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 Mixture_Word_Problems/315387: John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?1 solutions Answer 225652 by jim_thompson5910(28598)   on 2010-06-17 21:08:22 (Show Source): You can put this solution on YOUR website!Use the equation d=rt where d is the distance, r is the speed, and t is the time. So we're given that "a meeting that is 28 miles away. He needs to be there in 30 minutes.", which means that d=28 and t=0.5 (30 minutes = 0.5 hours). Plug these values in to get: Now divide both sides by 0.5 and flip the equation to get . So John needs to go 56 mph to go 28 miles in 30 minutes.
 logarithm/310544: given = .542 and = .804, find the following. My work so far... - 1 solutions Answer 222056 by jim_thompson5910(28598)   on 2010-06-01 22:45:02 (Show Source): You can put this solution on YOUR website!Hint: and
 Trigonometry-basics/310476: if cos(x)=4/5, find sin(2x)1 solutions Answer 222008 by jim_thompson5910(28598)   on 2010-06-01 20:23:03 (Show Source): You can put this solution on YOUR website!Hint: Use the identities and
 Equations/310505: What is -|-6|-3?1 solutions Answer 222007 by jim_thompson5910(28598)   on 2010-06-01 20:20:35 (Show Source): You can put this solution on YOUR website!Remember that the absolute value of ANY number is ALWAYS positive. So . This means that which means that .
 Rational-functions/310502: Simplify:  (27B^1/3C^3/4 ) ^4/3 (-------------) ( 8B^-2/3C^1/2)  Entire expression is in parenthesis with outer exponent 4/31 solutions Answer 222003 by jim_thompson5910(28598)   on 2010-06-01 20:11:05 (Show Source): You can put this solution on YOUR website!We're going to use the following identities 1) 2) 3) Start with the given expression. Use identity # 1 to divide the variable terms. Rewrite as Multiply by to get Combine the fractions by combining the numerators over the common denominator. Combine like terms. Reduce. Now use identity # 3 Rewrite as Use identity # 2 to multiply the exponents. Multiply 3 and to get Reduce. Evaluate to get 16 Rewrite 27 as Use identity # 2 to multiply the exponents. Multiply 3 and to get Reduce. Raise 3 to the 4th power to get 81 So where every variable is positive.
 Equations/310257: Hi guys, Please can you tell me the following: 5^0 (5 to the power 0) - does this equal 1 or does it remain 5? Also 2x^0 - does the x fall away and I only use 2 in the equation?1 solutions Answer 221850 by jim_thompson5910(28598)   on 2010-06-01 01:20:26 (Show Source): You can put this solution on YOUR website!Any non zero number to the zeroth power is 1. So for any 'x' that isn't zero. So and
 expressions/310210: what is 3 multiply by -1 equal 1 solutions Answer 221843 by jim_thompson5910(28598)   on 2010-05-31 21:34:26 (Show Source): You can put this solution on YOUR website!3 * -1 = -3
 expressions/309983: find the slope if it exists (5,4) and (7,-10) 1 solutions Answer 221713 by jim_thompson5910(28598)   on 2010-05-31 07:04:45 (Show Source): You can put this solution on YOUR website! 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
 Square-cubic-other-roots/309970: I need help to find the product of each pair of conjugates. (2sqrt3 - sqrt7)(2sqrt3 + sqrt7)1 solutions Answer 221706 by jim_thompson5910(28598)   on 2010-05-31 04:08:05 (Show Source): You can put this solution on YOUR website!If we let and we get the expression . FOILing this expression gives us which is a difference of squares. Plug and back in to get Now just multiply out and simplify the right side to get: and do a bit more arithmetic to get
 Numeric_Fractions/309973: I need help with this equation (I got help last night, but its conflicting with a few other views) 12 1/2 + 1/ 1/3 = The 1 over the 1/3 confuses me, cause according to me this is 3 So is it right to go 12 1/2 + 3 = ? (If you use funny signs...can you tell me what they are please?) Thanks for the help!1 solutions Answer 221705 by jim_thompson5910(28598)   on 2010-05-31 04:04:22 (Show Source): You can put this solution on YOUR website!Well, think of 1 as . So this means that So our goal is to simplify Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction (ie 'flip' the second fraction and multiply) Combine the fractions. Multiply Reduce. So . It turns out that for any 'x' that is not zero. For instance, if , then . So this will save time in the future (hopefully you'll understand how it all works). So then becomes . Does this help you get moving in the right direction?
 Square-cubic-other-roots/309967: Could I get help with this problem? Simplify the products. (√2+5)(√2+5)1 solutions Answer 221704 by jim_thompson5910(28598)   on 2010-05-31 02:38:50 (Show Source): You can put this solution on YOUR website! Start with the given expression. FOIL Combine the roots using the identity Multiply Take the square root of 4 to get 2. Combine like terms. So
 Radicals/309961: 2/√3x1 solutions Answer 221703 by jim_thompson5910(28598)   on 2010-05-31 02:04:12 (Show Source): You can put this solution on YOUR website!Hint: Multiply both the numerator and denominator by to rationalize the denominator.
 Surface-area/309894: Area of a Parallelogram. Find the trinomial A(x) that represents the area, whose base is 3x + 2 meters and whose height is 2x + 3 meters. Find A(3). My answer: 3(3+2)2(3+3)= (9+6)(6+6)=15*12=180 meters. Is this correct?1 solutions Answer 221701 by jim_thompson5910(28598)   on 2010-05-31 02:02:08 (Show Source): You can put this solution on YOUR website!To find the trinomial, simply FOIL to get which means that the trinomial is Now plug in x=3 and evaluate: So the area is 99 square meters
Graphs/309917: 7+x=21
1 solutions

Answer 221700 by jim_thompson5910(28598)   on 2010-05-31 01:57:42 (Show Source):
You can put this solution on YOUR website!
For more help with solving linear equations, check out this linear equation solver.

 Solved by pluggable solver: Linear Equation Solver Start with the given equation. Subtract from both sides. Combine like terms on the right side.---------------------------------------------------------------------- Answer: So the solution is

 Quadratic-relations-and-conic-sections/309908: i need help knowing what formula to use on circles please help me1 solutions Answer 221699 by jim_thompson5910(28598)   on 2010-05-31 01:56:58 (Show Source): You can put this solution on YOUR website!Well the circumference formula is where is roughly 3.14159... and 'r' is the radius. This is used to find the distance around a circle. and the area formula is which is used to find the area that a circle encloses.
Polynomials-and-rational-expressions/309886: 2t2 + 4t - 30
1 solutions

Answer 221698 by jim_thompson5910(28598)   on 2010-05-31 01:55:01 (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor this.

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 :
1,3,5,15
-1,-3,-5,-15

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

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

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

First NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+5=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

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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).

 Rectangles/309856: If you have 2b^3+b/b^2+b. can you take two b's from the b^3 to cancel the b^2 on the bottom.1 solutions Answer 221697 by jim_thompson5910(28598)   on 2010-05-31 01:53:53 (Show Source): You can put this solution on YOUR website!You can only factor out one 'b'. which means that
 Linear-systems/309872: 5x+5y=-13, 7x-3y=11 using the elimination method solve this please.1 solutions Answer 221696 by jim_thompson5910(28598)   on 2010-05-31 01:51:59 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 3. Distribute and multiply. Multiply the both sides of the second equation by 5. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent.
 Radicals/309929: Use the product rule to simplify. All variables represent nonnegative real numbers. √20x^5y1 solutions Answer 221695 by jim_thompson5910(28598)   on 2010-05-31 01:50:42 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Rearrange and multiply the terms. ================================================== Answer: So simplifies to In other words, where every variable is non-negative.
 Graphs/309877: Help solving theses problems: 1.Simplify √256x^2 2.Simplify √18x^4y^3 3. Simplify -4√32xy 4.Multiply and simplify 3√10(4+2√2) 5.Evaluate. Type the numerical answer. 256^1/4 6. Evaluate. Type the numerical answer. 8^4/3 7.Write an equivalent expression using radical notation and, if possible, simplify. (9y8)^3/2 8.Use rational exponents to simplify 6√x^301 solutions Answer 221694 by jim_thompson5910(28598)   on 2010-05-31 01:48:06 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. Start with the given expression. Break up the square root using the identity . Take the square root of to get . Take the square root of to get . ================================================== Answer: So simplifies to In other words, where
Trigonometry-basics/309944: 8z^4-32z^3+30z^2
1 solutions

Answer 221693 by jim_thompson5910(28598)   on 2010-05-31 01:46:27 (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor.

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 4 and 15 respectively.

Now multiply the first coefficient 4 and the last coefficient 15 to get 60. Now what two numbers multiply to 60 and add to the middle coefficient -16? Let's list all of the factors of 60:

Factors of 60:
1,2,3,4,5,6,10,12,15,20,30,60

-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 60
1*60
2*30
3*20
4*15
5*12
6*10
(-1)*(-60)
(-2)*(-30)
(-3)*(-20)
(-4)*(-15)
(-5)*(-12)
(-6)*(-10)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -16

First NumberSecond NumberSum
1601+60=61
2302+30=32
3203+20=23
4154+15=19
5125+12=17
6106+10=16
-1-60-1+(-60)=-61
-2-30-2+(-30)=-32
-3-20-3+(-20)=-23
-4-15-4+(-15)=-19
-5-12-5+(-12)=-17
-6-10-6+(-10)=-16

From this list we can see that -6 and -10 add up to -16 and multiply to 60

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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So our expression goes from and factors further to

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

So competely factors to

In other words,

 Equations/309947: How would I solve this equation? 2y^2 - 3y - 6 = 01 solutions Answer 221692 by jim_thompson5910(28598)   on 2010-05-31 01:44:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "y": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . or Break up the expression. So the solutions are or
 Radicals/309949: How would I simplify this problem to get the product? (3sqrt3 - sqrt2)( sqrt2 + sqrt3)1 solutions Answer 221691 by jim_thompson5910(28598)   on 2010-05-31 01:43:46 (Show Source): You can put this solution on YOUR website! Start with the given expression. FOIL Combine the roots. Multiply Take the square root of 9 and 4 to get 3 and 2 respectively. Multiply Combine like terms. So
 Radicals/309962: √6/1-√31 solutions Answer 221690 by jim_thompson5910(28598)   on 2010-05-31 01:39:17 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply both the numerator and the denominator by FOIL the denominator Combine like terms. Distribute. Combine the last two roots. Multiply Rewrite 18 as 9*2 Break up the second root. Take the square root of 9 to get 3. Factor out a negative 1. Distribute that negative 1 through the numerator. So
 Radicals/309960: √2/51 solutions Answer 221689 by jim_thompson5910(28598)   on 2010-05-31 01:32:44 (Show Source): You can put this solution on YOUR website! Start with the given expression. Break up the root. Multiply both the numerator and the denominator by Combine the fractions Multiply and to get Combine the roots. Multiply So
 Radicals/309959: 5/√21 solutions Answer 221688 by jim_thompson5910(28598)   on 2010-05-31 01:29:41 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply both the numerator and the denominator by Combine the fractions Multiply and to get So
 Rational-functions/309888: reduce the following expression to lowest terms. r^2-s^2/s-r1 solutions Answer 221663 by jim_thompson5910(28598)   on 2010-05-30 20:07:42 (Show Source): You can put this solution on YOUR website! So
Graphs/309896: Use the intercepts to graph the equation.
x + 4y = 8
1 solutions

Answer 221661 by jim_thompson5910(28598)   on 2010-05-30 20:05:08 (Show Source):
You can put this solution on YOUR website!

#### x-intercept

To find the x-intercept, plug in and solve for x

Plug in .

Multiply and 0 to get 0.

Simplify.

So the x-intercept is .

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

#### y-intercept

To find the y-intercept, plug in and solve for y

Plug in .

Simplify.

Divide both sides by to isolate .

Reduce.

So the y-intercept is .

Now let's plot the points and which are the x and y intercepts respectively.

Now draw a straight line through the plotted points to graph .

Graph of