To find the measure of angle OPQ, we have two equations...
y+5x-17=180 because angles OPN and OPQ are supplementary...
AND
x+17+2x-4+y=180 because the total degrees of a triangle must add up to 180.
The equations...
5x+y=197
3x+y=167
solce the system of equations...
x=15
y=122
Since we wanted to solve for y, 122 is the answer.
The measure of angle OPQ is 122.
Sorry this took forever. The website is hard to use because I'm used to using the app:)
Best of wishes!
Answer:
no, its 11 for the first one and 45 for the second
Step-by-step explanation:
Something funny is that the x value of the vertex lies directl in the middle of the x intercepts
so
we see the x intercepts or 0's at x=8 and 2
the average is x=5
so find f(5) to find the y value of the vertex
f(5)=(5-8)(5-2)
f(5)=(-3)(3)
f(5)=-9
vertex is at (5,-9)
the actual way the teacher wants is to expand then compltete the square to get into the form f(x)=a(x-h)^2+k where the vertex is (h,k)
but whatever
verrtex is at (5,-9)
-16t^2+400=0
16t^2=400
take square root on both sides.

4t=20
t=20/4
t=5
Answer:
y+11=-2/3(x-6)
Step-by-step explanation:
To find the parallel line, we would just plug in the numbers in the point-slope form from what we're given. We have y=-2/3x+12 and (6,-11).
Point-slope form:
y-y1=m(x-x1) → y+11=-2/3(x-6)
m represents the slope, which is -2/3 in this situation.
y1 represents the y coordinate, which is -11 in this situation. However, when we plug in negative numbers in a point-slope form, we would do the opposite of the negative number, which is to make it a positive in point-slope form.
x1 represents the x coordinate, which is 6 in this situation.