AdamTaurus

But it could be worse. I got a 62% on my last math test, so yeah....

If Profit=Revenue-Costs, then \(p(x)=(5x+15,000)-(2x-2,000)\).

First distribute the negative into (2x-2000), then drop the parenthesis because they are no longer needed.

\(p(x)=5x+15,000-2x+2,000\)

Combine like terms.

So, your profit function is \(p(x)=3x+17,000\).

Yes, you are correct.

(2x+5y)(3x^2-4xy+2y^2)

First, multiply the first term in the first parenthesis by every term in the polynomial.

\((2x)(3x^2)+(2x)(-4xy)+(2x)(2y^2)+(5y)(3x^2-4xy+2y^2)\)

Simplify.

\((2x)(3x^2)=6x^3, (2x)(-4xy)=-8x^2y, (2x)(2y^2)=4xy^2\)

\(6x^3-8x^2y+4xy^2+(5y)(3x^2-4xy+2y^2)\)

Now distribute the 5y.

\(6x^3-8x^2y+4xy^2+(5y)(3x^2)+(5y)(-4xy)+(5y)(2y^2)\)

Simplify.

\((5y)(3x^2)=15x^2y, (5y)(-4xy)=-20xy^2, (5y)(2y^2)=10y^3\)

\(6x^3-8x^2y+4xy^2+15x^2y-20xy^2+10y^3\)

Reorganize.

\(6x^3-8x^2y+15x^2y+4xy^2-20xy^2+10y^3\)

Combine like terms.

\(-8x^2y+15x^2y=7x^2y, 4xy^2-20xy^2=-16xy^2\)

\(6x^3+7x^2y-16xy^2+10y^3\)

This is the same as Guest's answer but LaTeX makes it easier to read.

It is an exclamation point. i flipped = !

How can you delete a question? I have never been able to do it.

I'm going to assume that there is an original equation of y=(-1/2)x+b with a y-value of 2 and an x-value of -3, solve for b.

\(2=-\frac{1}{2}(-3)+b\)

Multiply.

\(2=\frac{3}{2}+b\)

Subtract b from both sides.

\(\frac{4}{2}-\frac{3}{2}=b\)

\(b=\frac{1}{2}\)

Now plug back into original equation.

\(y=-\frac{1}{2}x+\frac{1}{2}\)

In a problem with mx+b format, m is the slope, or in this problem \(m=-\frac{1}{2}\).

For this, plug values 2 and 4 in for x.

\(f(2)=(4)^2-1, f(4)=(4)^4-1\)

\(f(2)=16-1, f(4)=256-1\)

\(f(2)=15, f(4)=255\)

For the average, add the two values and divide by 2.

\(\frac{15+255}{2}=\frac{270}{2}=135\)

So the average increase is 135 students.

To find that you have to complete the square. The formula for that is \((\frac{b}{2})^2\).

In this equation b is -1.

\((-\frac{1}{2})^2=\frac{1}{4}\)

So it would be \(x^2-x+\frac{1}{4}\).