1. (x² + 24) factors as the difference of two squares (x² - (-24)) where -24 is the square of the complex number i√24 = 2i√6. The factoring is
(x - 2i√6)(x + 2i√6)
2. The square of half the coefficient of the x-term needs to be added: 4.5² = 20.25
This number goes in both boxes.
3. This is the square of (y² +20), so the factorization is similar to that for problem 1.
y⁴ + 40y² + 400 = (y² + 20)² = (y -2i√5)²(y +2i√5)²
Answer:
-9 + 7√5.
Step-by-step explanation:
(3 - √5)(2 + 3√5)
= 3(2 + 3√5) - √5(2 + 3√5))
= 6 + 9√5 - 2√5 - 15
= -9 + 7√5.
okay? and? so what if he did draw it. what's the problem?
For ease of solving, let's first find the rate of Mia and Luke per minute. Since Mia can do 4 pieces every 3 minutes, then she can do

of a piece per minute. Luke on the other hand can do

of a piece per minute.
To find how many pieces they made, we first need to find the time it took for them to make the pieces. We assign

as the time Mia spent making origami. Since Luke spent 5 more minutes, we can denote his time as

.
Putting this into an equation we'll get:




Therefore, Mia made pieces of origami for 39 minutes. Knowing this, we can find out the number of pieces of origami she made:
ANSWER: Mia made 52 pieces of origami.
I think the answer is 0.25 seconds later
Hope this helped