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test/631843:
1 solutions

Answer 397840 by jim_thompson5910(28595) on 2012-07-25 13:56:30 (Show Source):

You can put this solution on YOUR website!
Problem missing.

Equations/631794: 20(3+4x)-7(8-6x)=150
1 solutions

Answer 397839 by jim_thompson5910(28595) on 2012-07-25 13:55:16 (Show Source):

You can put this solution on YOUR website!
20%283%2B4x%29-7%288-6x%29=150

Start with the given equation.

60%2B80x-56%2B42x=150

Distribute.

122x%2B4=150

Combine like terms on the left side.

122x=150-4

Subtract

from both sides.

122x=146

Combine like terms on the right side.

x=%28146%29%2F%28122%29

Divide both sides by 122

to isolate

Reduce.

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

Answer:

So the solution is x=73%2F61

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Jim
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Exponents/631817: Write the expression using exponents.
m*m
1 solutions

Answer 397838 by jim_thompson5910(28595) on 2012-07-25 13:54:21 (Show Source):

You can put this solution on YOUR website!
$m*m = {\color{red}m^2}$

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

Jim
--------------------------------------------------------------------------------------------------------------

Polynomials-and-rational-expressions/631810: -6c+8+4c=-3c+13
1 solutions

Answer 397837 by jim_thompson5910(28595) on 2012-07-25 13:52:07 (Show Source):

You can put this solution on YOUR website!
-6c%2B8%2B4c=-3c%2B13

Start with the given equation.

-2c%2B8=-3c%2B13

Combine like terms on the left side.

-2c=-3c%2B13-8

Subtract

from both sides.

-2c%2B3c=13-8

Add

to both sides.

c=13-8

Combine like terms on the left side.

c=5

Combine like terms on the right side.

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

Answer:

So the solution is c=5

logarithm/631831: ln(x+9)+ln(7x)
1 solutions

Answer 397836 by jim_thompson5910(28595) on 2012-07-25 13:50:21 (Show Source):

You can put this solution on YOUR website!
ln%28x%2B9%29%2Bln%287x%29

simplifies to ln%287x%5E2%2B63x%29

Points-lines-and-rays/631845: what is the slope of a line at (-3,0) and(4,3) ?
1 solutions

Answer 397834 by jim_thompson5910(28595) on 2012-07-25 13:48:52 (Show Source):

You can put this solution on YOUR website!
Note:

is the first point

. So this means that x%5B1%5D=-3

and

.
Also,

is the second point

. So this means that x%5B2%5D=4

and

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

Start with the slope formula.

m=%283-0%29%2F%284--3%29

Plug in

, and

Subtract

from

to get

Subtract

from

to get

So the slope of the line that goes through the points

and

Number-Line/631844: Solve the inequality and graph on a number line.
7x + 4 ≤ x – 2
1 solutions

Answer 397833 by jim_thompson5910(28595) on 2012-07-25 13:48:05 (Show Source):

You can put this solution on YOUR website!
7x%2B4%3C=x-2

Start with the given inequality.

7x%3C=x-2-4

Subtract

from both sides.

7x-x%3C=-2-4

Subtract

from both sides.

6x%3C=-2-4

Combine like terms on the left side.

6x%3C=-6

Combine like terms on the right side.

x%3C=%28-6%29%2F%286%29

Divide both sides by

to isolate

Reduce.

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

Answer:

So the solution is x%3C=-1

Here's the graph of the solution set (on the number line)

Notice the closed circle is at the endpoint.

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

Jim
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Graphs/631834: Multiply:
5x^4(-3x^2+8x-1)

Multiply:
(x^2+x+1)(2x^3-x^2+3)
I need some help thanks in advance!
I selected the wrong topic sorry! I couldnt change it! It was suppose to be exponents

1 solutions

Answer 397832 by jim_thompson5910(28595) on 2012-07-25 13:45:14 (Show Source):

You can put this solution on YOUR website!
5x%5E4%28-3x%5E2%2B8x-1%29+

5x%5E4%28-3x%5E2%29%2B5x%5E4%288x%29%2B5x%5E4%28-1%29+

distributes to -15x%5E6%2B40x%5E5-5x%5E4+

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

%28x%5E2%2Bx%2B1%29%282x%5E3-x%5E2%2B3%29

x%5E2%282x%5E3-x%5E2%2B3%29%2Bx%282x%5E3-x%5E2%2B3%29%2B1%282x%5E3-x%5E2%2B3%29

2x%5E5-x%5E4%2B3x%5E2%2B2x%5E4-x%5E3%2B3x%2B2x%5E3-x%5E2%2B3

So the answer is 2x%5E5%2Bx%5E4%2Bx%5E3%2B2x%5E2%2B3x%2B3

Linear-systems/631837: The first step to solving the equation 3 (x + 7) = 12x – 51 is to
combine like terms.
add the opposite to both sides.
distribute.
none of the above.
The second step to solving the equation 2x – 7 – (x – 5) = 0 is to
combine like terms.
add the opposite to both sides.
distribute.
divide both sides.
1 solutions

Answer 397831 by jim_thompson5910(28595) on 2012-07-25 13:39:37 (Show Source):

You can put this solution on YOUR website!
The first step to solving the equation 3 (x + 7) = 12x – 51 is to
combine like terms.
add the opposite to both sides.
distribute.
none of the above.

You start off by distributing to get 3x + 21 = 12x - 51

From there, you need to move all the x terms to one side and get everything else to the other. Then you simplify. Afterwards, you can completely isolate x.
-------------------------------------------------------
The second step to solving the equation 2x – 7 – (x – 5) = 0 is to
combine like terms.
add the opposite to both sides.
distribute.
divide both sides.

The first step is to distribute (like in the first problem before this). This will give you

2x – 7 – x + 5 = 0

Then you combine like terms to get

x - 2 = 0

I'm sure you see what to do from here (if not, let me know)

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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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Polynomials-and-rational-expressions/631646: Have I done this problem correctly?
(q+3/4)(q+3/4)= q^2+3/4q+9/16
1 solutions

Answer 397724 by jim_thompson5910(28595) on 2012-07-25 00:31:06 (Show Source):

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$\left(q+\frac{3}{4}\right)\left(q+\frac{3}{4}\right)$

$q*q+\frac{3}{4}q+\frac{3}{4}q+\left(\frac{3}{4}\right)\left(\frac{3}{4}\right)$

$q^2+\frac{3}{4}q+\frac{3}{4}q+\frac{9}{16}$

$q^2+\frac{6}{4}q+\frac{9}{16}$

$q^2+\frac{3}{2}q+\frac{9}{16}$

So $\left(q+\frac{3}{4}\right)\left(q+\frac{3}{4}\right) = q^2+\frac{3}{2}q+\frac{9}{16}$

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Functions/631649: f(x)=2x^2-16x-7
I found the vertex which is (4, -39)
I am looking to find the domain of "f" I'm not understanding how this is obtained.
1 solutions

Answer 397722 by jim_thompson5910(28595) on 2012-07-25 00:27:45 (Show Source):

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You can plug any number in for x and get some number out for f(x) (or y)

So the domain is the set of all real numbers.

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logarithm/631619: How do I write this as a single logarithm?
2(log x - log y)
I put 2log x/y But I'm not sure
1 solutions

Answer 397709 by jim_thompson5910(28595) on 2012-07-24 22:34:08 (Show Source):

You can put this solution on YOUR website!
You can also write it as

$2\log \left( \frac{x}{y} \right )$

$\log \left( \left( \frac{x}{y} \right )^2\right )$

$\log\left( \frac{x^2}{y^2} \right )$

Either one works (since they're all equivalent)

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test/631580: Hi how do you find the center and radius of a circle?
The equation is:
x^2 + y^2 = 4
Thanks
1 solutions

Answer 397683 by jim_thompson5910(28595) on 2012-07-24 19:48:18 (Show Source):

You can put this solution on YOUR website!
x^2 + y^2 = 4

is in the form

(x-h)^2 + (y-k)^2 = r^2

where in this case, h = 0, k = 0 and r = 2

So the center is (h,k) = (0,0) and the radius is r = 2

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Subset/631570: Let A={6,4,1, {3,0,8},{9}}. Determie whether the state is true or false.
{3,0,8} is a subset of A
1 solutions

Answer 397671 by jim_thompson5910(28595) on 2012-07-24 19:10:48 (Show Source):

You can put this solution on YOUR website!
{3,0,8} is indeed a subset of set A since it is a member of the set A.

So the statement is true.

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Equations/631564: Solve the equation and check the solution?
4(5z-1)-3(z+6)=10(z+1)
1 solutions

Answer 397667 by jim_thompson5910(28595) on 2012-07-24 18:45:19 (Show Source):

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4%285z-1%29-3%28z%2B6%29=10%28z%2B1%29

Start with the given equation.

20z-4-3z-18=10z%2B10

Distribute.

-22%2B17z=10z%2B10

Combine like terms on the left side.

17z=10z%2B10%2B22

Add

to both sides.

17z-10z=10%2B22

Subtract

from both sides.

7z=10%2B22

Combine like terms on the left side.

7z=32

Combine like terms on the right side.

z=%2832%29%2F%287%29

Divide both sides by

to isolate

.

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

Answer:

So the solution is z=32%2F7

To perform the check, you plug the solution back into the given equation. Then you simplify. If you get a true equation, then the solution is verified.

I'll let you do the check.

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Travel_Word_Problems/631553: If a car drove for 30 minutes and went 10 miles what was his average speed?
1 solutions

Answer 397651 by jim_thompson5910(28595) on 2012-07-24 17:27:14 (Show Source):

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30 min = 0.5 hours

d = rt

10 = r*0.5

10/0.5 = r

20 = r

r = 20

So his average speed is 20 miles per hour.

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Money_Word_Problems/631531: If I make 10 cents on every barrel of salt water, and there are 33,405 barrels of salt water, how many dollars do I get? $3340.50 or $334.05?
1 solutions

Answer 397642 by jim_thompson5910(28595) on 2012-07-24 16:33:07 (Show Source):

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(33,405 barrels )*(10 cents/1 barrel) = 33,405*10 = 334,050 cents

(334,050 cents)*(1 dollar/100 cents) = 334,050/100 = 3340.50 dollars

So the answer is $3340.50

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test/631524:
1 solutions

Answer 397635 by jim_thompson5910(28595) on 2012-07-24 16:12:56 (Show Source):

You can put this solution on YOUR website!
Problem missing. Please post the full problem.

Permutations/631516: find the probability of rolling a die three times and rolling a 2 each time
1 solutions

Answer 397631 by jim_thompson5910(28595) on 2012-07-24 15:55:18 (Show Source):

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There are 6^3 = 216 ways to roll a die 3 times. However, there is only 1 way to roll 3 twos.

So the probability is 1%2F216

Triangles/631508: classify a triangle with sides 18 18 18
1 solutions

Answer 397624 by jim_thompson5910(28595) on 2012-07-24 15:26:25 (Show Source):

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All three sides are equal, so this is an equilateral triangle.

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logarithm/631503: Log3(x)=-2
1 solutions

Answer 397622 by jim_thompson5910(28595) on 2012-07-24 15:24:26 (Show Source):

You can put this solution on YOUR website!
log%283%2C%28x%29%29=-2

Complex_Numbers/631497: Please simplify and solve
4√(-13) - 6√(-13)
1 solutions

Answer 397614 by jim_thompson5910(28595) on 2012-07-24 15:03:40 (Show Source):

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4√(-13) - 6√(-13)

(4 - 6)√(-13)

-2√(-13)

-2√(-1)*√(13)

-2i*√13

So the answer is $\LARGE -2i\sqrt{13}$

Note: $\LARGE 2i\sqrt{13}$

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Distributive-associative-commutative-properties/631487: Which axiom is illustrated by the equation 3(x+2)=3(2+x)?
1 solutions

Answer 397610 by jim_thompson5910(28595) on 2012-07-24 14:59:46 (Show Source):

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You're rearranging x+2 to get 2+x.

You're using the commutative property of addition since you can add in any order.

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Distributive-associative-commutative-properties/631493: Can you help me solve these questions: Apply the distributive property. Then simplify by combining like terms: (2w+4)(-3)+w and -(6y-5)+6y?
1 solutions

Answer 397609 by jim_thompson5910(28595) on 2012-07-24 14:58:50 (Show Source):

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# 1

%282w%2B4%29%28-3%29%2Bw

So the answer is -5w-12

---------------------------------------------------------------
# 2

-%286y-5%29%2B6y

So the answer is

Probability-and-statistics/631485: Construct a sample space of a couple who wants to have five children(excluding multiples)
1 solutions

Answer 397607 by jim_thompson5910(28595) on 2012-07-24 14:56:09 (Show Source):

You can put this solution on YOUR website!
The sample space is

{ B, B, B, B, B }
{ B, B, B, B, G }
{ B, B, B, G, B }
{ B, B, B, G, G }
{ B, B, G, B, B }
{ B, B, G, B, G }
{ B, B, G, G, B }
{ B, B, G, G, G }
{ B, G, B, B, B }
{ B, G, B, B, G }
{ B, G, B, G, B }
{ B, G, B, G, G }
{ B, G, G, B, B }
{ B, G, G, B, G }
{ B, G, G, G, B }
{ B, G, G, G, G }
{ G, B, B, B, B }
{ G, B, B, B, G }
{ G, B, B, G, B }
{ G, B, B, G, G }
{ G, B, G, B, B }
{ G, B, G, B, G }
{ G, B, G, G, B }
{ G, B, G, G, G }
{ G, G, B, B, B }
{ G, G, B, B, G }
{ G, G, B, G, B }
{ G, G, B, G, G }
{ G, G, G, B, B }
{ G, G, G, B, G }
{ G, G, G, G, B }
{ G, G, G, G, G }

Notice there are 2^5 = 32 ways to have 5 children.

Note: an element like "{ G, B, G, B, B }" tells us that the first child is a girl, the second is a boy, the third is a girl, and the last two kids are boys.

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Polynomials-and-rational-expressions/631478: perform the indicated operations on the expression
(5a^3+3a-2)-(4a^3+a^2+5)
a. a^3+a^2+3
b. a^3-a^2+3a-7
c. 20a^3+3a^2-10
d. 3a^6-7
If you could please explain I would really appreciate it
1 solutions

Answer 397602 by jim_thompson5910(28595) on 2012-07-24 14:39:21 (Show Source):

You can put this solution on YOUR website!
%285a%5E3%2B3a-2%29-%284a%5E3%2Ba%5E2%2B5%29

Start with the given expression.

5a%5E3%2B3a-2-4a%5E3-a%5E2-5

Distribute

%285a%5E3-4a%5E3%29%2B%28-a%5E2%29%2B%283a%29%2B%28-2-5%29

Group like terms

a%5E3-a%5E2%2B3a-7

Combine like terms

So the answer is a%5E3-a%5E2%2B3a-7

, which is choice B

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Polynomials-and-rational-expressions/631479: comp;etely factor the expression 7(x-y)-z(x-y)
a. (x-y)(7-z)
b. (x-y)^2(7-z)^3
c. prime
d. (x-y)(7+z)^3
If you could please explain I would really appreciate it
1 solutions

Answer 397601 by jim_thompson5910(28595) on 2012-07-24 14:37:14 (Show Source):

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Factor out the GCF x-y to get %287-z%29%28x-y%29

and you can flip the terms to get %28x-y%29%287-z%29

So the answer is choice A

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Polynomials-and-rational-expressions/631473: solve the equation 3z^3-300z=0
a. z=0
b. z=-4 and z=1
c. prime
d. z=0, z=-10
If you could please explain I would really appreciate it
1 solutions

Answer 397600 by jim_thompson5910(28595) on 2012-07-24 14:36:12 (Show Source):

You can put this solution on YOUR website!
Hint:

Factor out the GCF 3z to get

3z%28z%5E2-100%29=0

Then use the difference of squares rule to get

3z%28z-10%29%28z%2B10%29=0

Polynomials-and-rational-expressions/631475: completely factor the expression 2a^3-128
a. 2(a-4)(a^2+4a+16)
b. 2(a^3-64)
c. prime
d. 2(a-4)^3
If you could please explain I would really appreciate it
1 solutions

Answer 397599 by jim_thompson5910(28595) on 2012-07-24 14:34:38 (Show Source):

You can put this solution on YOUR website!
2a%5E3-128

Start with the given expression

2%28a%5E3-64%29

Factor out the GCF 2

2%28a%5E3-4%5E3%29

Rewrite 64 as 4%5E3

Now use the difference of cubes rule to factor

So 2a%5E3-128

completely factors to 2%28a-4%29%28a%5E2%2B4a%2B16%29

Which means that the answer is choice A

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Polynomials-and-rational-expressions/631477: completely factor the expression r^2-2r+1
a. prime
b. r(r-2)+1
c. (r-1)(r-1)
d. (r+1)(r-1)
If you could please explain I would really appreciate it
1 solutions

Answer 397597 by jim_thompson5910(28595) on 2012-07-24 14:31:20 (Show Source):

You can put this solution on YOUR website!

Looking at the expression r%5E2-2r%2B1

, 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
-1

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

These factors pair up and multiply to

.
1*1 = 1
(-1)*(-1) = 1

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

First Number	Second Number	Sum
1	1	1+1=2
-1	-1	-1+(-1)=-2

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 -2r

with

. Remember,

and

add to

. So this shows us that -r-r=-2r

Replace the second term -2r

with

Group the terms into two pairs.

r%28r-1%29%2B%28-r%2B1%29

Factor out the GCF

from the first group.

r%28r-1%29-1%28r-1%29

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.

%28r-1%29%28r-1%29

Combine like terms. Or factor out the common term r-1

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

Answer:

So r%5E2-2r%2B1

factors to %28r-1%29%28r-1%29

.

In other words, r%5E2-2r%2B1=%28r-1%29%28r-1%29

for all values of 'r'

So the answer is choice c).

Note: you can check the answer by expanding %28r-1%29%5E2

to get

or by graphing the original expression and the answer (the two graphs should be identical).

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Polynomials-and-rational-expressions/631467: completely factor the expression 4q^2+27r^4
a. 31q^2+27r^4
b. 27r^4(4q^2+1)
c. 4q(q+27r)
d. prime
If you could please explain I would really appreciate it
1 solutions

Answer 397596 by jim_thompson5910(28595) on 2012-07-24 14:28:59 (Show Source):

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There are no common factors between the coefficients 4 and 27. There are also no common factors between the variables q^2 and r^4

So the GCF is 1. This means that it's trivial to factor out the GCF (since we get the same thing really after we do)

Also, this is a binomial. This means that only the difference of squares rule is used to factor, but we have a sum (and not a difference) of terms.

So we can't use that method either.

So this expression is prime since it can't be factored.

Note: you can also go through the other options and rule them out. For example, choice C) is 4q(q+27r) which distributes to 4q^2 + 108rq, which is NOT the original expression. So choice C is out. You would do the same for the other answer choices.

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