**Answer: **-5/12

**Step-by-step explanation: **Before multiplying two fractions together by multiplying across their numerators and multiplying across their denominators, you should always try to cross-cancel as your first step.

So in this problem, the 2 and 8 cross-cancel to 1 and 4.

Also, watch out for your signs. In this problem we have a negative times a positive so we know that our answer will be negative.

Now we can multiply across the numerators and across the denominators.

So we have 5 · 1 which is 5 and 4 · 3 which is 12.

So our answer is -5/12.

Be very careful with your signs!

**Answer:**

150 and 30

**Step-by-step explanation:**

Hello!

Supplementary angles are angles that when added up equal 180

Which can be shown by

x + x = 180

Since one has to be 5 times bigger we put a 5 in front of one of the x's

5x + x = 180

5x is an angle and x is the other

Now we solve for x

5x + x = 180

Combine like terms

6x = 180

Divide by 6

x = 30

Now we put that into each angle

5(30) = 150

30

The answer is 150 and 30

Hope this Helps!

For this case we have the following fraction:

(1-cos ^ 2 (θ)) / (sin ^ 2 (θ))

We must take into account the following trigonometric identity:

cos ^ 2 (θ) + sin ^ 2 (θ) = 1

Therefore rewriting we have:

sin ^ 2 (θ) = 1 - cos ^ 2 (θ)

Substituting in the given fraction we have:

(1-cos ^ 2 (θ)) / (sin ^ 2 (θ))

= (sin ^ 2 (θ)) / (sin ^ 2 (θ))

= 1

**Answer:**

**1**

**Answer:**

Yes

**Step-by-step explanation: There are four apples.**