Answer:
Option C is right.
Step-by-step explanation:
Given is a graph with two triangles marked on it.
Triangle ABC is in the I quadrant with vertices (2,2) (2,10) and (8,12)
Triange A'B'C' is in the III quadrant with vertices (-1,-1), (-1,-5) and (-4,-6)
On comparison we find corresponding side of AB is A'B'
Length of AB = 8 and Length of A'B' = 4.
Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2.
Now since moved to III quadrant from I quadrant we find that there is a rotation of triangle ABC about the origin. The degree of rotation is 180 degrees.
Hence A'B'C' is obtained by dilating ABC by a scale factor of 1/2 and then rotating it about the origin by 180 degrees
Area,for rectangles is length x width so 2 1/4 inches x 3 1/2 inches is 7 7/8
It’s 3 . You multiply 2 three times to get 8
Answer: x= -1, z=2, y= -4
Step-by-step explanation:
System of equations:
-5x - 4y - 3z= 15 +
<u>-10x + 4y + 6z= 6</u>
-15x + 3z = 21 ------> 3 (-5x + z) = 7.3
-5x + z = 7
now,
-10x + 4y + 6z= 6
2(-5x + z) + 4y + 4z = 6
14 + 4y + 4z = 6
7 + 2y + 2z = 3
2y + 2z= -4
y+z=-2
Now we were using the equation: 20x + 4y + 4z = -28
20x + 4(y+z) = 20x -8= - 28
20 x = -20
x= -1
With this we can find y and z
X=-1
-5x + z = 7
z= 2
y+z=-2
y=-4
Finally we have: x= -1, z=2, y= -4
I hope this can help you.
Thank you
The first chair can be any one of the 15.
For each of those ...
The second chair can be any one of the remaining 14.
For each of those ...
The third chair can be any one of the remaining 13.
For each of those ...
The fourth chair can be any one of the remaining 12.
Number of ways to fill the 4 chairs = (15 x 14 x 13 x 12) = 32,760 .
But ...
Each set of 4 people can be seated in (4 x 3 x 2 x 1) = 24 orders.
So each group of 4 people is represented 24 times among the 32,760.
If the order doesn't matter, you're really asking how many different
groups of 4 people can occupy the front row.
That's (32,760) / (24) = 1,365 sets of 4 members, in any order.