(-8)=-7
2-42+(-4)=-2
-18-1+8=7
-24-2+4=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 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).

 Equations/729203: how do you substitute y=7x y=5x-141 solutions Answer 445762 by jim_thompson5910(28595)   on 2013-03-21 19:48:04 (Show Source): You can put this solution on YOUR website!Hint: y=5x-14 7x=5x-14 ... plug in y = 7x now solve for x, then use the answer for x to get the value for y
Conjunction/729129: Construct a truth table for the statement, (p <--->q) --->p
Any help would be greatly appreciated. Or an example of a very similar problem with the exact same punctuations etc. Please help!!! Thank you
1 solutions

Answer 445739 by jim_thompson5910(28595)   on 2013-03-21 17:48:54 (Show Source):
You can put this solution on YOUR website!
Here's what the completed table looks like

Keep in mind that p <--> q is only true if BOTH p AND q have the same truth value (ie both are true or false together)

Also, p --> q is only false when p is true and q is false. Otherwise it's true.

 p q p <--> q (p <--> q) --> p T T T T T F F T F T F T F F T F

 Inequalities/729116: what is the answer for -4x+2>10 1 solutions Answer 445734 by jim_thompson5910(28595)   on 2013-03-21 17:14:27 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Age_Word_Problems/729100: One CD player is 3 times as much as another. Together the two CD players would be $320. What is the price of the more expensive CD player?1 solutions Answer 445721 by jim_thompson5910(28595) on 2013-03-21 16:47:14 (Show Source): You can put this solution on YOUR website!Let x = price of cheaper player y = price of more expensive player Since "One CD player is 3 times as much as another", we can say (according to the definition made above) y = 3x Together the two CD players would be$320, so x and y must add to 320 x+y = 320 x + 3x = 320 .... plug in y = 3x 4x = 320 Solve for x. Then use it to find y. I'll let you finish up.
 Linear_Equations_And_Systems_Word_Problems/729099: Maggie is sitting in park. She counted 16people and dogs combined and 38 legs. How many people did Maggie see walk by?1 solutions Answer 445715 by jim_thompson5910(28595)   on 2013-03-21 16:41:04 (Show Source): You can put this solution on YOUR website!Hint: d = # of dogs p = # of people "She counted 16people and dogs combined" ----> d+p = 16 ----> d = 16 - p "...and 38 legs" ----> 4d + 2p = 38 4d + 2p = 38 4(16-p) + 2p = 38 64 - 4p + 2p = 38 I'll let you finish
 Probability-and-statistics/729071: A probability experiment consist of two possible outcomes: Event A and Event B. Event A is 3 times more likely that Event B. Calculate the probability of Event A (rounded to two decimals).1 solutions Answer 445714 by jim_thompson5910(28595)   on 2013-03-21 16:39:03 (Show Source): You can put this solution on YOUR website!Let x = P(B) P(A) = 3*P(B) ... This is given when you are told that "Event A is 3 times more likely that Event B" There are only two outcomes A and B. So their probabilities must add to 1 P(A) + P(B) = 1 3*P(B) + P(B) = 1 3*x + x = 1 4x = 1 x = 1/4 P(B) = 1/4 = 0.25 P(A) = 3*P(B) P(A) = 3*(1/4) P(A) = 3/4 = 0.75 So the probability of event A is 0.75
 Equations/729057: Is x < 3 the same as that for 3 > x? Explain your answer. I think it is the same because either way you put the answer 3 is still greater than x. if you wrote it out is would be x is less than 3 for the first problems and the second problem would be 3 is greater than x. They are both stating the 3 is bigger than x and x is smaller than three. I'm just not 100% sure so I am checking.1 solutions Answer 445710 by jim_thompson5910(28595)   on 2013-03-21 16:28:08 (Show Source): You can put this solution on YOUR website!Yes the two are the same since x is on the pointed end of the > sign So that means that x is less than 3. x < 3 is a much better way to write it since you read from left to right naturally (assuming you do) compared to 3 > x where you have to read this from right to left (which is the opposite) Also, when isolating variables, it's always a good idea to place them on the left side.
 test/729021: Find the slope intercept form of line that passes through a(1,5) and b(-4,-5)1 solutions Answer 445708 by jim_thompson5910(28595)   on 2013-03-21 16:24:28 (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 5 to both sides. Combine like terms. So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and
 Probability-and-statistics/729014: True or False? And Why? If P(E U F) = P(E) + P(F), what can be concluded about P(E and F)? AND P(A U B) - P(B) = P(A)1 solutions Answer 445707 by jim_thompson5910(28595)   on 2013-03-21 16:22:53 (Show Source): You can put this solution on YOUR website!If P(E U F) = P(E) + P(F), then P(E and F) must be zero since the more general formula is P(E U F) = P(E) + P(F) - P(E and F) The same applies to the second equation as well
 Geometry_Word_Problems/729089: a square is inscribed in a circle .if one side of the square measures 5 cm , what is the circumference of the circle1 solutions Answer 445706 by jim_thompson5910(28595)   on 2013-03-21 16:21:35 (Show Source): You can put this solution on YOUR website!The diagonal of the square is 5*sqrt(2) cm So the diameter is 5*sqrt(2) This makes the circumference to be 5*sqrt(2)*pi cm, which is the exact circumference The approximate circumference is roughly 22.2144146907919 cm
 expressions/729090: Solve for y: 6y=3y^21 solutions Answer 445705 by jim_thompson5910(28595)   on 2013-03-21 16:20:00 (Show Source): You can put this solution on YOUR website!6y=3y^2 0=3y^2-6y 3y^2-6y = 0 3y(y-2) = 0 3y = 0 or y-2 = 0 3y = 0 or y = 2 y = 0/2 or y = 2 y = 0 or y = 2 Solutions: y = 0 or y = 2
 Probability-and-statistics/728909: an unbiased coin is tossed three times in succession . what is the probability of obtaining 'tail' at least once1 solutions Answer 445703 by jim_thompson5910(28595)   on 2013-03-21 16:18:28 (Show Source): You can put this solution on YOUR website!P(3 heads) = (1/2)^3 = 1/8 P(At least one tail) = 1 - P(3 heads) P(At least one tail) = 1 - 1/8 P(At least one tail) = 7/8
 Numeric_Fractions/728846: Write the fraction 36/40 in simple form1 solutions Answer 445620 by jim_thompson5910(28595)   on 2013-03-21 01:19:41 (Show Source): You can put this solution on YOUR website!The GCF of 36 and 40 is 4 divide each by the GCF to get 36/4 = 9 40/4 = 10 So 36/40 = 9/10
 Permutations/728857: 10 students are participating in a competition .In how many ways can the 1st 3 prizes be won?1 solutions Answer 445619 by jim_thompson5910(28595)   on 2013-03-21 01:00:51 (Show Source): You can put this solution on YOUR website!10 ways to fill slot 1 (first place) 9 ways to fill slot 2 (second place) 8 ways to fill slot 3 (third place) There are 10*9*8 = 720 ways to do this
 Permutations/728858: a student is declared pass if he passes in all 6 subjects .in how many ways he can fail1 solutions Answer 445617 by jim_thompson5910(28595)   on 2013-03-21 00:59:16 (Show Source): You can put this solution on YOUR website!There is only one way to pass overall (by passing each subject) This is out of 2^6 = 64 ways total (to either pass or fail any class, with any combo of pass/fail) So there are 64 - 1 = 63 ways to fail overall.
 test/728860: Is this possible?? a²+a Im in year 8 and my teacher "doesn't want to confuse me cos its year 10 stuff" she doesn't realise that im not an idiot...1 solutions Answer 445616 by jim_thompson5910(28595)   on 2013-03-21 00:53:57 (Show Source): You can put this solution on YOUR website!You cannot combine these terms as they aren't like terms, so you leave it as Optionally you could factor it to get , but there's not much you can do to simplify it.
Quadratic_Equations/728634: how to factor the folowing
15x^2+7x-2
16x^2-81
3x^2+12x-63

1 solutions

Answer 445542 by jim_thompson5910(28595)   on 2013-03-20 16:44:28 (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

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 :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-30) = -30
2*(-15) = -30
3*(-10) = -30
5*(-6) = -30
(-1)*(30) = -30
(-2)*(15) = -30
(-3)*(10) = -30
(-5)*(6) = -30

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1

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 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).

 Circles/728625: The diameter of a bicycle wheel is 14 inches. What is the distance travelled in feet when the wheel makes 3 rotations. Use 22/7 as an approximation 1 solutions Answer 445534 by jim_thompson5910(28595)   on 2013-03-20 16:30:10 (Show Source): You can put this solution on YOUR website!C = pi*d C = (22/7)*14 C = 44 The wheel travels 44 inches (roughly) in one full rotation. So it travels 44*3 = 132 inches (11 ft) roughly in 3 full rotations.
 Finance/722657: If a car costs £3000 and it goes up by 8% what is the answer?1 solutions Answer 445503 by jim_thompson5910(28595)   on 2013-03-20 14:47:26 (Show Source): You can put this solution on YOUR website!3000 + 8% of 3000 3000 + 0.08*3000 3000 + 240 3240 Answer: 3240
 Numeric_Fractions/728562: (-1)-(+5)-(-7) 1 solutions Answer 445502 by jim_thompson5910(28595)   on 2013-03-20 14:43:17 (Show Source): You can put this solution on YOUR website!(-1)-(+5)-(-7) -1-5+7 1 ------------------------------------------------------- So (-1)-(+5)-(-7) = 1
 expressions/728567: (a2 + 9a + 5) - (a2 - 9a + 5)......(2 BEING POWER OF) Simplify and show work. PLEASE AND THANK YOU.1 solutions Answer 445501 by jim_thompson5910(28595)   on 2013-03-20 14:42:16 (Show Source): You can put this solution on YOUR website!(a^2 + 9a + 5) - (a^2 - 9a + 5) a^2 + 9a + 5 - a^2 + 9a - 5 (a^2 - a^2) + (9a+9a) + (5 - 5) (0a^2) + (18a) + (0) 0a^2 + 18a + 0 0 + 18a + 0 18a
 expressions/728560: simplify 6w - 8w + 10w + (-9w) PLEASE!!!! Show work please Smjacobson69@aol.com1 solutions Answer 445496 by jim_thompson5910(28595)   on 2013-03-20 14:11:35 (Show Source): You can put this solution on YOUR website!6w - 8w + 10w + (-9w) 6w - 8w + 10w - 9w (6 - 8 + 10 - 9)w (-1)w -1w -w So the final answer is -w
 Subset/728523: A is the set of whole number factors of 12, and B is the set of whole number factors of 9. Determine whether the statement B⊆A is true or false. Use a Venn diagram to support your answer. 1 solutions Answer 445495 by jim_thompson5910(28595)   on 2013-03-20 14:10:07 (Show Source): You can put this solution on YOUR website!Draw a circle to represent the factors of 12. So the numbers 1, 2, 3, 4, 6, 12 go in this circle. The question is: Does the circle representing the factors of 9 go completely in the circle we just drew? Surely 1 and 3, which are factors of 9, are also factors of 12. However, 9 is a factor of 9, but it is NOT a factor of 12. So you'll have a circle that overlaps the previous circle, but a piece of it will be outside of the previous circle. The factors 1,3 go in the piece that's inside the "factors of 12 circle" and the number "9" goes in the piece that's outside the "factors of 12 circle" So B⊆A is false since not all elements in B are also in A.
 Exponents/728511: Perform the indicated operation and simplify. Write the answer in the form a + bi. (4-2i)2 Possible answers: A) None B) 16 - 12i C) 16 - 20i D) 20 - 16i E) 12 - 16i1 solutions Answer 445491 by jim_thompson5910(28595)   on 2013-03-20 14:00:25 (Show Source): You can put this solution on YOUR website!(4-2i)^2 (4-2i)(4-2i) 4(4-2i)-2i(4-2i) 16-8i-8i+4i^2 16-8i-8i+4(-1) 16-8i-8i-4 12-16i which is Choice E)
Graphs/728507: I need to make a table for y=√(x) with x as 0,1,2,3,4,6,9,12 and 16. I don't know how to do it. Please help.
Thank you
1 solutions

Answer 445488 by jim_thompson5910(28595)   on 2013-03-20 13:53:33 (Show Source):
You can put this solution on YOUR website!
Plug in each x to get a corresponding y value.

So for instance, when x = 0,

Plug in x = 0

Take the square root of 0 to get 0

So when x = 0, y is y = 0

This is one row in your table.
-------------------------------------------------------

Another example: When x = 4

Plug in x = 4

Take the square root of 4 to get 2

So when x = 4, y is y = 2

So another row will have 4, then 2

-------------------------------------------------------

Last example: When x = 6

Plug in x = 4

You'll have to use a calculator here to get an approximation

So when x = 6, y is y = 2.449

-------------------------------------------------------

You use these steps to generate the y value of each of the x values.

Doing so will give you this table

x y
0 0
1 1
2 1.414
3 1.732
4 2
6 2.449
9 3
12 3.464
16 4

 Functions/728488: inverse of the function f(x) = 3x + 2. State the answer in slope-intercept form.1 solutions Answer 445486 by jim_thompson5910(28595)   on 2013-03-20 13:44:14 (Show Source): You can put this solution on YOUR website!f(x) = 3x + 2 y = 3x + 2 x = 3y + 2 x - 2 = 3y x/3 - 2/3 = y y = x/3 - 2/3 y = (1/3)x - 2/3 So the inverse function is $\large f^{-1}(x) = \frac{1}{3}x - \frac{2}{3}$