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 Equations/333894: 3x over x-1 equals 21 solutions Answer 239241 by jim_thompson5910(28598)   on 2010-08-22 17:06:53 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by x-1. Distribute. Subtract from both sides. Combine like terms on the left side. ---------------------------------------------------------------------- Answer: So the solution is
 Numeric_Fractions/333893: I need help solving this problem: -5/9 + - 1/3 ________ 1 solutions Answer 239238 by jim_thompson5910(28598)   on 2010-08-22 17:02:46 (Show Source): You can put this solution on YOUR website! which means that
 Equations/333892: im stuck!! and i dont know why but heres the question 3m-17=5m-1 1 solutions Answer 239235 by jim_thompson5910(28598)   on 2010-08-22 16:53:53 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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
 Travel_Word_Problems/333890: find the adverage speed for the given distance and time. include the units of measure in your answer. 16. An airplane travels 775 miles in 120 minutes. (I know that time goes into distance but i just dont understand the question)1 solutions Answer 239234 by jim_thompson5910(28598)   on 2010-08-22 16:53:20 (Show Source): You can put this solution on YOUR website!Since , this means that . Solve for r to get . So the average speed is about 6.46 mi/min Alternatively, 120 min = 2 hrs. So the average speed is also mi/hr
 Functions/333884: graph the line given a pair of points and find the slope (1,4) (-3,-4)1 solutions Answer 239233 by jim_thompson5910(28598)   on 2010-08-22 16:38:07 (Show Source): You can put this solution on YOUR website!See this page for a solution to a similar problem (same idea, but different numbers).
 Unit_Conversion_Word_Problems/333885: Chemistry: conversions An experiment requires that each student use an 8.5cm length of magnesium ribbon. How many students can do the experiment if theres a 570cm length of magnesium ribbon available. I got 8.5cm x 570cm/ 1 student = 4845 but i know that cant be right..please help me1 solutions Answer 239231 by jim_thompson5910(28598)   on 2010-08-22 16:35:42 (Show Source): You can put this solution on YOUR website!If you had 8.5 cm of ribbon, then only student can do the experiment. If you had 17 cm of ribbon, then students can do the experiment. So if you had 570 cm of ribbon, then which means that about 67 students can do the experiment (round down to the nearest whole number).
 test/333886: Hi can you please help me with the following problem I am stuck. Multiply (8z - u)(3z + 4u) Thanks1 solutions Answer 239230 by jim_thompson5910(28598)   on 2010-08-22 16:33:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, .
 Equations/333883: Please help me, I am soooo lost! Find an equation of the line having given slope and containing the given point. m = -8, (6, 8). The equation of the line is y = ?1 solutions Answer 239229 by jim_thompson5910(28598)   on 2010-08-22 16:28:26 (Show Source): You can put this solution on YOUR website!If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Distribute Multiply and to get Add 8 to both sides to isolate y Combine like terms and to get So the answer is
 Linear-equations/333866: write the equation of the line that parallel to f(x)=3x-7 and goes through the point (0,4)1 solutions Answer 239228 by jim_thompson5910(28598)   on 2010-08-22 16:26:52 (Show Source): You can put this solution on YOUR website!Note: is the same as We can see that the equation has a slope and a y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Distribute Multiply Add 4 to both sides. Combine like terms. So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .
 Numeric_Fractions/333870: I am subtracting fractions is the answer right? 9/10-1/4 (9/10*2/2=18/20) (1/4*5/5=5/20) 18/20-5/20=13/20 is 13/20 the lowest reduction?1 solutions Answer 239227 by jim_thompson5910(28598)   on 2010-08-22 16:22:27 (Show Source): You can put this solution on YOUR website!You are correct. and this is in lowest terms (since the numerator and denominator have a GCF of 1). Good job.
 Functions/333879: find the domain of the function g(x)=4/9-4x1 solutions Answer 239226 by jim_thompson5910(28598)   on 2010-08-22 16:19:50 (Show Source): You can put this solution on YOUR website! Start with the given function Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain. Subtract 9 from both sides Combine like terms on the right side Divide both sides by -4 to isolate x Reduce Since makes the denominator equal to zero, this means we must exclude from our domain So our domain is: which in plain English reads: x is the set of all real numbers except x CANNOT equal So our domain looks like this in interval notation note: remember, the parenthesis excludes 9/4 from the domain If we wanted to graph the domain on a number line, we would get: Graph of the domain in blue and the excluded value represented by open circle Notice we have a continuous line until we get to the hole at (which is represented by the open circle). This graphically represents our domain in which x can be any number except x cannot equal 9/4
 test/333873: Hi I need some help with solving this story problem I can work it up to the end but I am not sure where to go from there, but here it is. A launced rocket has an altitude, in meters, given by the polynomial h+xt-4.9t^2, where h is the height, in meters, from which the launch occurs, at velocity v in meters per second, and t is the number of seconds from which the rocket is airborne. If a rocket is launched from the top of a tower 60 meters high with an inital upward speed of 40 meters per second, what will its height be after 2 seconds. I know the altitude h+vt - 4.9t^2 = 60 + vt - 4.9t^2 = 60 + 40t - 4.9t^2 = 60 + 40(2) - 4.9 (2)^2 60 + 40(2)-4.9(2)^2 = this is where I am not sure what to multiply add or subtract. Please help me if you can and thanks :O) 1 solutions Answer 239224 by jim_thompson5910(28598)   on 2010-08-22 16:17:01 (Show Source): You can put this solution on YOUR website! So which means the height of the rocket is 120.4 meters at 2 seconds.
 Equations/333878: Use the graph of the function f to find f(-2), f(-1), and f(0). What does this mean? Please help!1 solutions Answer 239222 by jim_thompson5910(28598)   on 2010-08-22 16:13:58 (Show Source): You can put this solution on YOUR website!We would need to see the graph to help you out.
 expressions/333843: Simplify completely: x^2+5x+4/x+1 1 solutions Answer 239220 by jim_thompson5910(28598)   on 2010-08-22 15:45:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words,
 absolute-value/333868: O hai I'm not not entirely sure if the answer is 32 or but can someome please verify/ :D |a^2 - b^2| A = 6 & B = -21 solutions Answer 239219 by jim_thompson5910(28598)   on 2010-08-22 15:42:54 (Show Source): You can put this solution on YOUR website!. So you are correct. Good job.
 Average/333862: Algebra 2 test problem : a student scores on 5 test are 93%, 89%, 72%, 80% and 96% what must the student score on the 6th test so that the average is 88% . I need the formula, I have the answer.. Thank u....;)1 solutions Answer 239216 by jim_thompson5910(28598)   on 2010-08-22 15:26:07 (Show Source): You can put this solution on YOUR website!Convert each percentage to decimal form to get 0.93, 0.89, 0.72, 0.80, and 0.96 Now let x = score on 6th test So to find the average of the 6 tests, simply add them up and divide by 6 like so: Now set that equal to the given average of 0.88 (88% in decimal form) to get Start with the given equation. Multiply both sides by 6. Multiply 0.88 and 6 to get 5.28 Combine like terms. Subtract 4.3 from both sides. Combine like terms. So the score on the 6th test must be a 98% (multiply 0.98 by 100 to convert it to a percentage) to get an average score of 88%
 Average/333860: If susan can pain a house in four hours, John can pain a house in six hours, and Peter can paint a house in ten hours. How long will it take if all of them painted the house together? I tried averaging the numbers togther and then dividing it by three and sometimes its right and sometimes its wrong. Can you help?1 solutions Answer 239213 by jim_thompson5910(28598)   on 2010-08-22 15:17:13 (Show Source): You can put this solution on YOUR website!"If susan can pain a house in four hours", then she can paint of a house in 1 hour. So her rate is houses per hour. If "John can pain a house in six hours", then he can paint of a house in 1 hour. So his rate is houses per hour. Finally, if "Peter can paint a house in ten hours", then he can paint of a house in one hour, making his rate houses per hour. So the three rates are: , and houses per hour. Add them up to get So their combined rate is houses per hour. In other words, together they can paint of a house in one hour (which is close to 1/2 of a house). Now multiply this rate by some unknown time 't' to get and set that equal to 1 (since we want to paint one house) to get Next, multiply both sides by 60 to get and then divide both sides by 31 to isolate t to get So it will take them about 1.935 hours, or close to 2 hours, if they work together.
 Rectangles/333855: Find the perimeter of a square whose area is 144 inches square?1 solutions Answer 239206 by jim_thompson5910(28598)   on 2010-08-22 15:04:10 (Show Source): You can put this solution on YOUR website! Start with the area of a square formula. Take the square root of both sides (note: we're only taking the positive square root since a negative length doesn't make sense). Flip the equation. Plug in (the given area). Take the square root of to get . So if a square has an area of square inches, then it has a side length of inches. -------------------------------------------------- Now move onto the perimeter of a square formula. Plug in . Multiply and to get . So the perimeter of a square with a side length of inches is inches. This means that if a square has an area of 144 square inches, this means that has a perimeter of 48 inches.
 Graphs/333847: (2/5-1/4)(-1/9) equals? I really appreciate your help. Thanks!1 solutions Answer 239194 by jim_thompson5910(28598)   on 2010-08-22 14:24:08 (Show Source): You can put this solution on YOUR website! So in short,
 expressions/333845: Find the value of 2^-3-2^01 solutions Answer 239193 by jim_thompson5910(28598)   on 2010-08-22 14:22:48 (Show Source): You can put this solution on YOUR website! So
 Square-cubic-other-roots/333846: √54 1 solutions Answer 239192 by jim_thompson5910(28598)   on 2010-08-22 14:21:56 (Show Source): You can put this solution on YOUR website! which means that
 Travel_Word_Problems/333723: A projectile is fired from the ground with an upward speed of 245m/s. After how many seconds will it return to the ground? h= vt- 4.9t^21 solutions Answer 239144 by jim_thompson5910(28598)   on 2010-08-22 01:30:08 (Show Source): You can put this solution on YOUR website!Hint: In this case, which means that the equation is . From here, plug in h=0 to get and then use then solve for 't'.
Linear-equations/333721: Graph the linear equation
2x+4y=16
also find its x and y intercepts
1 solutions

Answer 239143 by jim_thompson5910(28598)   on 2010-08-22 00:59:30 (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.

Divide both sides by to isolate .

Reduce.

So the x-intercept is .

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

y-intercept

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

Plug in .

Multiply and 0 to get 0.

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

 Polynomials-and-rational-expressions/333720: what is t squared = 9t1 solutions Answer 239142 by jim_thompson5910(28598)   on 2010-08-22 00:57:42 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 9t from both sides. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "t": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or
Distributive-associative-commutative-properties/333713: Factor.
12x^2+xy-6y^2

1 solutions

Answer 239141 by jim_thompson5910(28598)   on 2010-08-21 23:50:37 (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 :
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72

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

These factors pair up and multiply to .
1*(-72) = -72
2*(-36) = -72
3*(-24) = -72
4*(-18) = -72
6*(-12) = -72
8*(-9) = -72
(-1)*(72) = -72
(-2)*(36) = -72
(-3)*(24) = -72
(-4)*(18) = -72
(-6)*(12) = -72
(-8)*(9) = -72

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

First NumberSecond NumberSum
1-721+(-72)=-71
2-362+(-36)=-34
3-243+(-24)=-21
4-184+(-18)=-14
6-126+(-12)=-6
8-98+(-9)=-1
-172-1+72=71
-236-2+36=34
-324-3+24=21
-418-4+18=14
-612-6+12=6
-89-8+9=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).

 Equations/333715: Simplify. v^2+8v+7/3v^2+18v-211 solutions Answer 239139 by jim_thompson5910(28598)   on 2010-08-21 23:49:49 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. Distribute. So simplifies to . In other words,
 Expressions-with-variables/333710: 2^2x4^2=1 solutions Answer 239122 by jim_thompson5910(28598)   on 2010-08-21 22:34:16 (Show Source): You can put this solution on YOUR website! or we can do it another way Either way, we get the answer of 64.
 Travel_Word_Problems/333704: you travel 60 kilometers in 1.5 hours. what us your average speed? how do you set up this problem?1 solutions Answer 239106 by jim_thompson5910(28598)   on 2010-08-21 21:01:04 (Show Source): You can put this solution on YOUR website!Hint: Distance = Rate * Time which symbolically means that . In this case, and
 Polynomials-and-rational-expressions/333697: For f(x) =-x^2-x+5 , find f(-3)1 solutions Answer 239104 by jim_thompson5910(28598)   on 2010-08-21 20:35:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in . Rewrite as . Square to get . Combine like terms.
 Functions/333690: g(x) =2/7 -6x what is the domain1 solutions Answer 239102 by jim_thompson5910(28598)   on 2010-08-21 20:29:03 (Show Source): You can put this solution on YOUR website!Since you cannot divide by zero, simply find all the x values that make the denominator equal to zero. So solve and exclude those solutions from the set of real numbers to find the domain.
 Polynomials-and-rational-expressions/333689: i need help on factoring using distibutive property: 1. 7x+49 2. 8m-6 thanks so much!1 solutions Answer 239101 by jim_thompson5910(28598)   on 2010-08-21 20:19:47 (Show Source): You can put this solution on YOUR website!1) 2) Let me know if you need more explanation.