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almond37 [142]
3 years ago
6

Which of the following represents a true statement?

Mathematics
1 answer:
larisa [96]3 years ago
6 0
<h3>Answer: Statement B in the lower left corner</h3>

When you raise an exponential expression to another exponent, you multiply the exponents. We have 8*5 = 40 as the final exponent. The rule is (x^y)^z = x^(y*z). The base stays the same.

Statement A is not true because we should be adding the exponents. The rule is x^y*x^z = x^(y+z). Note how the bases are all the same. We'll use this rule for statement C to show that it is also false.

A similar rule is (x^y)/(x^z) = x^(y-z). We subtract the exponents this time. This rule is used to show that statement D is false.

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How do you Simplify 16/12
vlada-n [284]
You need to find a common factor that both the numerator and denominator have. 16 and 12 have common divisible factors of 2 and 4(excluding 1, because 1 is self-defined but doesn't simplify values at all). 

We use the highest factor, in this case, 4. 

Divide 16 by 4 and 12 by 4.

16/4 = 4
12/4 = 3

We put 4 in place of the numerator and 3 in place of the denominator.

\frac{4}{3}
4 0
3 years ago
Read 2 more answers
The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i
kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

Now,

1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of 1+9\times2=19.

So, the sum of the first 1234 terms in the sequence is 2419.

8 0
2 years ago
What is the amount f rainfall that Miami receives, round to the nearest half or whole? 55 9/10"
Vlad1618 [11]

Answer:

56"

Step-by-step explanation:

3 0
3 years ago
Helppp plzzzzz mathhh
spayn [35]

Answer:

A) f^-1(x)=(x-8)^3+2

Step-by-step explanation:

To find the function inverse, switch the x with y and solve for y.

y=\sqrt[3]{x-2}+8 \\\\x=\sqrt[3]{y-2}+8\\\\(x-8)^3 = y-2\\\\ (x-8)^3 + 2 = y

5 0
3 years ago
John bought a car for $65.000. If the value depreciates by 8% each year,how much will the car be worth at the end of two years?​
earnstyle [38]

Answer:

$546000

Step-by-step explanation:

($65000×8%)(2)

7 0
3 years ago
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