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pickupchik [31]

3 years ago

15

The equation of a circle is (x - 3)^2 + (y - 1)^2 = 64. Find the equation of the circle after it is shifted 2 units to the right

and 4 units up. *

1 answer:

Sveta_85 [38]3 years ago

8 0

Answer:

(x-5)^2 + (y-5)^2 = 64

Step-by-step explanation:

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Round tables seating 8 people and rectangular tables seating 12 people are being used at a banquet for 8th graders. The ratio of

Tamiku [17]

Answer:

<u>36 tables are used to seat the students at the banquet: 12 rectangular and 24 round.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Round tables = 8 seats

Rectangular tables = 12 seats

Ratio of round tables to rectangular tables = 2:1

Number of students = 336

2. How many tables are used to seat 336 students at the banquet, if no table has an empty seat?

x = Number of rectangular tables

2x = Number of round tables

Let's solve for x, using this equation:

12x + 8 (2x) = 336

12x + 16x = 336

28x = 336

x = 336/28

x = 12 ⇒ 2x = 24

12 + 24 = 36

<u>36 tables are used to seat the students at the banquet: 12 rectangular and 24 round.</u>

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What is the sum of the geometric series in which a1 = −5, r = 3, and an = −405?

xxMikexx [17]

$a_1=-5;\ r=3;\ a_n=-405\\\\a_n=a_1r^{n-1}\\\\subtitute\\\\-5\cdot3^{n-1}=-405\ \ \ |divide\ both\ sides\ by\ (-5)\\\\3^{n-1}=81\\\\3^{n-1}=3^4\iff n-1=4\to n=5\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\S_5=\dfrac{-5(1-3^5)}{1-3}=\dfrac{-5(1-243)}{-2}=\dfrac{5\cdot(-242)}{2}=5\cdot(-121)=-605\\\\\\Answer:\boxed{S_5=-605}$

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