Answer:
49 children
Step-by-step explanation:
Adult : Child = 2 : 7
Adult = 14
2 = 14
So, 1 = 14/2 = 1 = 7 in the ratio.
So, 7 x 7 = 49 children are there.
9514 1404 393
Answer:
C. (9, 18)
Step-by-step explanation:
Given R(3, 5), a dilation by a factor of 3 will multiply each coordinate to give ...
(9, 15)
Then the translation up by 3 will give you the image coordinates ...
(x, y) ⇒ (x, y+3)
(9, 15) ⇒ (9, 15 +3) = (9, 18)
The coordinates of R' are (9, 18), matching choice C.
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<em>Comment on multiple choice answers</em>
As it often does, here it works to "guess" the answer that has the coordinates that are most-repeated. An x-coordinate of 9 is part of 3 answer choices; a y-coordinate of 18 is the only repeated value in the answer choices. If you were to guess, an appropriate guess would be (9, 18). That happens to be correct in this case.
You solve for the domain by setting the radicand less than or equal to 0 and solving for x. Dividing by a -x, we switch the sign so we have that the domain is less than or equal to 0, or all negative numbers. We know that it breaks every law in math to have a negative radicand with an even index, so if the domain is all negative values of x, taking a negative of a negative gives us a positive. The negative sign OUTSIDE the radical means you are flipping the graph upside down. So instead of having a range of y is greater than or equal to 0 as does the parent graph, you have flipped it upside down so it heads more negative in regards to the range. Therefore, the domain and the range both have the same sign, thee last choice from above.
I'm guessing the series is supposed to be
By the ratio test, the series converges if the following limit is less than 1.
The first
terms in the numerator's denominator cancel with the denominator's denominator:
also cancels out and the remaining factor of
can be pulled out of the limit (as it doesn't depend on
).
which means the series converges everywhere (independently of
), and so the radius of convergence is infinite.
