TheXSquaredFactor

The formula for finding the area of a parallelogram is:

Let A= area

Let b= base

Let h= height 

\(A=bh\)

\(-885y+3\)

The surface area of the prism with the isosceles right triangle base is \(685ft^2\).

The surface area of any prism can be calculated using the following formula:

Let S= Surface Area

Let L= Lateral Area (Area of everything but the base)

Let B= Area of one base

Let P= Perimeter of the base

Let H= height of prism
 

\(S=L+2B\)

\(L=PH\)

Okay, let's get started now that we have determined the formula. Let's start by solving for L, the lateral surface area.

P= perimeter of the base

\(P= (11+11+15.6)ft=37.6ft\)

\(H=15ft\)

To find the lateral surface area, multiply P by h.

\(L=PH=37.6ft*15ft=564ft^2\)

The only variable to find next is B, the area of a triangle is 1/2*bh. Because the base is a right isosceles triangle, the base and the height are both 11.

\(B=\frac{1}{2}bh=\frac{1}{2}*11*11=60.5ft^2\)

Remember, the formula requires us to find 2B:

\(2B=(2*60.5)ft^2=121ft^2\)

Now, plug L and 2B back into the formula to get the final answer:

\(S=L+2B\)

\(S=(564+121)ft^2=685ft^2\)

Normally, you would have to find the surface area of the other triangular prism, but the final answer only asked about the triangle with the right isosceles base, so there is no need to calculate the other one. 

Yes, Point C is at (-2,-2) when reflected over the x-axis and then over the y-axis.

\(9+10=19\)

Since this is not an equation, I will assume that you want to simpify this expression. This is the original:

\(7x+9*21\)

Here, the only like terms to combine is the 9*21. The rest of it cannot be simplified further.

\(7x+189\)

What you have provided is not an equation, so I will assume that you want to simplify this expression. First, this is the original equation:

\(25-5\sqrt{x}-5\sqrt{x}-x\)  

In this equation, the only like terms are the -5 multiplied by the square root of x. Therefore, the simplified expression would be:

\(25-10\sqrt{x}-x\)

As of further review, my solution is wrong, so I'll just delete this garble that I wrote...

Your answer in simplest radical form and corresponding decimal approximation:

\(c=\pm\frac{\sqrt{42}}{2}-1\)

\(c\approx2.24\) or \(c\approx-4.24\)

Let's see why. Your original equation in this:

\((c+1)^2=\frac{21}{2}\)     Take the square root of both sides

\(c+1=\pm\sqrt{\frac{21}{2}}\)     In quadratics, there are always 2 answers, hence plus or minus. First, let's place the square root of 21/2 in simplest radical form:

\(\sqrt{\frac{21}{2}}=\frac{\sqrt{21}}{\sqrt{2}}\)     First, distribute the radical to both the numerator and denominator. Notice how there is a radical in the denominator, which means we must rationalize it.

\(\frac{\sqrt21}{\sqrt2}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{42}}{2}\)     To rationalize this fraction, we multiply the fraction by the square root of 2 over the square root of two. This is the equivalent of multiplying the fraction by one, so the fraction's value is not being changed. 42 has no perfect square factors, so the radical is left as is. 

\(c+1=\pm\frac{\sqrt{42}}{2}\)Subtract one on both sides to get the final answer.

\(c=\pm\frac{\sqrt{42}}{2}-1\)

\(256+223=479\)