AnExtremelyLongName

a = 7

b = 13

ab = 7 * 13 = 91

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Zero is not positive or negative, but even, so we can't count it in the problem.

So really it just is

FLOOR of \(91/2\) = 45

When a shape is dilated, all of its side lengths are multiplied by the scale factor.

Original:

AB= 4

BC = 5

AC = \(\sqrt{41}\)

Dilated:

AB = 8

BC = 10

AC = \(2\sqrt{41}\)

Perimeter of dilated: 8 + 10 + \(2\sqrt{41}\) = 30.8062484748656974 = 31 units

Another Method:

Draw a line segment from M to the midpoint of DC. Call the midpoint of DC \(L\)

By simple operations:

\(ML=9\)

\(LC=3\)

By pythagorean theorem.

9²+3²

81 + 9 = 90

sqrt(90) = \(3\sqrt{10}\) = MC

Ok, can you provide the wrong answer next time? Just state that what incorrect answer you got, and people (believe it or not) will have more motivation to help you.

Hello helpppp! You have a suggestive name and you post long chains of homework questions! At least attempt them and explain your trouble or confusion!

Figure out the height of the entire triangle.

The height is the shorter side of the 30-60-90 triangle, so we divide the hypotenuse by 2 to find the height

Height = \(\sqrt{3}\)

To find the hypotenuse of a 45-45-90 triangle, you multiply the side by \(\sqrt{2}\)

X = \(\sqrt{2*3}=\sqrt{6}\)

The perimeter of the square is 48. All sides of a square are equal.

Side of the square = 48/4 = 12

Area of the square = 12² = 144

Area of triangle (48x)/2

Equation

(48x)/2= 144

x = 6

It is obviously different, and I think she intends it that way. If you learn their method, you can solve it easily.

I used to do AoPS forums, but it's more of chatting than actual problem solving.

Nice! Good job on all of your answers!

Plan:

Radians of a circle = \(2\pi\)

Find the area of the circle, then multiply that by a fraction with the numerator of the central angle and the denominator of the total radians.

Solve

1. \(\pi{r^2}=121\pi\)

2.\(121{\pi}*\frac{\frac{5\pi}{9}}{2\pi}\)

3.\(121{\pi}*\frac{\frac{5}{9}}{2}\)

4.\(121{\pi}*\frac{5}{18}\)

5.\(\frac{605\pi}{18}\)

That is the simplest form unless you want the answer in decimal