Answer:
Step-by-step explanation:
We are here given the slope of the line and one point through which it passes . The slope of the line is -4 and the point is (-9,-12) .
Here we can use the point slope form of the line as ,

Substitute the respective values ,

Simplify LHS and RHS ,

Open the brackets in RHS ,

Add 36 and 4x to both sides ,

Answer:
The total number of ways in which three winners can come in is 990 ways.
Step-by-step explanation:
It is provides that the number of automobiles entering the race is: <em>n</em> = 11.
It is also provided that there were no ties.
There are supposed to be three winners for the race.
- The number of ways the first winner can come in is: 11 ways.
- The number of ways the second winner can come in is: 10 ways.
- The number of ways the third winner can come in is: 9 ways.
Compute the total number of ways in which three winners can come in as follows:
Number of ways in which the first three finishers come in is

Thus, the total number of ways in which three winners can come in is 990 ways.
we have been given that in ΔFGH, the measure of ∠H=90°, GF = 53, HG = 28, and FH = 45. We are asked to find the ratio that represents the sine of ∠G.
First of all, we will draw a right triangle using our given information.
We know that sine relates opposite side of right triangle with hypotenuse.

We can see from the attachment that opposite side to angle G is FH and hypotenuse is GF.


Therefore, the ratio
represents the sine of ∠G.
By cutting a straight line in the middle, then 2 diagonal lines from opposite areas of the circle.
1. The terms of a sequence are denoted by

2.

3. so it is clear that the first columns add each time by one, and the second column add by 2, then by 4, by 6, by 8 and so on.
4. consider only the second column and how we get the terms, which we will call

:


5.
So
![u_{n}=(n+1)(1+2{1+2+3+....(n-1)}) =(n+1)(1+2 [(n-1)n/2]) = (n+1)(1+(n-1)n) =(n+1)( n^{2}-n+1 ) ](https://tex.z-dn.net/?f=u_%7Bn%7D%3D%28n%2B1%29%281%2B2%7B1%2B2%2B3%2B....%28n-1%29%7D%29%0A%20%20%20%20%20%20%20%20%0A%20%20%20%20%20%20%20%20%20%3D%28n%2B1%29%281%2B2%20%5B%28n-1%29n%2F2%5D%29%0A%0A%20%20%20%20%20%20%20%20%20%3D%20%28n%2B1%29%281%2B%28n-1%29n%29%0A%20%20%20%20%20%20%20%0A%20%20%20%20%20%20%20%20%20%3D%28n%2B1%29%28%20n%5E%7B2%7D-n%2B1%20%29%0A%20%20%20%20%20%20%20%20%20)
6. We can check:

7. Remark: Gauss addition formula: 1+2+3+....+n=n(n+1)/2