The answer would be A because each x only has one y. Hope that makes sense!
Answer:
Triangles A & C are right triangles.
Step-by-step explanation:
Triangles A & C are right triangles because they make a 90 degree angle were a pair of legs intersect. That box in the corner of each triangle indicates that the triangle is 90 degrees, therefore a right triangle.
Answer:
9 terms
Step-by-step explanation:
Given:
1, 8, 28, 56, ..., 1
Required
Determine the number of sequence
To determine the number of sequence, we need to understand how the sequence are generated
The sequence are generated using
![\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dn%26%26r%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
Where n = 8 and r = 0,1....8
When r = 0
![\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%260%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-0%29%210%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B8%210%21%7D%20%3D%201)
When r = 1
![\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-1%29%211%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B7%211%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%21%7D%7B7%21%20%2A%201%7D%20%3D%20%5Cfrac%7B8%7D%7B1%7D%20%3D%208)
When r = 2
![\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%262%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-2%29%212%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B6%212%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%21%7D%7B6%21%20%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%7D%7B2%20%2A1%7D%20%3D2%208)
When r = 3
![\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%263%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-3%29%213%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B5%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%21%7D%7B5%21%20%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%20%2A2%20%2A1%7D%20%3D%2056)
When r = 4
![\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%264%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-4%29%214%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B4%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%20%2A%204%21%7D%7B4%21%20%2A4%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%2A5%7D%7B4%2A3%20%2A2%20%2A1%7D%20%3D%2070)
When r = 5
![\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%265%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-5%29%215%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B5%213%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%20%2A%205%21%7D%7B5%21%20%2A3%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%7D%7B3%20%2A2%20%2A1%7D%20%3D%2056)
When r = 6
![\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-6%29%216%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B6%212%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%20%2A%206%21%7D%7B6%21%20%2A%202%20%2A1%7D%20%3D%20%5Cfrac%7B8%20%2A%207%7D%7B2%20%2A1%7D%20%3D%2028)
When r = 7
![\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%267%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-7%29%217%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B7%211%21%7D%20%3D%20%5Cfrac%7B8%20%2A%207%21%7D%7B7%21%20%2A%201%7D%20%3D%20%5Cfrac%7B8%7D%7B1%7D%20%3D%208)
When r = 8
![\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%26%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cfrac%7B8%21%7D%7B%288-8%29%218%21%7D%20%3D%20%5Cfrac%7B8%21%7D%7B8%210%21%7D%20%3D%201)
The full sequence is: 1,8,28,56,70,56,28,8,1
And the number of terms is 9
Answer:
there are 0 solutions to the equation
Step-by-step explanation:
To know how many solutions are in the problem, we have to solve for x and see what result we have left. According to the result, we will know how many solutions there are
8x + 47 = 8(x + 5)
8x + 47 = 8*x + 8*5
8x + 47 = 8x + 40
8x - 8x = 40 - 47
0 = -7
As we can see we are left with an equality that is not fulfilled, this means that there is no solution to the problem, at least in the field of real numbers
Answer:
3rd choice
Step-by-step explanation:
x = 300 sales
1.3(300) = 301.30
20,000 + 301.30 = $20,301.30