What is the remainder of (x^3-6x^2-9x+3)/(x-3)

Answers

Answer 1

Answer: Thw answer is -51
Found through long division

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Find 2 consecutive odd numbers given that difference between their resiprocal is 2/63

Answers

consecutive odd numbers are 2n+1, 2n+3

difference of reciprocals
1/(2n+1) - 1/(2n+3) = 2/63
((2n+3) - (2n+3))/(2n+1)(2n+3) =2/63
2/(4n^2 + 8n +3) =2/63
4n^2 + 8n +3 = 63
4n^2 + 8n -60 = 0
n^2 + 2n - 15 = 0
(n + 5)(n - 3) = 0
n = 3 (only positive)
numbers are 2(3)+1=7 and 9

Those odd numbers are nine and seven.

There are 90 yellow flowers, 54 red flowers, and 36 white flowers for centerpieces. If the flowers need to be divided equally into separate centerpieces with the same number of each color of flower in each centerpiece, how many different centerpieces will there be?

Answers

Answer:

You can create the fewest centerpieces for the smallest number of any color, which is 2 centerpieces using the white flowers. Therefore, you will have 2 centerpieces with an equal number of each color of flower in each centerpiece.

Step-by-step explanation:

First, find the GCD of 90, 54, and 36:

Find the GCD of 90 and 54:

GCD(90, 54) = 18

Find the GCD of the result (18) and 36:

GCD(18, 36) = 18

So, the GCD of 90, 54, and 36 is 18.

Now, you can create centerpieces with 18 flowers of each color (yellow, red, and white) in each centerpiece. To find out how many centerpieces you can create, divide the total number of each color by 18:

Number of yellow flowers / 18 = 90 / 18 = 5 centerpieces

Number of red flowers / 18 = 54 / 18 = 3 centerpieces

Number of white flowers / 18 = 36 / 18 = 2 centerpieces

Log x + log 8 = 2 ???

Answers

To start we will use the sum to product rule of logs to make logx + log 8 = 2 -> log8x = 2. now assuming that this is log base 10 we will get rid of the log by raising both sides to the power of ten.

8x = 10^2
8x = 100
x = 100/8

The solution to the equation $log(x) + log(8) = 2$ is $x = 12.5$ .