Answer:
MN=23
Step-by-step explanation:
For the midsegment:
MN=(WZ+XY)/2
10x+3=(11+8x+19)/2
10x+3=4x+15
6x=12
x=2
MN=10×2+3=23
Since A and B are the midpoints of ML and NP, we can say that AB is parallel to MN and LP. In order to find ∠PQN, we can work with the triangles PQB and NQB. According to SAS (Side-Angle-Side) principle, these triangles are congruent. BQ is a common side for these triangles and NB=BP and the angle between those sides is 90°, i.e, ∠NBQ=∠PBQ=90°. After finding that these triangles are equal, we can say that ∠BNQ is 45°. From here, we easily find <span>∠PQN. It is 180 - (</span>∠QNP + ∠NPQ) = 180 - 90 = 90°
The <u>correct answer</u> is:
<span>A) Yes, the points shown on the line would be part of y = 0.5x.
Explanation:
Looking at the graph, the line goes through (0, 0). If x=0, we have
y=0.5(0)=0.
This is the y-coordinate of the point, so it goes through this.
The equation for this line is in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. In this equation, m=0.5 and b=0. This means the slope is 0.5 or 1/2; since slope is rise/run, this means the line rises 1 for every horizontal increase of 2.
This means starting from (0, 0), we would go up 1 and over 2, creating the point (2, 1). Looking at the graph, the line goes through this point.
Next we would go up 1 and over 2 again, to (4, 2). Again, the line goes through this point.
We could follow all of the points on this line and they all fit.</span>
