First find the length of the diagonal of a square of side 4 inches:
d^2 = 4^2 + 4^2 = 2*4^2 = 32. Then the diagonal of the cube has length
sqrt( 32 + 4^2) = sqrt(32+16) = sqrt(48) = 4sqrt(3).
She can plant 34 plants in all. If you multiply 34 and 2 you will get 34 and I think that is the answer.
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 <3
Step-by-step explanation:
13x-4 < 12x-1
Subtract 12x from each side
13x-12x-4 < 12x-12x-1
x-4 <-1
Add 4 to each side
x-4+4<-1+4
x <3
Answer: 
Step-by-step explanation:
The formula for area is <em>length × width = area</em>
Sub in the values for length and width to solve
×
=
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