Write an equation for the sequence: 2, 24, 720, 40320, 3628800

Answers

Answer 1

Answer: The sequence forms a group of factorials.
Notice that
2! = 2
4! = 24
6! = 720
8! = 40320
10! = 3628800
Each number beside a factorial is an even number. The equation for even number is 2x. Therefore, the final equation is
f(x) = 2x!

Verify
x = 1, f(1) = 2(1)! = 2!
x = 2, f(2) = 2(2)! = 4!
x = 3, f(3) = 2(3)! = 6!
and so on.

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How do you graph y=lxl - 3 please explain

Answers

$y=x\n\n\Downarrow S_(OX\ for\ y < 0)\n\ny=|x|\n\n\Downarrow T_{\vec{a}=[0;-3]}\n\ny=|x|-3$

$y=x\n\nfor\ x=0\to y=0\to(0;\ 0)\n\nfor\ x=2\to y=2\to(2;\ 2)\n\n\nlook\ at\ the\ picture$

find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. round your answer to the nearest tenth. show all your work

Answers

The answer is 374.4 yards.

There are 2 ways to calculate the area of a a regular hexagon.
It is given:
apothem: b = 10.4 yards
side: a = 12 yards

1. The direct way is to use the formula for the regular hexagon without using an apothem:
$A= (3 √(3) )/(2) a^(2)$
where
A - the area of the hexagon
a - the side of the hexagon

Therefore:
$A= (3 √(3) )/(2) 12^(2)$
$A= (3 √(3) )/(2) 144$
$A= 374.4$

2. The indirect way is to sketch the hexagon with 3 diagonals and create 6 triangles. Then, it is necessary to calculate the area of one triangle and multiply it by 6. In this triangle, apothem is actually the height.
The area of the hexagon is:
A = 6 · A₁
where:
A - the area of the hexagon,
A₁ - the area of the triangle

$A_(1)= (a*h)/(2)$

where
h - height of the triangle.

Since apothem (b) of the hexagon is the height (h) of the triangle, then:
$A_(1)= (a*h)/(2)$
$A_(1)= (12*10.4)/(2)$
$A_(1)= 62.4$

Thus, the area of one triangle is 62.4 yards.

To calculate the area of the hexagon, we will multiply it by 6:
A = 6 · A₁
A = 6 · 62.4
A = 374.4 yards

In both cases, the result is 374.4 yards.The answer is

MATH HELP MIDPOINT…..

Answers

Step-by-step explanation:

Going from V to M :

x goes from 13 to 7 or a change of -6 go -6 more to reach U, x = 1

y goes from 8 to 12 or a change of + 4 go +4 more to reach U, y = 16

U = (1,16)

Three added to 8 times a number is the same as 3 times the value of 2 times the number minus 1. what is the number?

Answers

Let the number be y;
3+8y=3(2y-1)
8y+3=6y-3
Putting like terms together;
8y-6y=-3-3
2y=-6
y=-3
The number is -3

Answer: The required number is -3.

Step-by-step explanation: Given that three added to 8 times a number is the same as 3 times the value of 2 times the number minus 1.

We are to find the number.

Let x represents the given number.

Then, according to the given information, we have

$8x+3=3(2x-1)\n\n\Rightarrow 8x+3=6x-3\n\n\Rightarrow 8x-6x=-3-3\n\n\Rightarrow 2x=-6\n\n\Rightarrow x=-(6)/(2)\n\n\Rightarrow x=-3.$

Thus, the required number is -3.

Find the radius and circumference of a cd with a diameter of 4.75 inches

Answers

To calculate for the radius, we divide the given diameter by 2. That would be 4.75 inches/2. This operation would give us the answer of 2.375 inches. The circumference is calculated by the formula, C = 2πr: C = 2(π)(2.375 inches) = 14.92 inches

The first term of a geometric series is 3, and the sum of the first term and the second term is 15. What is the sum of the first six terms?

Answers

Hello,

Ok, i have seen the mistake the answer is 4095.

$u_(1)=3\nu_(2)=?\nu_(1)+u_(2)=15==>u_(2)=15-3=12=4*3$
$u_(1)+u_(2)+...u_(6)=3+3*4^1+3*4^2+...+3*4^5\n=3*(1+4+4^2+4^3+...+4^5)=3*(4^6-1)/(4-1)=3*(4^6-1)/3=4095$

Other Questions

Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.B. Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not.3(2x − 4) = 5x − 16x − 12 = 5x − 111x − 12 = –111x = 11x = 11

3/10 off the normal price 400

Find the range of {(3.2, –3), (7.6, 5.9), (1.4, –3), (–9.1, 8.3)}.

Need help with this question, can someone help me out?