CubeyThePenguin

\(\text{slope} = m = \frac{3 - 1}{-3 - (-2)} = -2\)

Plug in one of the points, such as (-2, 1).

\(y=mx+b\)

\(1 = -2(-2) + b\)

\(-3= b\)

Therefore, the equation is \(\boxed{y = -2x -3}\).

\(\cos 35 = \frac{10}{x}\)

\(x = \frac{10}{\cos 35} = \boxed{12.207}\)

round to the nearest tenth = 12.2

start: 20 buttons

1/2 sold to neighbors: 10 buttons

1/2 of the remainder = 1/2 * (1 - 1/2) = 1/4 ---> 5 buttons

buttons left = 20 - 10 - 5 = 5 buttons

from 1 to 1000:

2^0, 2^1, ..., 2^9 (10 numbers)

3^0, 3^1, ..., 3^6 (7 numbers)

2^0 = 3^0 = 1 was counted twice, so 16 numbers from 1 to 1000

from 1/1000 to 1:

1/2^9, 1/2^8, ..., 1/2 (9 numbers)

1/3^6, 1/3^5, ..., 1/3 (6 numbers)

Therre are 15 numbers from 1/1000 to 1.

Overall, there are 31 numbers.

If you don't know Pick's Theorem, you could also do it this way:

shaded = (area of total region) - (area not shaded)

= \((4 \cdot 4) - (\frac{2 \cdot 3}{2} + \frac{1 \cdot 1}{2} + 1 + \frac{1 \cdot 2}{2} + \frac{1 \cdot 3}{2})\)

= \(16 - 7\)

= \(\boxed{9}\)

You could also find the area of the shaded region directly, which is just made out of squares and triangles.

\(\frac{2 \cdot 2}{2} + 2 + \frac{3 \cdot 1}{2} + 1 + \frac{2 \cdot 1}{2} + \frac{3 \cdot 1}{2}\)

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

= \(\boxed{9}\)

3(2x + 4) = 2x - 4

6x + 12 = 2x - 4

4x = -16

x = -4

Add f(x) and g(x) by combining like terms.

\(f(x)+g(x) = (x^3 + 3x^2 + 4x - 7) + (- 7x^4 + x^3 + 5x^2 - 7)\)

\(-7x^4 + 2x^3 + 8x^2 + 4x - 14\)

The coefficient of the x^3 term is 2.

\(\text{GCF}(10p^2, 25pq, 15q^2) = \boxed{5}\)

To check, 10p^2/5 = 2p^2, 25pq/5 = 5pq, and 15q^2/5 = 3q^2, all of which have no factors in common.

V = (4)(7)(12) = 336 cm^3

SA = 2(4 * 7 + 4 * 12 + 7 * 12) = 320 cm^2

42 degrees

56 degrees