Part A. What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7?
Rewrite the equation −2y=3x+7 in the form
Here the slope of the given line is
If
is the slope of perpendicular line, then

Answer 1: 
Part B. The slope of the line y=−2x+3 is -2. Since
then lines from part A are not parallel to line a.
Since
both lines are not perpendicular to line a.
Answer 2: Neither parallel nor perpendicular to line a
Part C. The line parallel to the line 2x+5y=10 has the equation 2x+5y=b. This line passes through the point (5,-4), then
2·5+5·(-4)=b,
10-20=b,
b=-10.
Answer 3: 2x+5y=-10.
Part D. The slope of the line
is
Then the slope of perpendicular line is -4 and the equation of the perpendicular line is y=-4x+b. This line passes through the point (2,7), then
7=-4·2+b,
b=7+8,
b=15.
Answer 4: y=-4x+15.
Part E. Consider vectors
These vectors are collinear, then

Answer 5: 
Answer:

Step-by-step explanation:
step 1
Find the 
we know that
Applying the trigonometric identity

we have

substitute





Remember that
π≤θ≤3π/2
so
Angle θ belong to the III Quadrant
That means ----> The sin(θ) is negative

step 2
Find the sec(β)
Applying the trigonometric identity

we have

substitute




we know
0≤β≤π/2 ----> II Quadrant
so
sec(β), sin(β) and cos(β) are positive

Remember that

therefore

step 3
Find the sin(β)
we know that

we have


substitute

therefore

step 4
Find sin(θ+β)
we know that

so
In this problem

we have




substitute the given values in the formula



There isn't enough information shown to kniw
Answer:
Hii! Surface area= 207.35, volume= 226.19. Hope this helps!
Answer:

Step-by-step explanation:
this is the equation used to find the average of two numbers.