Answer:
Step-by-step explanation:
Answer:
y+7 = -3 ( x-4)
Step-by-step explanation:
First find two points on the graph to find the slope
( 1,2) and ( 3,-4)
The slope is given by
m = ( y2-y1)/(x2-x1)
m = ( -4-2)/(3-1)
= -6/2
=-3
We can use the point slope form
y - y1 = m(x-x1) where m is the slope and x1,y1 is a point on the line
We have two choices with a slope of -3
We can either use and x coordinate of -2 or 4
for -2, the y coordinate is not shown
for 4 , the y coordinate is -7
Using ( 4, -7) and m = -3
y--7 = -3( x- 4)
y+7 = -3 ( x-4)
Answer:
The set of solutions is ![\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D12%5C%5C-7-r%5C%5Cr%5Cend%7Barray%7D%5Cright%5D%3A%20%5Ctext%7Br%20is%20a%20real%20number%7D%20%20%5C%7D)
Step-by-step explanation:
The augmented matrix of the system is ![\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D3%266%266%26-9%5C%5C-2%26-3%26-3%263%5Cend%7Barray%7D%5Cright%5D)
.
We will use rows operations for find the echelon form of the matrix.
- In row 2 we subtract
from row 1. (R2- 2/3R1) and we obtain the matrix ![\left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%266%266%26-9%5C%5C0%261%261%26-7%5Cend%7Barray%7D%5Cright%5D)
- We multiply the row 1 by
.
Now we solve for the unknown variables:
The system has a free variable, the the system has infinite solutions and the set of solutions is
Rate of change is -2 because you can do rise over run to find the constant rate of change, and since you are going down you have a negative slope.
Answer:
No, triangles CDE and HGF are not necessarily congruent.
Step-by-step explanation:
Notice that just having one angle equal in value doesn't make the triangles congruent. To start with, we know that the three internal angles of a triangle must add up to 180 degrees, but all we know when one is 50 degrees, the other two must add up to 130 degrees, which can be done by an infinite number of different angle combinations: 110 + 20, 90 + 40, 80 + 50, etc.
,
,
then