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 Points-lines-and-rays/264578: Simplify: (m4)5 ÷ m16 1 solutions Answer 194771 by jim_thompson5910(28595)   on 2010-02-02 16:19:56 (Show Source): You can put this solution on YOUR website! So where
 Graphs/264512: Graph the function f(x)+1/2x+11 solutions Answer 194770 by jim_thompson5910(28595)   on 2010-02-02 16:18:18 (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 1 and the run is 2. This means that to go from point to point, we can go up 1 and over 2 So starting at , go up 1 unit and to the right 2 units 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
 Inequalities/264559: 4-3x-6=3x+2-x1 solutions Answer 194769 by jim_thompson5910(28595)   on 2010-02-02 16:16:54 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Combine like terms on the right side. Add to 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. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/264552: what are the steps for this equation? p-1=5p+3p-8?1 solutions Answer 194768 by jim_thompson5910(28595)   on 2010-02-02 16:16:15 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the right side. Add to 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. ---------------------------------------------------------------------- Answer: So the solution is
 Expressions-with-variables/264545: ((2x-9)/5)+3=2x1 solutions Answer 194767 by jim_thompson5910(28595)   on 2010-02-02 16:15:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply every term by the LCD 5 to clear out the fraction. Combine like terms on the left side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Linear-systems/264538: solve: 3x-2y=12 2x+3y=-5 by the addition method solve: 2x-1y=-5 3x-5y=-4 by substitution show steps please.1 solutions Answer 194765 by jim_thompson5910(28595)   on 2010-02-02 16:11:58 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. 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 2. 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. 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. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Length-and-distance/264536: simplify by removing factors of 1. t^2-9/(t+3)^2 1 solutions Answer 194764 by jim_thompson5910(28595)   on 2010-02-02 16:10:37 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator. Factor the denominator. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to In other words, where
 Inequalities/264568: -4x+9y=9 x-3y=-6 how do this problem by elimination?1 solutions Answer 194763 by jim_thompson5910(28595)   on 2010-02-02 16:07:38 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the second equation by 3. 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. Add to 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. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Money_Word_Problems/264541: PLEASE HELP ME SOLVE THIS PROBLEMS: in the period of a year, an investor lost twice as much as he gained. if he origanlly had 10,000 and now has 6,000, what amount did he gain and what did he lose?1 solutions Answer 194748 by jim_thompson5910(28595)   on 2010-02-02 14:11:02 (Show Source): You can put this solution on YOUR website!If he had \$10,000 and gained 'x' dollars, then lost twice that at 2x dollars, then he would then have dollars. Set this equal to 6,000 to get . Now simply solve for 'x' to find out how much he gained. Double that figure to find out how much he lost.
 Radicals/264531: simplify by taking roots of the numerator and the denominator.Assume all expressions under the radicals represent positive numbers. cubed rt of 512x^5/y^3 please help....1 solutions Answer 194741 by jim_thompson5910(28595)   on 2010-02-02 13:45:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Break up the root. Rewrite 512 as (since ) Rewrite as (since ) Break up the root in the numerator. Evaluate the cube root to get 8. Remember the cube root of anything cubed is simply that original expression. In other words, . This is why everything was broken down into parts dealing with cubes. Evaluate the cube root to get 'x'. Evaluate the cube root to get 'y'. So where
 Square-cubic-other-roots/264527: 5*squarerootof48-squarerootof27+3squarerootof541 solutions Answer 194737 by jim_thompson5910(28595)   on 2010-02-02 13:35:00 (Show Source): You can put this solution on YOUR website!Some scratch work: . So . So . So ----------------------------------------------------------------------------- Start with the given expression. Simplify the radicals (see scratch work above). Multiply Combine like terms. ============================================================================ Answer: So
 Linear_Algebra/264525: Solve the equation using factoring techniques (x+5)^2-16=01 solutions Answer 194733 by jim_thompson5910(28595)   on 2010-02-02 13:25:20 (Show Source): You can put this solution on YOUR website!Hint: Use the difference of squares formula . In this case, and
Graphs/264495: Given the line with equation y = 4/3x – 7, find an equation for the line that contains the point (6, 4) and is parallel to the givven line.
I am a retired music teacher. I have several music students that I have been teaching for several years at no cost to the student. I have a student that needs help and I know some algebra. However, I'm pretty much lost in algebra 2.

Bob Rietzke
bob@rietzke.net

1 solutions

Answer 194728 by jim_thompson5910(28595)   on 2010-02-02 13:17:49 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (6,4), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Make into equivalent fractions with equal denominators Combine the fractions Reduce any fractions So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

 Polynomials-and-rational-expressions/264509: find all numbers for the rational expression is not definded -3/2x1 solutions Answer 194727 by jim_thompson5910(28595)   on 2010-02-02 13:15:02 (Show Source): You can put this solution on YOUR website!Since division by zero is not allowed, we must make sure that the denominator is not equal to zero. If it is, then means that . So if , then the denominator is zero (which is not allowed). So when , the rational expression is not defined.
 Probability-and-statistics/264049: Suppose you randomly choose a number between 1 and 20.What are the odds in favor of choosing a prime number?1 solutions Answer 194470 by jim_thompson5910(28595)   on 2010-02-01 16:11:28 (Show Source): You can put this solution on YOUR website!Hint: P(prime number) = Number of primes from 1 to 20/Number of numbers from 1 to 20
 Polynomials-and-rational-expressions/264047: This is the question: A small box is placed inside a larger box. The dimensions of the small box are x+1 by x+2 by x-1. The dimensions of the larger box are 2x by x+4 by x+2. a)Write an equation for the volume of the space inside the larger box but outside the smaller box. I solved this and got x^3+10x^2+17x+2. b)If the volume of the space inside the larger box but outside the smaller box is equal to 33x+162 cubic units, what is x? I also solved this and got x=4. c)What is the volume of the smaller box? d)What is the volume of the larger box? I need help with c) and d) please. Thank you 1 solutions Answer 194468 by jim_thompson5910(28595)   on 2010-02-01 16:10:23 (Show Source): You can put this solution on YOUR website!For c) and d) simply plug in x=4 into the volume expressions that you found for the large and small boxes back in part a). Let me know if you still need help with that.
 Coordinate-system/264035: Ok, my question reads, "Graph both of the following functions on the same coordinate system. State the point of intersection as an ordered pair." The functions it gives me are and . But how can I solve them if I don't know what y or x are? Am I supposed to make my own number for either y or x to solve it, or am I missing something? I know how to graph, and I can find the point of intersection, but I can't figure out how to solve the functions without a function table. Please help if you can? Thank you.1 solutions Answer 194466 by jim_thompson5910(28595)   on 2010-02-01 15:59:52 (Show Source): You can put this solution on YOUR website!The point of intersection (x,y) is the solution to the given system. For instance, if the two points intersect at the point (0,1) (they don't, but let's say that they do), this would mean that and . Does that make sense?
Polynomials-and-rational-expressions/264016: Need help with finding the factor for the perfect square trinomial
64b to the second-112b+49 thanks
1 solutions

Answer 194459 by jim_thompson5910(28595)   on 2010-02-01 15:23:48 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 64 and the last term 49 to get 3136. Now we need to ask ourselves: What two numbers multiply to 3136 and add to -112? Lets find out by listing all of the possible factors of 3136

Factors:

1,2,4,7,8,14,16,28,32,49,56,64,98,112,196,224,392,448,784,1568,3136,

-1,-2,-4,-7,-8,-14,-16,-28,-32,-49,-56,-64,-98,-112,-196,-224,-392,-448,-784,-1568,-3136, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 3136.

1*3136=3136

2*1568=3136

4*784=3136

7*448=3136

8*392=3136

14*224=3136

16*196=3136

28*112=3136

32*98=3136

49*64=3136

56*56=3136

(-1)*(-3136)=3136

(-2)*(-1568)=3136

(-4)*(-784)=3136

(-7)*(-448)=3136

(-8)*(-392)=3136

(-14)*(-224)=3136

(-16)*(-196)=3136

(-28)*(-112)=3136

(-32)*(-98)=3136

(-49)*(-64)=3136

(-56)*(-56)=3136

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

Now which of these pairs add to -112? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -112

||||||||||||||||||||||
 First Number | Second Number | Sum 1 | 3136 | 1+3136=3137 2 | 1568 | 2+1568=1570 4 | 784 | 4+784=788 7 | 448 | 7+448=455 8 | 392 | 8+392=400 14 | 224 | 14+224=238 16 | 196 | 16+196=212 28 | 112 | 28+112=140 32 | 98 | 32+98=130 49 | 64 | 49+64=113 56 | 56 | 56+56=112 -1 | -3136 | -1+(-3136)=-3137 -2 | -1568 | -2+(-1568)=-1570 -4 | -784 | -4+(-784)=-788 -7 | -448 | -7+(-448)=-455 -8 | -392 | -8+(-392)=-400 -14 | -224 | -14+(-224)=-238 -16 | -196 | -16+(-196)=-212 -28 | -112 | -28+(-112)=-140 -32 | -98 | -32+(-98)=-130 -49 | -64 | -49+(-64)=-113 -56 | -56 | -56+(-56)=-112

We can see from the table that -56 and -56 add to -112. So the two numbers that multiply to 3136 and add to -112 are: -56 and -56

breaks down to this (just replace with the two numbers that multiply to 3136 and add to -112, which are: -56 and -56)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 8b out of the first group and factor a -7 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

which can also be written as since the factors repeat themselves

Notice how foils back to our original problem . This verifies our answer.

Polynomials-and-rational-expressions/264019: can you help me with this question:
factor the trimonial a to the second+2a-63 thanks
1 solutions

Answer 194458 by jim_thompson5910(28595)   on 2010-02-01 15:23:00 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 1 and the last term -63 to get -63. Now we need to ask ourselves: What two numbers multiply to -63 and add to 2? Lets find out by listing all of the possible factors of -63

Factors:

1,3,7,9,21,63,

-1,-3,-7,-9,-21,-63, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -63.

(-1)*(63)=-63

(-3)*(21)=-63

(-7)*(9)=-63

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

||||||
 First Number | Second Number | Sum 1 | -63 | 1+(-63)=-62 3 | -21 | 3+(-21)=-18 7 | -9 | 7+(-9)=-2 -1 | 63 | (-1)+63=62 -3 | 21 | (-3)+21=18 -7 | 9 | (-7)+9=2

We can see from the table that -7 and 9 add to 2. So the two numbers that multiply to -63 and add to 2 are: -7 and 9

breaks down to this (just replace with the two numbers that multiply to -63 and add to 2, which are: -7 and 9)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 1a out of the first group and factor a 9 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
==============================================================================

Notice how foils back to our original problem . This verifies our answer.

 Coordinate-system/264020: Is the line x=2 perpendicular to the line x=-7?1 solutions Answer 194456 by jim_thompson5910(28595)   on 2010-02-01 15:22:08 (Show Source): You can put this solution on YOUR website!No, the two lines are both vertical lines which means that they are parallel.
 Polynomials-and-rational-expressions/263999: 9x-4 1 solutions Answer 194443 by jim_thompson5910(28595)   on 2010-02-01 14:53:23 (Show Source): You can put this solution on YOUR website!What do you want to do here? Please post full instructions.
 logarithm/263991: log2^30-log2^101 solutions Answer 194440 by jim_thompson5910(28595)   on 2010-02-01 14:39:29 (Show Source): You can put this solution on YOUR website! Start with the given expression. Use the identity Reduce. So
 Radicals/263977: solve. sqrt(9x+67)=x+5 The solution is x= (simplify answer). Please help me solve.1 solutions Answer 194438 by jim_thompson5910(28595)   on 2010-02-01 14:19:19 (Show Source): You can put this solution on YOUR website!Hint: If you square both sides of you get . FOIL out the right side to get From there, get every term to one side to get . Now either factor or use the quadratic formula to solve for 'x'. Don't forget to check your answers by plugging them back into
 Geometry_Word_Problems/263934: two congruent squares touch at one corner. One side of the square measures 3 cm. The triangle created from two of the common sides is a right triangle. Find the area (to the nearest tenth) of the entire figure. 1 solutions Answer 194420 by jim_thompson5910(28595)   on 2010-02-01 12:40:09 (Show Source): You can put this solution on YOUR website!Remember that the area of a triangle is . In this case, both the base and the height are 3 cm. Simply plug this value into b and h to find A.
 Rectangles/263935: what is the area of a square with side length 34cm 1 solutions Answer 194419 by jim_thompson5910(28595)   on 2010-02-01 12:38:36 (Show Source): You can put this solution on YOUR website!Area = side * side = s^2 So . So the area is 1,156 square cm.
 Radicals/263911: Hi z^2 +14z +49 over 5z^2 +38z +21 times 5z^2 -17z-12 over z+7 I'm getting z-4 for an answer. Am I figuring this correctly? Thanks Rachel1 solutions Answer 194418 by jim_thompson5910(28595)   on 2010-02-01 12:36:15 (Show Source): You can put this solution on YOUR website!You are correct.
 Equations/263933: The height of a projectile fired vertically into the air at an initial velocity of 160 feet per second is a function of time, x, and is given by the equation f(x) = 160x – 16x2 I need help finding the highest point reached by the projectile. I just have no idea how to work this equation in order to do this. Your help would be greatly appreciated! 1 solutions Answer 194417 by jim_thompson5910(28595)   on 2010-02-01 12:30:54 (Show Source): You can put this solution on YOUR website!Hint: the highest point will be at the vertex of . The vertex is the point (h,k) where and . From the equation , we can see that and . Plug these values into to find h (the x coordinate of the vertex). Once you have this x value, plug it into to find k (the y coordinate of the vertex). It turns out that the highest point will be the y coordinate of the vertex. So once you find the y coordinate of the vertex, you will find the highest point.
 Conjunction/263743: Given p is true, q is false, and r is true, find the truth value of the statement (~p ^ q) ↔ ~r. its true. i made a truth table but i think im wrong1 solutions Answer 194336 by jim_thompson5910(28595)   on 2010-01-31 23:58:14 (Show Source): You can put this solution on YOUR website!If p is true, then ~p is false (since ~p is the opposite of p). Remember that "^" means "and". The statement p ^ q is only true if BOTH p AND q are true (hence the "and"). Since ~p is false, we automatically know that ~p ^ q is false (q doesn't have to be factored in at all). Finally, remember that p <-> q is only true if the truth values for p and q are the same. So if p and q are both true, or both false, then p <-> q is true. Think of this as an "equals" (ie p = q). Because r is true, ~r is false. Since ~p ^ q is false as well, ~p ^ q and ~r have the same truth values. So (~p ^ q) <-> ~r is true. So you are correct. Good job. Here's one way you could write all this out: (~p ^ q) <-> ~r (~T ^ F) <-> ~T (F ^ F) <-> F F <-> F T