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.
9514 1404 393
Answer:
v = 39; w = 47; x = 94; y = 39; z = 47
Step-by-step explanation:
The figure shows v° and 51° are complementary, as are z° and 43°.
v° = 90° -51° = 39°
z° = 90° -43° = 47°
Vertical angles are congruent.
y° = v° = 39°
w° = z° = 47°
And the angle x° is a vertical angle with the sum of 51° and 43°.
x° = 43° +51° = 94°
Answer:
You get paid $9 per hour
Step-by-step explanation:
