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8y + 2y = 6y + 16

Subtract 6y from both sides of the equation.

8y + 2y - 6y = 16

8 apples + 2 apples - 6 apples = 4 apples          so........

8y + 2y - 6y = 4y

8y + 2y - 6y = 16

4y = 16

Divide both sides of the equation by 4.

y = 16/4

y = 4

Since the DVD has 15% off its original price, then that means:

100% - 15% =85% which is the sale price you pay,

Since the original price was "y", then:

85%y + 5% sales tax =The final sale price, or

0.85y + 0.05(0.85y) =The final sale price.

We want the equation of a line that passes through   (1, 10129)   , and   (3, 11400)  .

slope = (change in y's) / (change in x's)

slope = (10129 - 11400) / (1 - 3)

slope = (-1271) / (-2)

slope = 635.5

So, the equation of this line is

(y - 10129) = 635.5(x - 1)

y - 10129 = 635.5x - 635.5

y = 635.5x - 635.5 + 10129

y = 635.5x + 9493.5

To predict the cost of tuition in 2004-2005, we want to know what y equals when x matches the year 2004 - 2005.

The x value for the year 2001 - 2002 is 4

The x value for the year 2002 - 2003 is 5

The x value for the year 2003 - 2004 is 6

The x value for the year 2004 - 2005 is 7

So..we want to know what y equals when x equals 7.

Plug in 7 for x and solve for y.

y = 635.5(7) + 9493.5

y = 4448.5 + 9493.5

y = 13942

So, our line predicts the cost of tuition will be $13,942 in the school year 2004 - 2005.

*edit*

Here is a graph of the line with all the points on it:

You have to convert minutes to degrees as follows: Example: 36 degrees and 24 minutes. You will divide 24 minutes by 60 =24/60 =0.4 degrees. Then you add this to 36 degrees and you get =36 + 0.4 =36.4 degrees. And that is it.

Let the amount of money that Mario started with = M
M - $3 =What Mario has left after 1st. day.
1/2[M - $3] = 1/2M - $1.5 - What Mario has left after 2nd day
1/2M - $1.5 - $3 =1/2M - $4.5 -What Mario has left after 3rd day
1/2*[1/2M - $4.5] =1/4M - $2.25 -What Mario has left after 4th day.
1/4M - $2.25 - $3 =1/4M - $5.25 - What Mario has left after 5 days.

Let the amount of money that Luigi started with =L
1/3L = What Luigi has left after 1st day.
1/3L - $1 =What Luigi has left after 2nd day. 
Now we have the following:
1/4M - 5.25 = 0, and:
1/2M - 1.5 =1/3L - 1, solve for L, M
L = $30 - amount of money that Luigi started with.
M = $21 -amount of money that Mario started with.

If you meant:

Does     -6 + f = 2     if     f = 8         ?

-6 + f   \(\stackrel{?}{=}\)   2

Replace  " f "  with  " 8 "  .

-6 + 8   \(\stackrel{?}{=}\)   2

Simplify left side of equation.

2   \(\stackrel{?}{=}\)   2

2   =   2        true

Yes,     -6 + f = 2     if     f = 8  .

I am a 7th grade student, and you may not believe me BUT I AM. It just happens to be that everyone in my family either has a college degree, or plans to get one. Including me. My mother and grandmother are gifted writers, and my mother raised me correctly. I am an african american pre-teen girl. I have goals in life because I actually want to be a succesful independent black woman. I know what I have to do in order to get in the academy (Bayside Health And Sciences Academy). The reason why I care so much, is because my mother and I believe that going to a regular high school won't help me as much as I need it to. Being around high school students who worked hard (as much as I am currently) to get into the academy, shows the dedication that they have to achieve their goals. I AM A 7th GRADE STUDENT. And I didn't complete grade seven yet, in fact I just took my reading sol yesterday. By the way, for an advanced english student, it was rather easy. :) 

** Here are links.

http://www.baysidehs.vbschools.com/pages/students/academy/

http://www.vbschools.com/curriculum/academyprog/appprocess.asp

http://www.vbschools.com/curriculum/academyprog/hs_acad.asp

Im sorry if I don't fit the "7th grade criteria" for you. I dont have social media because I am not allowed. I was taught that with social media the second you try to get a job, you social media will be looked up. And that will be a factor in landing the job and starting your career. The reason why I put the above comment, was because I just wanted a simple yes or no answer. Instead, I was given a disrespectful comment and no answer. I apoligize for not being the "normal" twelve year old. By the way, I go to Larkspur Middle School if you need any reassurance. There is a reason why I am in advanced english and other advanced classes. :)

As Max found, it takes 42 minutes to read 30 pages of fiction.

2 pages of History = 7 minutes

2 x 15 = 7 x 15

30 pages of History = 105 minutes. So, her total reading time:

42 + 105 = 147 minutes.

66% =66/100 x 12 = 7.92

I assume that you meant -6 + f = 2f - 8

\(-6+f = 2f-8\\ f-6=2f-8\\ f+2=2f\\ 2 =f\\ f=2\)

5 pages = 7 minutes

5 x 6 pages = 7 x 6 minutes

30 pages = 42 minutes :D

Wow that's way too much. But I will do it because it is math and math is awesome :D

1) √27 * √50 ∕ √54 = 3√3 * 5√2 / 3√6 = 5

2) Hey are you kidding me the solution is fractional.

3) √-4 is imaginary

4) Weight required = \(640\times \dfrac{4}{4+3+3}=\mathbf{256kg}\)

5) 4x²+20x+3xy+15y = 4x(x + 5) + 3y(x + 5) = (4x + 3y)(x + 5)

6) 

\(L = \dfrac{xh}{a(x+p)}\\ Lx + Lp = x\cdot(\dfrac{h}{a})\\ x(L-\dfrac{h}{a})=-Lp\\ x = \dfrac{-Lp}{L-\frac{h}{a}}=\mathbf{\dfrac{Lp}{h - aL}}\)

7) \(4:5 = \dfrac{4}{5}=0.8\)

8) 

\(7\dfrac{3}{5}\times \dfrac{17}{19}\div\dfrac{15}{25}\\ =\dfrac{38}{5}\times \dfrac{17}{19}\times \dfrac{5}{3}\\ =\dfrac{34}{3}\\ =\mathbf{11\dfrac{1}{3}}\)

9) 5hrs/1 week and 2 days = 5hrs/9 days = 5hrs/216hrs = 5 : 216.

10) 3 1/2 - 2 7/12 = 3 6/12 - 2 7/12 = 11/12.

11) Negative square. <--- That's the definition.

12) LCM(14a²b²,7ab, 28ab²) = 28a²b².

13) 

 \(1\dfrac{1}{3}+\dfrac{2}{4}\times \dfrac{12}{16}-\dfrac{5}{6}\\ =\dfrac{4}{3}+\dfrac{1}{2}\times \dfrac{3}{4}-\dfrac{5}{6}\\ =\dfrac{4}{3}+\dfrac{3}{8}-\dfrac{5}{6}\\ =\dfrac{32}{24}+\dfrac{9}{24}-\dfrac{20}{24}\\ =\mathbf{\dfrac{7}{8}}\)

14)

 \(\log_512.5-\log_52\\ =\log_5\dfrac{12.5}{2}\\ =\log_56.25\\ =\log_5\dfrac{25}{4}\\ =\log_525-\log_54\\ =\mathbf{2 - 2\log_52}\)

15) Working efficiency of each man = 245 hours per house per person.

Working efficiency of 12 men =245/12 hours per house = 20 hours 25 min. No answer like that....

16) required fraction = 1 - 1/5 - 2/5 = 2/5.

17) Selling price = 850 / (1 + 15%) * (1 + 20%) = 850 * 1.2 / 1.15 = 887 approximately.

18) 3/2

19) \(1\dfrac{6}{9}\times \dfrac{2}{3}-3\dfrac{1}{5}+2\dfrac{1}{2}\div\dfrac{1}{2}\\ =\dfrac{5}{3}\times \dfrac{2}{3}-\dfrac{16}{5}+5\\ =\dfrac{10}{9}-\dfrac{16}{5}+5\\ =\dfrac{50}{45}-\dfrac{144}{45}+\dfrac{225}{45}\\ =\dfrac{131}{45}\)

which is 2 41/45.

20) 16x⁵y⁴ * 48xy∕ 32xy* 24x³y² = 576x⁸y⁶.

\(\dfrac{\sqrt{27}\cdot\sqrt{50}}{\sqrt{54}}\\ =\dfrac{\sqrt{3^2\cdot 3}\cdot \sqrt{5^2\cdot 2}}{\sqrt{3^2\cdot 3\cdot 2}}\\ =\dfrac{\sqrt{3^2}\cdot \sqrt3 \cdot\sqrt{5^2}\cdot \sqrt2}{\sqrt{3^2}\cdot\sqrt{3}\cdot \sqrt{2}}\\ =\dfrac{3\cdot 5\cdot\sqrt3 \cdot \sqrt2}{3\cdot\sqrt3\cdot\sqrt2}\\ =5 \)

\(0.125x + 1 = \dfrac{1}{64}\\ x + 8 = \dfrac{1}{8}\\ x = \dfrac{1}{8} - 8 = -7.875\text{ or }-\dfrac{63}{8}\)

\(L=\dfrac{xh}{a(x+p)}\\ aLx + aLp = xh\\ xh - aLx = aLp\\ x = \dfrac{aLp}{h-aL}\)

Did you learn anything from my last answer?

\(\frac{\sqrt{27}\times\sqrt{50}}{\sqrt{54}}\)

Write the numbers as products of primes.

\(=\frac{\sqrt{3\times3\times3}\times\sqrt{2\times5\times5}}{\sqrt{2\times3\times3\times3}}\)

The 2 and 3s on the top and bottom cancel out.

\(=\sqrt{5\times5}\)

\(=5\)

66% is the same as 33/50.

33/50 * 12 = 198/25, or 7.92

3x+4y=12\\
-3x from both sides
 

4y=12-3x

divide both sides by 4

y= (12-3x)/4

In some countries, like the US, mathematics is shortened to math.

In other countries, like Australia, mathematics is shortened to maths.

I have 5 different pullover shirts and 4 different button-down shirts. In how many ways can I choose shirts for the next 9 days if I insist on wearing pullover shirts two days in a row at least once? Assume that I wear one shirt each day, and every shirt gets worn once.

There are 9! ways with no restrictions and

If 2 pullover shirts are NOT worn two days in a row then it will be

P B P B P B P B P      

So the pullovers will have to be in the 1st 3rd 5th 7th and 9th positions  

these can be arranged in 5! ways

The button shirts can be arranged  4! ways

so that is   5!*4! ways thate two button up will not be together

So the number of ways that at least 2 pullovers are worn on consecuative days is

9!  -  5!*4!

9!-5!*4! = 360000

I'm going to assume this is

cot^2(4x)sin^2(4x)   ....if so....

[ cos^2 (4x) / sin^2(4x)]  *  sin^2 (4x)   =

cos^2 (4x)   

Using  the reduction formula :

cos^2(θ)  =   [ 1  + cos (2θ) ]  /  2         we have

cos^2 (4x)   =  

[  1 + cos (8x) ]  / 2   =  

1 / 2   +   cos(8x) / 2

Did you put this:     \)

at the end

Like this:

\(    x  <  \frac{10}{7}     ,     y  \leq  \frac{16}{7}    \)

???

backslash open and backslash close 

Sometimes it does do funny stuff though, especially if your problem takes up more than one line...... but the button normally works right.