2+2=4
a^2+b^2=c^2
15^2-4^2
=225-16
=209
Answer:
181 units²
Step-by-step explanation:
Let's break up the polygon into 3 shapes
Step 1: Area of the left rectangle
4(7) = 28 units²
Step 2: Area of middle rectangle
9(13) = 117 units²
Step 3: Area of top square
6² = 36 units²
Step 4: Add them all up
28 + 117 + 36 = 181 units²
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
Answer:
x = 17.9
Step-by-step explanation:
rounded: 17.9
Hope this helps
