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Probability-and-statistics/219077: Write this fraction in lowest terms? 110/100
1 solutions

Answer 164824 by jim_thompson5910(28595)   on 2009-09-29 17:34:08 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Reducing Fractions Calculator In order to reduce , the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal. In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of and is (note: click here if you need help with finding the GCF). So divide both the numerator and denominator by In other words, to reduce the fraction you do this Plug in the numerator, denominator, and the GCF Now divide 110 by 10 to get 11. This is now the new numerator. Now divide 100 by 10 to get 10. This is now the new denominator. So This means that reduces to In other words,

 absolute-value/219071: how can i solve |18-26.8|1 solutions Answer 164819 by jim_thompson5910(28595)   on 2009-09-29 17:26:35 (Show Source): You can put this solution on YOUR website! Remember, the absolute value of any number is ALWAYS positive.
45x^2-32x+3
I have already tried factoring everything and have not been able to come up with a response.
1 solutions

Answer 164815 by jim_thompson5910(28595)   on 2009-09-29 17:15:32 (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 :
1,3,5,9,15,27,45,135
-1,-3,-5,-9,-15,-27,-45,-135

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

These factors pair up and multiply to .
1*135 = 135
3*45 = 135
5*27 = 135
9*15 = 135
(-1)*(-135) = 135
(-3)*(-45) = 135
(-5)*(-27) = 135
(-9)*(-15) = 135

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

First NumberSecond NumberSum
11351+135=136
3453+45=48
5275+27=32
9159+15=24
-1-135-1+(-135)=-136
-3-45-3+(-45)=-48
-5-27-5+(-27)=-32
-9-15-9+(-15)=-24

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).

 Distributive-associative-commutative-properties/219063: 487(6)1 solutions Answer 164814 by jim_thompson5910(28595)   on 2009-09-29 17:15:05 (Show Source): You can put this solution on YOUR website!487(6)=2922
 Distributive-associative-commutative-properties/219062: -5(24-17)1 solutions Answer 164812 by jim_thompson5910(28595)   on 2009-09-29 17:14:40 (Show Source): You can put this solution on YOUR website! So Here's another way you could do it So
 Inequalities/219058: 7a+12<6a+3 The symbol is supposed to be greater than or equal to. The answer just ask to be solved using principles Thanks!!!1 solutions Answer 164810 by jim_thompson5910(28595)   on 2009-09-29 17:09:14 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
 Equations/219044: how do i solve for c? c-8=2+5c1 solutions Answer 164804 by jim_thompson5910(28595)   on 2009-09-29 16:51:52 (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 which in decimal form is .
 Inequalities/219039: what is the inequality for x plus 5 is at least 451 solutions Answer 164801 by jim_thompson5910(28595)   on 2009-09-29 16:49:27 (Show Source): You can put this solution on YOUR website!The key word "at least" means that amount or more. For example, when I say "I have at least ten dollars", I'm saying that I have 10 or more dollars. In your case, "x plus 5 is at least 45" translates to
 Linear-equations/219034: x-4y=-81 solutions Answer 164800 by jim_thompson5910(28595)   on 2009-09-29 16:47:20 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. 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 4. This means that to go from point to point, we can go up 1 and over 4 So starting at , go up 1 unit and to the right 4 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
 Graphs/219036: Graph y equals x-51 solutions Answer 164798 by jim_thompson5910(28595)   on 2009-09-29 16:45:43 (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 1. This means that to go from point to point, we can go up 1 and over 1 So starting at , go up 1 unit 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
 Equations/219031: 9x-(6x-1)=21 solutions Answer 164797 by jim_thompson5910(28595)   on 2009-09-29 16:42:51 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is which approximates to .
 Equations/219030: -6b+1+4b=3b+6 solve for b please1 solutions Answer 164795 by jim_thompson5910(28595)   on 2009-09-29 16:41:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left 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. ---------------------------------------------------------------------- Answer: So the solution is
 Inverses/219015: how would i solve -6+ 4y =31 solutions Answer 164791 by jim_thompson5910(28595)   on 2009-09-29 16:27:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is which in decimal form is .
 Distributive-associative-commutative-properties/219013: x2+16x+a = (x+b)2 In the equation above, a and b are constants. If the equation is true for all values of x, what is the value of a ?1 solutions Answer 164790 by jim_thompson5910(28595)   on 2009-09-29 16:26:39 (Show Source): You can put this solution on YOUR website! Start with the given equation. FOIL the right side. Take note that the terms 16x and 2xb both have "x" terms (without an exponent). So this means that . Divide both sides by 2x to get or Notice how the term "a" does not have an "x" and doesn't have an "x" either. So this means that . Plug in to get . So So this tells us that
 Geometry_Word_Problems/219004: a.Identify the slope and the vertical intercept of the graph. y= 1/3x-41 solutions Answer 164788 by jim_thompson5910(28595)   on 2009-09-29 16:24:08 (Show Source): You can put this solution on YOUR website!Note: the vertical intercept is the same as the y-intercept. Notice how is in slope-intercept form where m is the slope and b is the y-intercept. So this shows us that the slope is and the y-intercept is
Number-Line/219003: i need help
i dont know how to graph 3.5, - 2.4, - 1.8 and 0.9 on a number line
how would the numbers go on the number line
1 solutions

Answer 164786 by jim_thompson5910(28595)   on 2009-09-29 16:21:19 (Show Source):
You can put this solution on YOUR website!
Plot of the number 3.5:
 Solved by pluggable solver: Plot a number on a number line

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Plot of the number -2.4:
 Solved by pluggable solver: Plot a number on a number line

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Plot of the number -1.8:
 Solved by pluggable solver: Plot a number on a number line

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Plot of the number 0.9:
 Solved by pluggable solver: Plot a number on a number line

Note: this is NOT on the value 1 (but really close to it)
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If you need more help with plotting numbers on a number line, check out this solver

 Number-Line/219000: i need help i dont know how to graph 3/4, - 1/3 and 5 on a number line i know that 3/4 is equal to 0.75 and - 1/3 is equal to -0.33 but how would the numbers go on the number line 1 solutions Answer 164784 by jim_thompson5910(28595)   on 2009-09-29 16:17:30 (Show Source): You can put this solution on YOUR website!Step 1) Draw a straight horizontal line Step 2) Draw tick marks at equal distances and label them with whole numbers (think of a ruler). To plot , realize that Since 0.75 is less than 1 but greater than zero, this means that 0.75 goes in between 0 and 1. Also, note that 0.75 > 0.5 (which is one-half). So 0.75 is in between 1/2 and 1. If you follow the same logic used above to plot -1/3 and 5, you should get:
 Equations/218928: The cost of 4 pillows, plus 5% sales tax, was 46.20. How much did each pillow cost? if possible i need it to be step by step on how to do this problem so i will understand how to do it??1 solutions Answer 164753 by jim_thompson5910(28595)   on 2009-09-29 13:14:29 (Show Source): You can put this solution on YOUR website!Let x = original cost of 4 pillows (ie cost without sales tax added) Since 5% of the original cost 'x' is , this means that the sales tax is dollars. Add this to the original cost 'x' to get and set that expression equal to the final cost $46.20 to get If you are stumped on any part of the explanation above, go over it again. If you are still stuck on the translation, then feel free to ask me. It's very important to know how to translate word problems into algebraic ones. -------------------------------- Now let's solve for 'x': Start with the previous equation. Combine like terms. Divide both sides by 1.05 to isolate 'x'. Divide. Since and we let x=original cost of 4 pillows, this means that 4 pillows cost$44 without sales tax. Now just divide that last figure by 4 (since there are 4 pillows) to find the individual cost per pillow: So each pillow costs $11.  Triangles/218860: a right triangle has sides whose lengths are consecutive integers. Find the lengths of the sides. i dont know how to find the lengths of the sides.1 solutions Answer 164730 by jim_thompson5910(28595) on 2009-09-29 09:51:50 (Show Source): You can put this solution on YOUR website!First a definition: Consecutive integers are simply whole numbers that follow one another. Example: 1, 2, 3, 4, 5, 6, etc are consecutive integers. In general, the terms x, x+1, x+2, x+3, x+4, ... are consecutive integers (where 'x' is a whole number). Since we're given that "a right triangle has sides whose lengths are consecutive integers", we're basically told that , , and where 'a' and 'b' are the legs of the triangle and 'c' is the hypotenuse. Now remember that we can relate the sides of a triangle using the Pythagorean theorem: Just plug in the values of 'a', 'b', and 'c' to get: FOIL Get everything to one side. Combine like terms. From here, just use the quadratic formula or factor to find 'x'. I'll let you do that.  Triangles/218859: on a right triangle if side A = 30ft. and side B = 40ft. What does side C =.1 solutions Answer 164729 by jim_thompson5910(28595) on 2009-09-29 09:46:20 (Show Source): You can put this solution on YOUR website!Hint: use the Pythagorean theorem . In this case, and and we'll let . So plugging this in gets us . From here, just solve for 'x' to find the length of 'c'. Let me know if this is enough to get you started.  Equations/218439: 2x^3-3x^2=12-8x? here's my work: x^2(2x-3) 4(2x-3) (x^2+4)(2x-3) x^2+4=0 2x-3=0 x=2i x=3/21 solutions Answer 164642 by jim_thompson5910(28595) on 2009-09-28 20:29:34 (Show Source): You can put this solution on YOUR website!When solving , the solutions are or (don't forget about the plus/minus of the square root). So the three solutions are , or . Take note how the degree of the equation is 3 and that there are 3 solutions.  Numeric_Fractions/218414: 2x-3=71 solutions Answer 164508 by jim_thompson5910(28595) on 2009-09-28 16:35:18 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is  Linear-systems/218387: Substitution method y=-3x+13 2x+9y=-81 solutions Answer 164489 by jim_thompson5910(28595) on 2009-09-28 15:51:29 (Show Source): You can put this solution on YOUR website! Start with the second equation. Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute Combine like terms on the left side Subtract 117 from both sides Combine like terms on the right side Divide both sides by -25 to isolate x Divide Now that we know that , we can plug this into to find Substitute for each Simplify So our answer is and which also looks like Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer. Graph of and (red) and (green)  Polynomials-and-rational-expressions/218390: I think this is the topic for factoring polynomials and using the zero property.. well im completely lost on the difference and how to do them. Can you help me and give me some problems??1 solutions Answer 164487 by jim_thompson5910(28595) on 2009-09-28 15:47:43 (Show Source): You can put this solution on YOUR website!Ex: Solve Start with the given equation. Factor. or Use the zero product property. or Solve each equation for 'x'. So the solutions are or  Graphs/218389: Addition method 5x-2y=-1 7x+4y=531 solutions Answer 164486 by jim_thompson5910(28595) on 2009-09-28 15:45:58 (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 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. Notice how the y terms cancel out. 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 our answer is 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)  Equations/218384: solve 20=-4(f+6)+141 solutions Answer 164484 by jim_thompson5910(28595) on 2009-09-28 15:42:23 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the right side. Subtract from both sides. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which in decimal form is .  Graphs/218385: 2x+y=10 6x+3y=301 solutions Answer 164483 by jim_thompson5910(28595) on 2009-09-28 15:41:32 (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. 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. Notice how the x terms cancel out. Simplify. Since is always true, this means that there are an infinite number of solutions. So the system is consistent and dependent.  Equations/218377: whats the answer to this equation -8(x+3)-4x=601 solutions Answer 164478 by jim_thompson5910(28595) on 2009-09-28 15:31:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is  Matrices-and-determiminant/218378: I'm confused about finding the size of a martice. Example- what size is the following matrix? (3 -2 0 1) Please explain how I find the correct answer. thank you.1 solutions Answer 164477 by jim_thompson5910(28595) on 2009-09-28 15:29:57 (Show Source): You can put this solution on YOUR website!The size of a matrix is just the number of rows x the number of columns. In this case, there's one row and 4 columns (assuming that you typed it in the correct format). So the size of the matrix is 1 x 4. Signed-numbers/218372: One of the wrenches has a measurement of 7/16” and the other has a size of 3/8”. Which one is larger? 1 solutions Answer 164470 by jim_thompson5910(28595) on 2009-09-28 15:13:29 (Show Source): You can put this solution on YOUR website!  Solved by pluggable solver: Compare two Ratios To compare two ratios, we can use cross multiplication. We can arrive at the answer in the following way: ? Cross multiplying: 7*8 ? 3*16 => 56 ? 48 since 56 > 48, we get that > So this means that the 7/16" wrench is larger.  Money_Word_Problems/218358:$40 at 4% (compounded daily) how long will it take for me to have $50?1 solutions Answer 164468 by jim_thompson5910(28595) on 2009-09-28 15:03:57 (Show Source): You can put this solution on YOUR website! Start with the compounding interest formula. Plug in , , (note: 0.04 is the decimal equivalent of 4%) and Divide to get . Add. Divide both sides by . Divide to get . Divide to get . Pull down the exponent. Divide both sides by . Evaluate the left side with a calculator. Divide both sides by to isolate 't'. Divide. Rearrange the equation. Round to the nearest hundredth. So it will take about 5.58 years for an initial investment of$40 to grow to \$50 (compounded 365 times a year at 4%).