Solve by using the perfect squares method.* x2 – 12x + 36 = 0

Answers

Answer 1

Answer: $x^2 -12x + 36 = 0\n \n (x-6)^2= 0 \n \n x-6=0 \n \n x=6$

Answer 2

Answer: x2 - 12x + 36 = 0
x2 - 2*x*6 +6^2 = 0
(x-6)^2 = 0
x-6 = 0
x = 6

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4. Find the sum of the first eighteen terms of the arithmetic sequence whose nthterm is an = 15 + 8n.
a. 1438
b. 1638
c. 1836
d. 1783

Answers

Answer:

The sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

Step-by-step explanation:

We need to find the sum of the first eighteen terms of the arithmetic sequence whose nth term is an = 15 + 8n

The formula used to calculate sum of arithmetic sequence is: $S_n=(n)/(2)(a_1+a_n)$

Finding a₁ by putting n=1

$a_n=15+8n\na_(1)=15+8(1)\na_(1)=15+8\na_(1)=23$

We have $a_1=23$

Finding 18th term n=18

$a_n=15+8n\na_(18)=15+8(18)\na_(18)=15+144\na_(18)=159$

So, the sum of first eighteen terms of the arithmetic sequence is:

$S_n=(n)/(2)(a_1+a_n)\nS_(18)=(n)/(2)(a_1+a_(18))\nS_(18)=(18)/(2)( 23+159)\nS_(18)=9(182)\nS_(18)=1638$

So, the sum of first eighteen terms of the arithmetic sequence is $\mathbf{S_(18)=1638}$

Option B is correct option.

A cone has a radius of 5 inches and a height of 18 inches.What is the exact volume of the cone?

A.
150π in3

B.
300π in3

C.
450π in3

D.
540π in3

Answers

It would be C., because to find the volume, you would have to multiply the radius by itself, to get the diameter. Then, the answer you get will have to be multiplied by the height.: 5 times 5 equals 25, and then 25 times 18 equals 450.

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

The area of a circle is 9pi square meters. What is the circumference?

Answers

The answer is r=3, If you have any questions to how I got this answer please ask away c:

Consider the the first six terms in the sequence 10, 29, 48, 67, 86, 105. Which statements are correct? A) The 10th term in this sequence is 199. B) The 15th term in this sequence is 276. C) The 20th term in this sequence is 389. D) The recursive formula is an - 2ₙ₋₁ + 19. E) The explicit formula is a, = 19n - 9.

Answers

Answer:

Step-by-step explanation:

This is an arithmetic sequence when each term is 19 higher than the previous. You can use the formula 19(n-1)+10 when n is the desired term you wish to find. So options A and C are wrong because when plugged into the formula we get another solution. D is wrong because it provides us with an incorrect formula for both the recursive and explicit versions.

The correct answer is B, when the 15th term is 276.

X varies directly as the cube root of y .x=6when y=8.Find the value of x when y=64.