hectictar

3 cookies + 3 cookies  =  6 cookies

3 eighteenths + 3 eighteenths  =  6 eighteenths

\(\frac{3}{18}+\frac3{18}=\frac6{18}\)

We can divide the numberator and denominator by 6 .

\(\frac{3}{18}+\frac3{18}=\frac6{18}=\frac1{3}\)

The goats produce milk at a rate of 21.7 litres per day.

21.7 liters per day * 280 days  =  6,076 liters   total

And...     6,076 liters / 0.5 liters per bottle  =  12,152 bottles

This makes sense, because if each bottle holds 1 liter, and she has a total of 6,076 liters, then it will take 6,076 bottles. But since each bottle holds half a liter, it will take two times as many bottles.

    (-7a) * (-4b)

=  -7 * a * -4 * b

                                  Multiplication can be done in any order.

=  -7 * -4 * a * b

=  28 * a * b

=  28ab

What is the height is increased by?

\(3^{-3}\,=\,\frac{1}{3^3}\,=\,\frac1{27}\)

g(x)  =  -x² - x

a.  To find  g(4) , replace every instance of  x  in the function with  4  .

g(4)  =  -4² - 4

g(4)  =  -16 - 4

g(4)  =  -20

b.  To find g(-3) , replace every instance of  x  with  -3  .

g(-3)  =  -(-3)² - (-3)

g(-3)  =  -9 + 3

g(-3)  =  -6

If I am seeing this correctly...... your first two steps are:

\(2(x-3)=-\frac12(6+8x)\)                  This is the given equation, and you want to solve for  x  .

\(2x-6=-\frac6{12}+\frac8{16}x\)

You have distributed the  2  on the left side of the equation correctly, but the right side should be...

\(2(x-3)=-\frac12(6+8x) \\~\\ 2x-6=(-\frac12)(6)+(-\frac12)(8x) \\~\\ 2x-6=(-\frac12)(\frac61)+(-\frac12)(\frac{8}{1})(x) \\~\\ 2x-6=-\frac{(1)(6)}{(2)(1)}+-\frac{(1)(8)}{(2)(1)}(x) \\~\\ 2x-6=-\frac62+-\frac{8}{2}x \\~\\ 2x-6=-3+-4x \\~\\ 2x-6=-3-4x\)

Depending on your browser, you may be able to right click and select  "Open Image in New Tab" or "View Image" or "Properties" and then go to this address:

You're right!    Here's an explanation:

perimeter of a rectangle  =  length + length + width + width 

P  =  L + L + W + W

P  =  2L + 2W

                                 To solve this equation for  L , subtract  2W  from both sides.

P - 2W  =  2L

                                 Divide both sides of the equation by  2 .

(1/2)(P - 2W)  =  L

P/2 - W  =  L

L  =  P/2 - W             This is a formula just like the quadratic formula is a formula.