Here is a set of signed numbers: 10,-4, 3,-0.8, 0.8, -1, -2

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

3 0

2 years ago

Plz help me ill give u brainlist

iren2701 [21]

Total Area = 2( 32 x 79) + (26 x 42) = 6148 m²

Number of 4 m² = 6148 ÷ 4 = 1537

Answer: The zoo can have 1537 plants.

8 0

3 years ago

Read 2 more answers

Keisha is riding her bike on Bayview Bike path. Keisha‘s bike got a flat tire 2/3 of the way down the path, so she had to stop.

Leona [35]

Answer:

$\frac{7}{12}$ miles.

Step-by-step explanation:

Please consider the complete question.

Bay View Bike Path is 7/8 miles. Keisha is riding her bike on Bay View bike path. Keisha's bike got a flat tire 2/3 of the way down the oath and she had to stop. How far did Keisha ride?

To find the distance covered by Keisha while riding the bike, we need to find 2/3 of 7/8 miles.

$\text{Distance that Keisha ride}=\frac{2}{3}\times \frac{7}{8}$

$\text{Distance that Keisha ride}=\frac{1}{3}\times \frac{7}{4}$

$\text{Distance that Keisha ride}=\frac{1\times 7}{3\times 4}$

$\text{Distance that Keisha ride}=\frac{7}{12}$

Therefore, Keisha ride $\frac{7}{12}$ miles.

3 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Points A and B

8090 [49]

Answer:

answer is 11 12

Step-by-step explanation:

4 0

3 years ago

Answer me before tomorrow

Margarita [4]

The ex- suffix often correlates a word to mean "outside", while the in- suffix often correlates a word to mean "inside". An exterior angle of a polygon would mean "an angle outside of a polygon". An interior angle of a polygon would mean "an angle inside of a polygon". Three exterior angles of this polygon would be angle B, angle D, and angle A. This is because these angles are outside of the polygon due to the extending lines from the shape. Two interior angles of this polygon would be angle 6 and angle 8 (explanation was given when I first began answering this question). Angle 9 would be exterior since it is outside of the polygon. Two exterior angles of the polygon that are congruent are angle D and angle 9, since they are both 90 degrees (right angles).

8 0

3 years ago