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polet [3.4K]
3 years ago
10

How many integers n leave remainder 4 when divided by 7, if n satisfies the given inequality?

Mathematics
1 answer:
bekas [8.4K]3 years ago
4 0

Consider inequality |-n| This inequality is equivalent to inequality |n|

This means that -46

The greatest integer number n, such that -46 when dividing by 7 gives the remainder 4 is 39. Then subtract 7, you get 32, then 25 and so on.

When n=-39, -32, -25, -18, -11, -4, 4, 11, 18, 25, 32, 39 then dividing by 7 the remainder is 4.

Answer: 12 integers.

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How do you do this question?
likoan [24]

Answer:

a) -7/9

b) 16 / (n² + 15n + 56)

c) 1

Step-by-step explanation:

When n = 1, there is only one term in the series, so a₁ = s₁.

a₁ = (1 − 8) / (1 + 8)

a₁ = -7/9

The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.

sₙ = sₙ₋₁ + aₙ

(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ

(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ

aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)

If you wish, you can simplify by finding the common denominator.

aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]

aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)

aₙ = 16 / (n² + 15n + 56)

The infinite sum is:

∑₁°° aₙ = lim(n→∞) sₙ

∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)

∑₁°° aₙ = 1

8 0
3 years ago
Daniels mom gave him $8 for his allowance He wants to buy new shoelaces for his vans that cost $5. What percentage of his money
adell [148]
75% cus u divide the denominator by the numerator is 5 and 8
3 0
3 years ago
HELPP!!! WILL GIVE BRAINLIEST AND 5 STARS!!!
seraphim [82]

Answer:

F=73.74 degrees

Step-by-step explanation:

sin=opposite/hypotenuse

opp=24 hyp=25

sin(F)=24/25 (to find angle have to use inverse sin)

sin-1(24/25)=73.74

6 0
3 years ago
I will give brainlest answer
KonstantinChe [14]
4 units right and 4 units down
4 0
4 years ago
Kerrie uses the work shown below to determine 35% of 280.
lys-0071 [83]

For this case we must find 35% of 280.

Kerrie gets 10% and then 25%. So:

10% of 280:

280 ------------> 100%

x -----------------> 10%

Where "x" represents the amount given by 10% of 280.

x = \frac {10 * 280} {100}\\x = 28

Thus, 10% of 280 is 28.

Now, we find 25% of 280:

280 ------------> 100%

x -----------------> 25%

Where "x" represents the amount given by 25% of 280.

x = \frac {25 * 280} {100}\\x = 70

Thus, 25% of 280 is 70.

So we have that 35% of 280 is given by:

28 + 70 = 98

So, Kerrie's solution is correct.

Answer:

Option A

6 0
3 years ago
Read 2 more answers
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