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 Triangles/593946: In the given 30-60-90 triangle, one leg is 10 mm, find the measure of the other leg and the hypotenuse.1 solutions Answer 376550 by jim_thompson5910(28595)   on 2012-04-01 01:10:56 (Show Source): You can put this solution on YOUR website!Is this "one leg" the shorter leg? Or is this the longer leg? If it's the shorter leg, then the hypotenuse is twice that at 2*10 = 20 mm Again, if it's the shorter leg, then the longer leg is mm In general, if x is the shorter leg in a 30-60-90 triangle, then 2x is the hypotenuse and is the longer leg. ------------------------------------------------------- OR If the "one leg" is the longer leg, then the shorter leg 'x' is ----> So the shorter leg 'x' is mm long and the hypotenuse 'h' is So the hypotenuse 'h' is mm long
 Triangles/593943: In a 45°-45°-90° triangle where the hypotenuse measures m, find the area of the triangle 1 solutions Answer 376549 by jim_thompson5910(28595)   on 2012-04-01 01:05:35 (Show Source): You can put this solution on YOUR website!If the legs are x, then So in short, . Now solve for x to get This means that the leg 'x' is Now use this to find the area: Therefore, if the hypotenuse is 'm' units long, then the area of the 45-45-90 degree triangle is $\Large A = \frac{m^2}{4}$
 Rational-functions/593935: Solve 3/w=9/w-1/111 solutions Answer 376548 by jim_thompson5910(28595)   on 2012-04-01 00:56:56 (Show Source): You can put this solution on YOUR website! So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Proofs/593929: I can only use the 8 implicational rules to solve this problem. 1. ~Fv~G 2. ~F > Z 3. ~G > ~R 4. (Zv~R) > (U > P) 5. ~P :. ~U1 solutions Answer 376547 by jim_thompson5910(28595)   on 2012-04-01 00:54:43 (Show Source): You can put this solution on YOUR website!1. ~F v ~G 2. ~F > Z 3. ~G > ~R 4. (Z v ~R) > (U > P) 5. ~P :. ~U ----------------------------------------------------------------------- 6. (~F > Z) . (~G > ~R) 2,3 Conjunction 7. Z v ~R 6,1 Constructive Dilemma 8. U > P 4,7 Modus Ponens 9. ~U 8,5 Modus Tollens 
 Proofs/593928: I can only use the 8 implicational rules. I've tried but can seem to get it. someone please help 1. (FvE)> ~D 2. SvD 3. E :. S 1 solutions Answer 376546 by jim_thompson5910(28595)   on 2012-04-01 00:52:03 (Show Source): You can put this solution on YOUR website!1. (F v E)> ~D 2. S v D 3. E :. S -------------------------------------------------------------- 4. F v E 3 Addition 5. ~D 1,4 Modus Ponens 6. S 2,5 Disjunctive Syllogism 
 Proofs/593930: I can only use the 8 implicational rules 1. (A v ~B) >(F v (R . G)) 2. A 3. F > L 4. (R . G) > T 5. (L v T) > S :. S1 solutions Answer 376545 by jim_thompson5910(28595)   on 2012-04-01 00:50:28 (Show Source): You can put this solution on YOUR website!1. (A v ~B) > (F v (R . G)) 2. A 3. F > L 4. (R . G) > T 5. (L v T) > S :. S -------------------------------------------------------------------------------------------------------------- 6. A v ~B 2 Addition 7. F v (R . G) 1,6 Modus Ponens 8. (F > L) . ( (R . G) > T ) 3,4 Conjunction 9. L v T 8,7 Constructive Dilemma 10. S 5,9 Modus Ponens 
 Bodies-in-space/593925: True of False: All lines intersecting a sphere are tangent to the sphere. Every plane that intersects a sphere creates a great circle. The eastern hemisphere of Earth is congruent to the western hemisphere of Earth. The diameter of a sphere is congruent to the diameter of its great circle. PLEASE!!! And THANK YOU! 1 solutions Answer 376529 by jim_thompson5910(28595)   on 2012-03-31 20:31:49 (Show Source): You can put this solution on YOUR website!All lines intersecting a sphere are tangent to the sphere. False, a line may intersect a sphere twice. -------------------------------------------------------------------------- Every plane that intersects a sphere creates a great circle. False, only planes that go through the center of the sphere create create circles. -------------------------------------------------------------------------- The eastern hemisphere of Earth is congruent to the western hemisphere of Earth. True, they are two equal halves of the sphere. -------------------------------------------------------------------------- The diameter of a sphere is congruent to the diameter of its great circle. True, the radii of a sphere and any great circle are equal (this can be shown with a drawing). This applies to diameters as well.
 Rational-functions/593910: Give an equation of the form f(x)=a^x to define the exponential function whose graph contains the point (4,81). 1 solutions Answer 376524 by jim_thompson5910(28595)   on 2012-03-31 19:45:26 (Show Source): You can put this solution on YOUR website! Answer: The equation is
 Polygons/593920: How do you find the sum of the measures of the interior angles of a convex 24-gon? 1 solutions Answer 376523 by jim_thompson5910(28595)   on 2012-03-31 19:43:52 (Show Source): You can put this solution on YOUR website!S = 180(n-2) S = 180(24-2) S = 180(22) S = 3960 So the sum of all of the measures of the interior angles of a convex 24-gon is 3960 degrees.
 Numeric_Fractions/593913: 4.5 convert to a fraction1 solutions Answer 376522 by jim_thompson5910(28595)   on 2012-03-31 19:42:37 (Show Source): You can put this solution on YOUR website!4.5 = 4 + 0.5 = 4 + 1/2 = 8/2 + 1/2 = 9/2 This means that $\Large 4.5 = \frac{9}{2}$ or $\Large 4.5 = 4\frac{1}{2}$
 Numeric_Fractions/593915: what percent of 70 is 42?1 solutions Answer 376520 by jim_thompson5910(28595)   on 2012-03-31 19:40:54 (Show Source): You can put this solution on YOUR website!(x/100)*70 = 42 x/100 = 42/70 x/100 = 0.6 x = 0.6*100 x = 60% Answer: 60% of 70 is 42.
 Numeric_Fractions/593919: 20 is 50% of what?1 solutions Answer 376519 by jim_thompson5910(28595)   on 2012-03-31 19:39:52 (Show Source): You can put this solution on YOUR website!20 = 0.5x 20/0.5 = x 40 = x x = 40 So 20 is 50% of 40
 Numeric_Fractions/593916: convert to a fraction in lowest terms 22.6%1 solutions Answer 376518 by jim_thompson5910(28595)   on 2012-03-31 19:39:13 (Show Source): You can put this solution on YOUR website!22.6% = 22.6/100 = 226/1000 = 113/500 So 22.6% = 113/500
 Numeric_Fractions/593918: convert the decimal to a fraction 0.341 solutions Answer 376517 by jim_thompson5910(28595)   on 2012-03-31 19:38:30 (Show Source): You can put this solution on YOUR website!0.34 = 34/100 = 17/50 So 0.34 = 17/50
 Mixture_Word_Problems/593899: how many pounds are in a box that contains 675 pieces that weigh 4.1 ounces?1 solutions Answer 376516 by jim_thompson5910(28595)   on 2012-03-31 18:30:22 (Show Source): You can put this solution on YOUR website!675*4.1 = 2767.5 So 675 pieces weigh 2,767.5 oz Now divide by 16 to convert to pounds: 2767.5/16 = 172.96875 So 675 pieces weigh 172.96875 pounds
 Equations/593898: 7s squared -28s=01 solutions Answer 376513 by jim_thompson5910(28595)   on 2012-03-31 18:02:33 (Show Source): You can put this solution on YOUR website! or or So the solutions are or -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Miscellaneous_Word_Problems/593892: 240 hours split up into 49 hours a week is how many months?1 solutions Answer 376511 by jim_thompson5910(28595)   on 2012-03-31 17:57:19 (Show Source): You can put this solution on YOUR website!240/49 = 4.897959 weeks So its about 5 weeks, which is 2 months.
 Linear-equations/593882: The slope of a) y=4 b) x=61 solutions Answer 376510 by jim_thompson5910(28595)   on 2012-03-31 17:55:34 (Show Source): You can put this solution on YOUR website!a) Slope: m = 0 Keep in mind that the slope of any horizontal line of the form y = k is zero. ======================================================= b) Slope: Undefined All vertical lines of the form x = k have undefined slopes.
1 solutions

Answer 376508 by jim_thompson5910(28595)   on 2012-03-31 16:10:20 (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 :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

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

These factors pair up and multiply to .
1*12 = 12
2*6 = 12
3*4 = 12
(-1)*(-12) = 12
(-2)*(-6) = 12
(-3)*(-4) = 12

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

First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7

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).

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If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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 Proofs/593872: Can you help me with this proof? (O>R)>S / (P>R)~S // ~R The > is a horseshoe. I've been at this all day and I can't even think of how to start.1 solutions Answer 376502 by jim_thompson5910(28595)   on 2012-03-31 15:39:30 (Show Source): You can put this solution on YOUR website!1. (O > R) > S 2. (P > R) > ~S // ~R ------------------------------------------------------- 3. (~O v R) > S 1 MI 4. ~(~O v R) v S 3 MI 5. (~~O & ~R) v S 4 DM 6. (O & ~R) v S 5 DN 7. S v (O & ~R) 6 Comm 8. (S v O) & (S v ~R) 7 Dist 9. (S v ~R) & (S v O) 8 Comm 10. S v ~R 9 Simp 11. ~R v S 10 Comm 12. R > S 11 MI 13. ~S > ~R 12 Trans 14. (~P v R) > ~S 2 MI 15. ~(~P v R) v ~S 14 MI 16. (~~P & ~R) v ~S 15 DM 17. (P & ~R) v ~S 16 DN 18. ~S v (P & ~R) 17 Comm 19. (~S v P) & (~S v ~R) 18 Dist 20. (~S v ~R) & (~S v P) 19 Comm 21. ~S v ~R 20 Simp 22. ~R v ~S 21 Comm 23. R > ~S 22 MI 24. R > ~R 23,13 HS 25. ~R v ~R 24 MI 26. ~R 25 Taut  Notes: The abbreviations used are... MI: Material Implication DM: De Morgan's Law DN: Double Negation Dist: Distribution Comm: Commutation Simp: Simplification Trans: Transposition HS: Hypothetical Syllogism Taut: Tautology
 Functions/593859: Given the function f(x) = 16x + 9, evaluate f(16).1 solutions Answer 376497 by jim_thompson5910(28595)   on 2012-03-31 14:40:36 (Show Source): You can put this solution on YOUR website!f(x) = 16x + 9 f(16) = 16(16) + 9 f(16) = 256 + 9 f(16) = 265 So the answer is f(16) = 265
 Linear-equations/593817: what is the equation of the line that passes through points (-4,2) and (4,0)? 1 solutions Answer 376496 by jim_thompson5910(28595)   on 2012-03-31 14:24:06 (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 Rewrite as Distribute Multiply Add 2 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 -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Trigonometry-basics/593849: Find S4 for the sequence 2,4,8,12,...1 solutions Answer 376495 by jim_thompson5910(28595)   on 2012-03-31 14:22:51 (Show Source): You can put this solution on YOUR website!S4 = Sum of the first four terms = 2+4+8+12 = 26
 Exponential-and-logarithmic-functions/593858: Solve for x. 7^x = 3y1 solutions Answer 376494 by jim_thompson5910(28595)   on 2012-03-31 14:21:34 (Show Source): You can put this solution on YOUR website! So the solution is -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------
 Trigonometry-basics/593772: Express 9,104,000 in scientific notation.1 solutions Answer 376445 by jim_thompson5910(28595)   on 2012-03-31 01:23:05 (Show Source): You can put this solution on YOUR website!Notice that if you start with 9.104, you'll have to move the decimal point 6 places to the right to get 9,104,000 So this means that $\large 9,104,000 = 9.104 \times 10^{6}$
 Graphs/593754: Find the distance between (9, -3) and (-1, 3)1 solutions Answer 376438 by jim_thompson5910(28595)   on 2012-03-30 23:04:39 (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 distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . Simplify the square root. So the exact distance is Which approximates to So the distance between the two points is approximately 11.662 units.
 Linear_Equations_And_Systems_Word_Problems/593672: Dennis takes care of private swimming pools. He charges $40 to travel to a home and then$45 per hour. The equation t = 40 + 45h models the total charge t for h hours of service. Which ordered pair (h, t) is NOT a solution for the equation?1 solutions Answer 376391 by jim_thompson5910(28595)   on 2012-03-30 15:05:58 (Show Source): You can put this solution on YOUR website!You've got the problem written out fine, but you are missing the possible ordered pairs to choose from. Please repost.
Polynomials-and-rational-expressions/593670: 6x^4-18x^3+12x^2

1 solutions

Answer 376390 by jim_thompson5910(28595)   on 2012-03-30 15:04:57 (Show Source):
You can put this solution on YOUR website!
I'm guessing you want to factor this. Let me know if my assumption is correct or not.

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
-1,-2

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

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

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

First NumberSecond NumberSum
121+2=3
-1-2-1+(-2)=-3

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).

 percentage/593667: I need help with math. If I have $10,000, I invest and loose 50% the first year. The second year I make 90%. What is my growth percentage? How much$ do I have?1 solutions Answer 376389 by jim_thompson5910(28595)   on 2012-03-30 14:56:35 (Show Source): You can put this solution on YOUR website!You lost 50% of 10,000, so you now have 10000 - 0.5*10000 = 10000 - 5000 = 5000 So after the first year, you'll have $5,000 Then you make 90%. This means that you're adding 90% of 5 thousand to 5 thousand, so... 5000 + 0.9*5000 = 5000 + 4500 = 9500 This means that after the second year, you'll have$9,500 ------------------------------------------------------- Your growth percentage is then Percent Growth = [(New - Old)/Old] * 100 Percent Growth = [(9500-10000)/10000] * 100 Percent Growth = [-500/10000] * 100 Percent Growth = -0.05 * 100 Percent Growth = -5% This means that you really lost 5% (and didn't grow at all)
6x^2+7x-3
1 solutions

Answer 376349 by jim_thompson5910(28595)   on 2012-03-30 00:14:12 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.

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 :
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18

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

These factors pair up and multiply to .
1*(-18) = -18
2*(-9) = -18
3*(-6) = -18
(-1)*(18) = -18
(-2)*(9) = -18
(-3)*(6) = -18

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

First NumberSecond NumberSum
1-181+(-18)=-17
2-92+(-9)=-7
3-63+(-6)=-3
-118-1+18=17
-29-2+9=7
-36-3+6=3

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).

--------------------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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 Numeric_Fractions/593475: If f(x) = 3x + 2, find f(2). 1 solutions Answer 376348 by jim_thompson5910(28595)   on 2012-03-30 00:00:19 (Show Source): You can put this solution on YOUR website!f(x) = 3x + 2 f(2) = 3(2) + 2 f(2) = 6 + 2 f(2) = 8 So the answer is f(2) = 8