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Vlad [161]
3 years ago
8

What is the distance from (-4,0) to (2,5)

Mathematics
2 answers:
Svetllana [295]3 years ago
5 0

Answer:

√61 ≈ 7.81

Step-by-step explanation:

Distance formula:

√(x₂ - x₁)² + (y₂ - y₁)²

√(2 - (-4))² + (5 - 0)²

√(2 + 4)² + 5²

√6² + 5²

√36 + 25

√61

Lostsunrise [7]3 years ago
4 0

Answer:

The answer is d=7.810249675906654

Step-by-step explanation:

Square root sign. (2−−4)^2+(5−0)^2

Square root sign. (2++0)^2+(5+0)^2

Square root sign.(6)^2+(5)^2

Square root sign. 36+25

Square root 61

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2 years ago
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
Viktor [21]

When n=0, we have

5^{3^0} + 1 = 5^1 + 1 = 6

3^{0 + 1} = 3^1 = 3

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for n=k, that

3^{k + 1} \mid 5^{3^k} + 1

Now for n=k+1, we have

5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)

so we know the left side is at least divisible by 3^{k+1} by our assumption.

It remains to show that

3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1

which is easily done with Fermat's little theorem. It says

a^p \equiv a \pmod p

where p is prime and a is any integer. Then for any positive integer x,

5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3

Furthermore,

5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3

which goes all the way down to

5^{3^k} \equiv 5 \pmod 3

So, we find that

\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3

QED

5 0
2 years ago
Kent and Bradley both work at a car dealership. Kent makes $10/hour + 3% on the amount of sales he completes. Bradley only makes
Masteriza [31]

Answer: There is difference of $660 in their paychecks.

Step-by-step explanation:

Since we have given that

Number of hours in one week they worked = 40

Amount of sales = $78000

Kent makes $10 per hour plus 3% on the amount of sales .

So, the equation for Kent becomes,

10\times 40+\frac{3}{100}\times 78000\\\\=400+3\times 780\\\\=400+2340\\\\=\$2740

Similarly, Bradley only makes $7 per hour but he makes 4% on the amount of his sales .

So, the equation for Bradley becomes,

7\times 40+\frac{4}{100}\times 78000\\\\=280+4\times 780\\\\=280+3120\\\\=\$3400

hence, the difference between of their paychecks is given by

\$3400-\$2740\\\\=\$660

Therefore, there is difference of $660 in their paychecks.

3 0
3 years ago
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