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What is ∛2197? Explain how you got your answer.

user100 [1]

Answer:

13

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is $13^{3}$ . This will go inside of your cube root. You now have $\sqrt[3]{13^{3} }$ . Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

5 0

3 years ago

Read 2 more answers

Using interval notation, the domain off is [- 3, 5] and the domain of g is [- 2, 7] . On what domain is f defined

Scorpion4ik [409]

Note: I am assuming you mean ''on what domain is f+g is defined''.

Answer:

We conclude that

Dom(f+g) = [-2, 5]

Step-by-step explanation:

Given the domain of f

[-3, 5]

Given the domain of g

[-2, 7]

The domain of a composition f+g would include the intersection of both domains.

In other words, the domain of a composition f+g includes all the inputs of x-values that are in the domain of both functions i.e. f and g.

so

Domain of f = [-3, 5]

The x-values lie in the domain of f interval are:

x = -3, -2, 1, 0, 1, 2, 3, 4, 5

Domain of g = [-2, 7]

The x-values lie in the domain of g interval are:

x = -2, 1, 0, 1, 2, 3, 4, 5, 6, 7

Therefore, the common x-values in both f and g would be:

-2, 1, 0, 1, 2, 3, 4, 5

Thus, we conclude that

Dom(f+g) = [-2, 5]

3 0

3 years ago

List the angles in order from largest to smallest. A) ∠R, ∠P, ∠Q B) ∠R, ∠Q, ∠P C) ∠Q, ∠P, ∠R D) ∠Q, ∠R, ∠P

mars1129 [50]

Answer: A

Step-by-step explanation:

Angles opposite shorter sides of a triangle are smaller, and angles opposite longer sides in a triangle are larger.

8 0

2 years ago

Some people think it is unlucky if the 13th day of a month falls on a Friday. Show that in every calendar year (non leap or leap

MakcuM [25]

We will set a variable, d, to represent the day of the week that January starts on. For instance, if it started on Monday, d + 1 would be Tuesday, d + 2 would be Wednesday, etc. up to d + 6 to represent the last day of the week (in our example, Sunday). The next week would start over at d, and the month would continue. For non-leap years:
If January starts on d, February will start 31 days later. Following our pattern above, this will put it at d + 3 (28 days would be back at d; 29 would be d+1, 30 would be d+2, and 31 is at d+3). In a non-leap year, February has 28 days, so March will start at d+3 also. April will start 31 days after that, so that puts us at d+3+3=d+6. May starts 30 days after that, so d+6+2=d+8. However, since we only have 7 days in the week, this is actually back to d+1. June starts 31 days after that, so d+1+3=d+4. July starts 30 days after that, so d+4+2=d+6. August starts 31 days after that, so d+6+3=d+9, but again, we only have 7 days in our week, so this is d+2. September starts 31 days after that, so d+2+3=d+5. October starts 30 days after that, so d+5+2=d+7, which is just d. November starts 31 days after that, so d+3. December starts 30 days after that, so d+5. Remember that each one of these expressions represents a day of the week. Going back through the list (in numerical order, and listing duplicates), we have d, d, d+1, d+2, d+3, d+3, d+3, d+4, d+5, d+5, d+6 and d+6. This means we have every day of the week covered, therefore there is a Friday the 13th at least once a year (if every day of the week can begin a month, then every day of the week can happy for any number in the month).
For leap years, every month after February would change, so we have (in the order of the months) d, d+3, d+4, d, d+2, d+5, d, d+3, d+6, d+1, d+4, and d+6. We still have every day of the week represented, so there is a Friday the 13th at least once. Additionally, none of the days of the week appear more than 3 times, so there is never a year with more than 3 Friday the 13ths.

5 0

3 years ago

What is the average of the following numbers: 18, 64, 23, 78, 82, 91

Katen [24]

To Find The Answer, We Need To Add All Of Them Together, Then Divide By the Number Of Values. So:
64+23+78+82+91
-----------------------
5

64+23+78+82+91 = 338.

338
-----
5

338/5 = 67.6

So, The Average Is 67.6

3 0

3 years ago