Answer:.04/n
Step-by-step explanation:solidus represents division
Answer:
72
Step-by-step explanation:
words per minutes= 1800÷25=72
Answer:
5.) 39
6.) 52
Step-by-step explanation:
5.) 90-51= 39
6.) 74 + 34= 108
180-108= 72
56+72= 128
180-128= 52
x=52
Answer:
Step-by-step explanation:
the common difference of the arithmetic sequence is -7
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.