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2 years ago

What is |–14|A. 1/14B. -7C. -14 D. 7E. 14

Mathematics

1 answer:

expeople1 [14]2 years ago

5 0

Answer:

Step-by-step explanation:

absolute value works where it doesnt matter if the number is positive or negative. the absolute value is the number positive. an absolute value can not be negative.

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Please solve 1 through 6

Degger [83]

1. 3x³-2x²+1x
2. 6y⁴+2y³-8y
3.-3m³-12m²+3m
4. 4d⁴-3d³+d²
5. -w⁵-3w³
6. -a⁴-3a³

7 0

2 years ago

A system of equations is shown below

wariber [46]

Answer:

No solution

Step-by-step explanation:

7 0

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

1 year ago

Find the median of the following frequency distribution

solmaris [256]

Answer:

Step-by-step explanation:

First right out all the data in numerical order from left to right.

2, 2, 2, 3, 4, 5, 7

The median is the middle number in the set. If there is an even amount of data points, find the average of the two middle numbers. If there is an odd number of data points, like in this data set, just take the middle number as you median.

There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.

When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3. Therefore, 3 is the median of this data set.

8 0

3 years ago

Help me with the part b!

ra1l [238]

Average speed = (distance final - distance initial)/(time final - time initial)
Average speed = (30-0)km /(100 -0)min = 3/10 km/min

3/10 km/min *60 min/1 h = 180/10 km/h= 18 km/h

7 0

2 years ago

What is |–14|A. 1/14B. -7C. -14 D. 7E. 14​

What is |–14|A. 1/14B. -7C. -14 D. 7E. 14