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2 years ago

Reasoning Explain why either a or b must be 0 if ab = 0, but neither a nor b

1 answer:

7 0

By the zero product property, a or b must be 0 if ab = 0. Or you could solve for each variable.

Divide both sides by b:
b=0/a —> b=0

Divide both sides by b:
a=0/b —> a=0

Hmm A could be 4 and b could be 1 because 4*1=4

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For an integer n ≥ 0, show that (n/2) - (-n/2) = n. Use greatest integer function

mars1129 [50]

The greatest integer function returns the largest integer smaller than the number you provide it. That is, if n ≤ x < n + 1, where n is an integer, then the "greatest integer of x" is [x] = n.

• Let n be even. Then we can write n = 2k for some integer k ≥ 0. Now,

[n/2] = [k] = k

while

[-n/2] = [-k] = -k

so that

[n/2] - [-n/2] = 2k = n

• Let n be odd. Then n = 2k + 1 for some integer k ≥ 0. Every odd integer occurs between two even integers, so that

n - 1 < n < n + 1

or equivalently,

2k < n < 2k + 2

so that

k < n/2 < k + 1

It follows that [n/2] = k.

Similarly, if we negative the previous inequality, we have

-k > -n/2 > -(k + 1), or -k - 1 < -n/2 < -k

which means [-n/2] = -k - 1.

So we make the same conclusion,

[n/2] - [-n/2] = k - (-k - 1) = 2k + 1 = n

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How do you simplify (-5x^5+14)-(11x^2+1+11x^5)

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(-5x ⁵+14)-(11x ²+1+11x ⁵)
Like terms: -5x ⁵-11x ⁵ = -16x ⁵
Like terms also: 14-1 = 13
Simplified all together: -16x ⁵ - 11x ²+ 13
(Always put highest degree first)

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Step-by-step explanation:

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