proyaop

you can also guess and check

Every 20 minutes, it goes down by 1 degree celsius.

That means from 1:40 to 2 it was -7 celsius. 1:20 to 1:40 -6, 1 to 1:20 was -5.

-2 was 12:00 to 12:20

1 was 11:00 to 11:20

4 was 10:00 to 10:20

7 was 9:00 to 9:20 => 8 was 8:40 to 9:00

you can generalize this, but:

-9*C was from 8:20 to 8:40 AM

If you know (x + 7)^2 = 36, then square rooting both sides would get rid of the squared symbol on the left side of the equation. Hence, you can get that x + 7 = +/- 6

You have two cases, x + 7 = 6 and x + 7 = -6.

Solving for both, you obtain: x = -1 and x = -13

75 + 72 + 69 + 66 + ... + 3 + 0 + -3 ... + -78 + -81

If you notice, every single term on the left and right side cancel out except for -78 and -81

-78 - 81 = -(78 + 81) = -159

$\sqrt{28 + 16\sqrt{3}}$

If you want to turn that to $a+ b\sqrt{c}$, here's how.

First the c is obviously a 3, because what else would it be duhhh. 

$28 + 16\sqrt{3} = (a + b\sqrt{3})^2 = a^2 + 2ab\sqrt{3} + 3b^2$

$2ab\sqrt{3} = 16\sqrt{3}$ 

$ab = 8$

$a^2 + 3b^2 = 28$

If a and b are integers, you can guess and check a little bit. After some testing, you will find that:

$(a, b) = (4, 2)$

So: $\sqrt{28+16\sqrt{3}} = 4 + 2\sqrt{3}$

Sorry, but 3p-+3p-+p = 45 = -p not 7p - 12.

Thus we obtain p = -45. 3p - (+3p) is distributing -1 to 3p, so it become -3p w/o the parenthesis. It turns out that -+ the minus takes priority.

-9x + 15 = 3(2-x)

Distribute => -9x + 15 = 6 - 3x

Add 9x to both sides => 15 = 6 + (-3 + 9)x

Subtract 6 and distribute => 9 = 6x 

x = 3/2

If you subtract 15 from both sides, yes you get -9 because 6 - 15 = -9, but if you subtract 6 from both sides, you get positive 9 on the other side. Combining like terms can give negative numbers.

It is the distance the number is from 0

|x| is used to denote the absolute value of x, if x = -3, then |-3| = 3, because it is 3 units away from 0. |3| = 3. |x| is always positive.

There is one choice for row 1

Three choices for row 2

5 choices for row 3

7 choices for row 4

1 x 3 x 5 x 7 = 105 ways

If x is the grade on the final exam, then it is equivalent to having three x's. 

(68 + 79 + 78 + 63 + 3x)/7 = y = average grade

${3x + 288\over7} = y$