Simplify. Show your work.

5. 12√3

6. 46 - 14√5

Step-by-step explanation:

5.

We want to simplify these radicals. Look at the first term: -3√3. Well, since 3 is a prime number, we cannot square root any of the factors of 3 further, so this is already in its simplest form.

Look at the next term: 3√12. Remember that 12 = 3 * 4, and 4 = 2², so we can actually write 3√12 as 3 * √3 * √4 = 3 * √3 * 2 = 6√3.

Look at the final term: 3√27. Remember that 27 = 3 * 9 and 9 = 3², so we can write 3√27 as 3 * √3 * √9 = 3 * √3 * 3 = 9√3.

Our new expression is -3√3 + 6√3 + 9√3. We can now combine them because they're like terms: 12√3.

6.

Let's use FOIL to expand this. FOIL is first, outer, inner, and last.

-3 and -2 are the first terms, so multiply them: (-3) * (-2) = 6.

-3 and 2√5 are the outer terms, so multiply them: (-3) * (2√5) = -6√5.

4√5 and -2 are the inner terms, so multiply them: (4√5) * (-2) = -8√5.

4√5 and 2√5 are the last terms, so multiply them: (4√5) * (2√5) = 8 * √25 = 8 * 5 = 40.

Now, add all these up:

6 + (-6√5) + (-8√5) + 40 = 46 - 14√5.

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm