Answer:
- If angle C is 90 degrees (def. of right angle) then the sum of angle A and B has to 90 degrees since angle A + B + C (90°) = 180°
Statements and Reasons:
3. Angle C is 90 degrees because of the definition of right angle.
4. Angle A + angle B + angle C is 180 degrees because of triangle sum.
5. Angle A + angle B + 90 = 180 because of substitution postulate.
6. Angle A + angle B is 90 degrees because of subtraction postulate. (subtract 90 from both sides from the equation above this step).
7. Angle A and angle B are complementary.
Answer:
Step-by-step explanation:
The identities you need here are:
and 
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
And there's your circle! Third choice down is the one you want.
Fun, huh?
C = 5/9(F - 32)
C = -30
-30 = 5/9(F - 32)
-30 = 5/9F - 160/9
-30 + 160/9 = 5/9F
-270/9 + 160/9 = 5/9F
-110/9 = 5/9F
-110/9 * 9/5 = F
- 990/45 = F
- 22 = F
C = 5/9(F - 32)
C = 130
130 = 5/9F - 160/9
130 + 160/9 = 5/9F
1170/9 + 160/9 = 5/9F
1330/9 = 5/9F
1330/9 * 9/5 = F
11970/45 = F
266 = F
So in Fahrenheit temp, the the car is protected between -22 F and 266 F
There are 4 possible letters to start with.
The pass word is 3 letters long.
The first letter can be A, B, C, D = 4 different letters.
The 2nd letter can be 4 - 1 = 3 letters ( Can't have repeats)
The 3rd letter can be 3-1 = 2 letters ( no repeats)
Number of possible passwords = 4 x 3 x 2 = 24
10 yards. The amount of yards is 1 third the amount of feet so you just divide 30 by 3 to get the amount of yards
