CubeyThePenguin

Factor: x^2 + 4x - 12 = (x + 6)(x - 2)

The width is x-2 units.

\(7a^7 \cdot a^7 = \boxed{7a^{14}}\)

C to F: (0°C × 9/5) + 32 = 32°F

F to C: (32°F − 32) × 5/9 = 0°C

Replace the numbers with ones of your choosing.

\(99^2 = (100 - 1)^2 = 100^2 - 2(100) +1 = \boxed{9801}\)

\(-6 = \frac{b}{18} \quad \rightarrow \quad b= \boxed{-108}\)

Break the figure into triangles and rectangles.

The triangle at the left has side lengths 4 and 3, so it has area (4 * 3)/2 = 6.

The adjacent rectangle has side lengths 12 and 4, so it has area (12)(4) = 48.

The top rectangle has side lengths 5 and 6, so it has area (5)(6) = 30.

Add to get 6 + 48 + 30 = 84.

Let x be the number of months that have passed.

115 + 3x= 145 - 2x

5x = 30

x = 6

It takes 6 months for Rupert to weigh the same as Michael.
 

edit: sniped

9/11 of the people are bored by cable news, so 2/11 of the people are not bored by cable news.

\(126 \cdot \frac{11}{2} = \boxed{693}\) people are bored by cable news.

Let m be the number of miles driven.

Primo: 30 + 0.25m

Ultimo: 20 + 0.8m

The Ultimo charge is three times the Primo charge:

20 + 0.8m = 3(30 + 0.25m)

20 + 0.8m = 90 + 0.75m

0.05m = 70

m = 1400 miles

Let the cost of a hot dog be x and the cost of a hamburger be y. We can write a system of equations:

5x + 2y = 10.25

2x + 5y = 12.50

Add both equations:

7x + 7y = 22.75

x + y = 22.75/7 = $3.25