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Polynomials-and-rational-expressions/708977: What is the degree of the polynomial 8y squared - square root of 2
1 solutions

Answer 436339 by jim_thompson5910(28595) About Me  on 2013-01-31 18:03:36 (Show Source):
You can put this solution on YOUR website!
The largest exponent is 2, so the degree is 2.


Proportions/708962: on a map the scale is 1/2 inches =25 miles and I k=need to find the actual distance. Can you help me find the actual distance for 8 and 3/4inches?

1 solutions

Answer 436337 by jim_thompson5910(28595) About Me  on 2013-01-31 17:56:35 (Show Source):
You can put this solution on YOUR website!
8 and 3/4 = 8 + 3/4

8 and 3/4 = 32/4 + 3/4

8 and 3/4 = 35/4
------------------------------------------

1/2 inches = 25 miles

1 inch = 2*25 miles

1 inch = 50 miles

35/4 inches = (35/4)*50 miles

35/4 inches = (35*50)/4 miles

35/4 inches = 1750/4 miles

35/4 inches = 875/2 miles

35/4 inches = (874 + 1)/2 miles

35/4 inches = 874/2 + 1/2 miles

35/4 inches = 437 + 1/2 miles

35/4 inches = 437 and 1/2 miles

8 and 3/4 inches = 437 and 1/2 miles


Equations/708957: -m/5=3
Solve the equation.
1 solutions

Answer 436329 by jim_thompson5910(28595) About Me  on 2013-01-31 17:37:44 (Show Source):
You can put this solution on YOUR website!
multiply both sides by -5 to go from

-m/5 = 3

to

m = -15


Equations/708954: 6y+34=2y-2 solve.

1 solutions

Answer 436328 by jim_thompson5910(28595) About Me  on 2013-01-31 17:36:29 (Show Source):
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6y%2B34=2y-2 Start with the given equation.


6y=2y-2-34 Subtract 34 from both sides.


6y-2y=-2-34 Subtract 2y from both sides.


4y=-2-34 Combine like terms on the left side.


4y=-36 Combine like terms on the right side.


y=%28-36%29%2F%284%29 Divide both sides by 4 to isolate y.


y=-9 Reduce.


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Answer:

So the solution is y=-9


Inequalities/708947: Please solve it for me 2x+6<5(x-3)
1 solutions

Answer 436326 by jim_thompson5910(28595) About Me  on 2013-01-31 17:34:18 (Show Source):
You can put this solution on YOUR website!

2x%2B6%3C5%28x-3%29 Start with the given inequality.


2x%2B6%3C5x-15 Distribute.


2x%3C5x-15-6 Subtract 6 from both sides.


2x-5x%3C-15-6 Subtract 5x from both sides.


-3x%3C-15-6 Combine like terms on the left side.


-3x%3C-21 Combine like terms on the right side.


x%3E%28-21%29%2F%28-3%29 Divide both sides by -3 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E7 Reduce.


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Answer:

So the solution is x%3E7


Inequalities/708940: 9x-2x>=14-9(-x-4)
1 solutions

Answer 436320 by jim_thompson5910(28595) About Me  on 2013-01-31 17:27:24 (Show Source):
You can put this solution on YOUR website!

9x-2x%3E=14-9%28-x-4%29 Start with the given inequality.


9x-2x%3E=14%2B9x%2B36 Distribute.


7x%3E=14%2B9x%2B36 Combine like terms on the left side.


7x%3E=9x%2B50 Combine like terms on the right side.


7x-9x%3E=50 Subtract 9x from both sides.


-2x%3E=50 Combine like terms on the left side.


x%3C=%2850%29%2F%28-2%29 Divide both sides by -2 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C=-25 Reduce.


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Answer:

So the solution is x%3C=-25


logarithm/708946: logb27=3
1 solutions

Answer 436318 by jim_thompson5910(28595) About Me  on 2013-01-31 17:26:35 (Show Source):
You can put this solution on YOUR website!
logb27=3

b^3 = 27

b^3 = 3^3

b = 3


Triangles/708891: Hi! I was wondering if I have a triangle where two of the angles are 60 and the third angle is y and one side is labled 4x how would I find the variables? It also says the perimeter is 54 too.
1 solutions

Answer 436301 by jim_thompson5910(28595) About Me  on 2013-01-31 16:12:30 (Show Source):
You can put this solution on YOUR website!
All 3 angles in a triangle add up to 180 degrees, so

60+60+y = 180

120 + y = 180

y = 180 - 120

y = 60

So the third angle is 60

Since each angle is 60, we have an equilateral triangle. So we have 3 sides equal to 4x

They add to the perimeter of 54, which means

4x+4x+4x = 54

12x = 54

x = 54/12

x = 27/6

x = 9/2

x = 4.5

So in the end, x = 4.5 and y = 60

Because x = 4.5, each side is therefore 4.5*4 = 18 units long.


Equations/708894: how to factor? -2x^2-3x+6
1 solutions

Answer 436298 by jim_thompson5910(28595) About Me  on 2013-01-31 16:09:15 (Show Source):
You can put this solution on YOUR website!

-2x%5E2-3x%2B6 Start with the given expression.


-%282x%5E2%2B3x-6%29 Factor out the GCF -1.


Now let's try to factor the inner expression 2x%5E2%2B3x-6


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


Looking at the expression 2x%5E2%2B3x-6, we can see that the first coefficient is 2, the second coefficient is 3, and the last term is -6.


Now multiply the first coefficient 2 by the last term -6 to get %282%29%28-6%29=-12.


Now the question is: what two whole numbers multiply to -12 (the previous product) and add to the second coefficient 3?


To find these two numbers, we need to list all of the factors of -12 (the previous product).


Factors of -12:
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 -12.
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 3:


First NumberSecond NumberSum
1-121+(-12)=-11
2-62+(-6)=-4
3-43+(-4)=-1
-112-1+12=11
-26-2+6=4
-34-3+4=1



From the table, we can see that there are no pairs of numbers which add to 3. So 2x%5E2%2B3x-6 cannot be factored.


===============================================================



Answer:


So -2x%5E2-3x%2B6 simply factors to -%282x%5E2%2B3x-6%29


In other words, -2x%5E2-3x%2B6=-%282x%5E2%2B3x-6%29.


Average/708899: if i have 85% final mark in bio, and i get 50% on my final exam, or even 40%, and the test is worth 70% of my mark. what will my grade go down to?
1 solutions

Answer 436296 by jim_thompson5910(28595) About Me  on 2013-01-31 16:07:48 (Show Source):
You can put this solution on YOUR website!
If you got a 50% on the final exam:

0.85*0.30 + 0.50*0.70 = 0.605

which means your grade would go down to a 60.5%

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

If you got a 40% on the final exam:

0.85*0.30 + 0.40*0.70 = 0.535

which means your grade would go down to a 53.5%


Inequalities/708803: solve the inequality and graph the solution set 3(4m-1)+7>28
1 solutions

Answer 436293 by jim_thompson5910(28595) About Me  on 2013-01-31 15:51:22 (Show Source):
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3%284m-1%29%2B7%3E28 Start with the given inequality.


12m-3%2B7%3E28 Distribute.


12m%2B4%3E28 Combine like terms on the left side.


12m%3E28-4 Subtract 4 from both sides.


12m%3E24 Combine like terms on the right side.


m%3E%2824%29%2F%2812%29 Divide both sides by 12 to isolate m.


m%3E2 Reduce.


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

Answer:

So the solution is m%3E2

To graph m%3E2, follow these steps

Step 1) Draw out a number line. Make sure that this number line includes the number 2.

Step 2) Plot a circle at the point 2 on the number line.

Step 3) Make sure you keep this circle an open circle (ie NOT filled in). You don't fill in the circle because we have a > sign. This tells you to exclude the endpoint.

Step 4) Shade to the right of this circle to completely graph m>2. You shade to the right because there is a > sign.


So to sum things up, you plot an OPEN circle at 2 and shade to the RIGHT.


Polynomials-and-rational-expressions/708860: y^3+8y^2-y-8
1 solutions

Answer 436290 by jim_thompson5910(28595) About Me  on 2013-01-31 15:24:06 (Show Source):
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y%5E3%2B8y%5E2-y-8 Start with the given expression


%28y%5E3%2B8y%5E2%29%2B%28-y-8%29 Group the terms in two pairs


y%5E2%28y%2B8%29-1%28y%2B8%29 Factor out the GCF y%5E2 out of the first group. Factor out the GCF -1 out of the second group


%28y%5E2-1%29%28y%2B8%29 Since we have the common term y%2B8, we can combine like terms


%28y-1%29%28y%2B1%29%28y%2B8%29 Factor y%5E2-1 to get %28y-1%29%28y%2B1%29 using the difference of squares rule


So y%5E3%2B8y%5E2-y-8 factors to %28y-1%29%28y%2B1%29%28y%2B8%29


In other words, y%5E3%2B8y%5E2-y-8=%28y-1%29%28y%2B1%29%28y%2B8%29 for all values of y


Linear-equations/708864: 3x – y = 28
3x + y = 14
1 solutions

Answer 436289 by jim_thompson5910(28595) About Me  on 2013-01-31 15:22:11 (Show Source):
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Hint:

Add the equations to get

3x – y = 28
3x + y = 14
------------
6x+0y = 42

6x = 42

solve 6x = 42 for x, then use this to find y.


Polynomials-and-rational-expressions/708861: 4x^2-16x=0
1 solutions

Answer 436285 by jim_thompson5910(28595) About Me  on 2013-01-31 15:03:09 (Show Source):
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Hint:

4x^2-16x=0

factors to

4x(x - 4) = 0

and that breaks into

4x = 0 or x-4 = 0


Equations/708871: -x+14=7(2+3x)
1 solutions

Answer 436284 by jim_thompson5910(28595) About Me  on 2013-01-31 15:02:21 (Show Source):
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-x%2B14=7%282%2B3x%29 Start with the given equation.


-x%2B14=14%2B21x Distribute.


-x=14%2B21x-14 Subtract 14 from both sides.


-x-21x=14-14 Subtract 21x from both sides.


-22x=14-14 Combine like terms on the left side.


-22x=0 Combine like terms on the right side.


x=%280%29%2F%28-22%29 Divide both sides by -22 to isolate x.


x=0 Reduce.


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

Answer:

So the solution is x=0


Equations/708169: 10+3x=26-5x
1 solutions

Answer 436071 by jim_thompson5910(28595) About Me  on 2013-01-30 14:22:34 (Show Source):
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10%2B3x=26-5x Start with the given equation.


3x=26-5x-10 Subtract 10 from both sides.


3x%2B5x=26-10 Add 5x to both sides.


8x=26-10 Combine like terms on the left side.


8x=16 Combine like terms on the right side.


x=%2816%29%2F%288%29 Divide both sides by 8 to isolate x.


x=2 Reduce.


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

Answer:

So the solution is x=2


Equations/708170: 11-2x=31-7x
1 solutions

Answer 435997 by jim_thompson5910(28595) About Me  on 2013-01-30 02:37:30 (Show Source):
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11-2x=31-7x Start with the given equation.


-2x=31-7x-11 Subtract 11 from both sides.


-2x%2B7x=31-11 Add 7x to both sides.


5x=31-11 Combine like terms on the left side.


5x=20 Combine like terms on the right side.


x=%2820%29%2F%285%29 Divide both sides by 5 to isolate x.


x=4 Reduce.


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

Answer:

So the solution is x=4


Equations/708171: 16x+21=30+13x
1 solutions

Answer 435996 by jim_thompson5910(28595) About Me  on 2013-01-30 02:32:22 (Show Source):
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16x%2B21=30%2B13x Start with the given equation.


16x=30%2B13x-21 Subtract 21 from both sides.


16x-13x=30-21 Subtract 13x from both sides.


3x=30-21 Combine like terms on the left side.


3x=9 Combine like terms on the right side.


x=%289%29%2F%283%29 Divide both sides by 3 to isolate x.


x=3 Reduce.


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

Answer:

So the solution is x=3


Equations/708172: 4x+10=2(2x+5)
1 solutions

Answer 435995 by jim_thompson5910(28595) About Me  on 2013-01-30 02:31:48 (Show Source):
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4x%2B10=2%282x%2B5%29 Start with the given equation.


4x%2B10=4x%2B10 Distribute.


4x=4x%2B10-10 Subtract 10 from both sides.


4x-4x=10-10 Subtract 4x from both sides.


0x=10-10 Combine like terms on the left side.


0x=0 Combine like terms on the right side.


0=0 Simplify.


Since this equation is ALWAYS true for any x value, this means x can equal any number.


So there are an infinite number of solutions.


Exponents/708121: The product of 6x to the power of a and x is ?
1 solutions

Answer 435982 by jim_thompson5910(28595) About Me  on 2013-01-29 23:47:58 (Show Source):
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6x^a * x = 6x^a * x^1

6x^a * x = 6x^(a + 1)

Answer: 6x^(a + 1)


Inequalities/708122: Solve the inequalities, and express the solutions in terms of intervals
-3 ≤ x - 9 ≤ 3
1 solutions

Answer 435975 by jim_thompson5910(28595) About Me  on 2013-01-29 22:52:59 (Show Source):
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-3 ≤ x - 9 ≤ 3

-3+9 ≤ x - 9+9 ≤ 3+9

6 ≤ x + 0 ≤ 12

6 ≤ x ≤ 12

Answer: 6 ≤ x ≤ 12


test/708105: How do you solve
K^2-12k+35=0
1 solutions

Answer 435974 by jim_thompson5910(28595) About Me  on 2013-01-29 22:26:54 (Show Source):
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Hint: factor the left side

k^2 - 12k + 35 = 0

(k - 7)(k - 5) = 0


Problems-with-consecutive-odd-even-integers/708110: Gain of 15 yards in football ?

1 solutions

Answer 435973 by jim_thompson5910(28595) About Me  on 2013-01-29 22:26:12 (Show Source):
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Gain of 15 yards in football = +15 or just 15 as an integer


test/708077: The roots of the equation x^2-14x+48=0 are ...
1 solutions

Answer 435966 by jim_thompson5910(28595) About Me  on 2013-01-29 21:42:42 (Show Source):
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Hint:

In the equation

x^2-14x+48=0

The left side factors to

(x-6)(x-8)=0


Inequalities/708027: 4x+49<9-x
1 solutions

Answer 435952 by jim_thompson5910(28595) About Me  on 2013-01-29 20:47:25 (Show Source):
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4x%2B49%3C9-x Start with the given inequality.


4x%3C9-x-49 Subtract 49 from both sides.


4x%2Bx%3C9-49 Add x to both sides.


5x%3C9-49 Combine like terms on the left side.


5x%3C-40 Combine like terms on the right side.


x%3C%28-40%29%2F%285%29 Divide both sides by 5 to isolate x.


x%3C-8 Reduce.


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

Answer:

So the solution is x%3C-8


Numbers_Word_Problems/707958: The sum of two numbers is 20.
Their difference is 4.
Solve by elimination to find the two numbers.



1 solutions

Answer 435930 by jim_thompson5910(28595) About Me  on 2013-01-29 19:31:01 (Show Source):
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Hint:

x+y = 20
x-y = 4
---------
2x+0y = 24

2x = 24

Solve for x. Then use this to find y.


Percentage-and-ratio-word-problems/707941: in a group of 12 students, 7 of the students were girls. What is the fraction of boys and girls in the group
1 solutions

Answer 435929 by jim_thompson5910(28595) About Me  on 2013-01-29 19:30:10 (Show Source):
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There are 12 - 7 = 5 boys


Fraction of Girls: 7/12

Fraction of Boys: 5/12


Equations/707959: 3x-9=6x-14
1 solutions

Answer 435928 by jim_thompson5910(28595) About Me  on 2013-01-29 19:29:07 (Show Source):
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3x-9=6x-14 Start with the given equation.


3x=6x-14%2B9 Add 9 to both sides.


3x-6x=-14%2B9 Subtract 6x from both sides.


-3x=-14%2B9 Combine like terms on the left side.


-3x=-5 Combine like terms on the right side.


x=%28-5%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=5%2F3 Reduce.


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

Answer:

So the solution is x=5%2F3


test/707939: Tell whether the ordered pair is a solution of the equation.
y=5x; (15, -3)
1 solutions

Answer 435927 by jim_thompson5910(28595) About Me  on 2013-01-29 19:27:58 (Show Source):
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y = 5x

-3 = 5*15 ... plug in x = 15 and y = -3

-3 = 75

Since that last equation is FALSE, this means (15, -3) is NOT a solution.


Proofs/707955: I have been wrestling with trying to solve this proof.....Pleeaaassseee HELP!
(J->L)->(M->N),A,A->(J->L),(M->N)->[(J->L)->O],O->(A->B)|-B

1 solutions

Answer 435925 by jim_thompson5910(28595) About Me  on 2013-01-29 19:20:03 (Show Source):
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You have A (ie you're assuming A is true) and you have this

A -> (J -> L)

So you can use modus ponens to get J -> L

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

You have this statement

(J->L)->(M->N)

and you can use modus ponens with this and the "J -> L" you got earlier to get M -> N

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

Now you have M -> N and (M->N)->[(J->L)->O]

Use modus ponens to get (J->L)->O

Then use modus ponens again with J -> L and (J->L)->O to get O

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

You now have O and O -> (A -> B)

Use modus ponens to get A -> B

Finally, use modus ponens with A and A -> B to get B

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

So all of the given statements and using modus ponens a bunch of times leads us to the conclusion of B

This proves that the argument and conclusion is valid.


Equations/707938: -3(x+5)= 3(x-1)
1 solutions

Answer 435923 by jim_thompson5910(28595) About Me  on 2013-01-29 19:14:56 (Show Source):
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-3%28x%2B5%29=3%28x-1%29 Start with the given equation.


-3x-15=3x-3 Distribute.


-3x=3x-3%2B15 Add 15 to both sides.


-3x-3x=-3%2B15 Subtract 3x from both sides.


-6x=-3%2B15 Combine like terms on the left side.


-6x=12 Combine like terms on the right side.


x=%2812%29%2F%28-6%29 Divide both sides by -6 to isolate x.


x=-2 Reduce.


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

Answer:

So the solution is x=-2