The magnitude of YZ is 8.6
<u>Explanation:</u>
<u />
Y( -4, 12)
Z ( 1, 19)
Magnitude of YZ = ?
We know:

On substituting the value we get:

Thus, the magnitude of YZ is 8.6
Given the triangle
PQR
with points
P(8,0)
Q(6,2)
R(-2,-4)
And the triangle
P'Q'R'
with points
P'(4,0)
Q'(3,1)
R'(-1,-2)
Part A. Scale factor
Using the vertex
P( 8, 0)
P'(4,0)
the dilatation factor is given by

The triangle has a dilatation factor of 1/2
Part B:
P''Q''R'' after using P'Q'R' reflected about the y axis
to make a reflection over the y axis
coordinates (x,y) turn into coordinates (-x,y)
as follows



Then triangle P''Q''R'' has coordinates
P''(-4,0)
Q''(-3,1)
R''(1,-2)
Part C:
PQR is congruent to P''Q''R''?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Then the triangles are not congruent
The 22 students who answered juice would represent the smallest wedge in a pie chart.
Answer:
Step-by-step explanation:
x=1
y= -2
See step by step explanation below:
Hello!
We can solve this by using substitution
we can plug y = x - 1 into the other equation
So 2x - 3( x - 1) = -1
We can distribute the -3 to (x - 1)
2x - 3x + 3 = -1
Combine like terms
-x + 3 = -1
Subtract 3 from both sides
-x = -4
Since x is negative we can multiply both sides by -1
x = 4
We can plug x into the first equation
y = (4) - 1
y = 3
The answers are x = 4 and y = 3
Hope this helps!