I saw the image of this problem.
For the quadrilateral to be parallelogram, MP = PO
MP = y + 25
PO = 5y + 29
y + 25 = 5y + 29
y - 5y = 29 - 25
-4y = 4
y = 4/-4
y = -1
MO = MP + OP
MO = y + 25 + 5y + 29
MO = -1 + 25 + 5(-1) + 29
MO = -1 + 25 - 5 + 29
MO = -6 + 54
MO = 48 Choice B.
Y = -5/4x + b is the equation that represents a line that is perpendicular to the line 5y-4x=-15
If you want it in standard form, it is 5x+4y=-15
X= 8
Y= -7
If you use elimination:
–3y–4x=–11
3y–5x=–61
Add the two equations and get
–9x=–72
Divide by –9 on both sides
X=8
Substitute 8 in for x
–3y–4(8)=–11
Simplify
–3y–32=–11
Add 32 on both sides
–3y=21
Divide by –3 on both sides
Y=–7
General equation of Ellipse centered at (h,k) is given as
where a is the radius along x-axis
and b is radius along y-axis.
Given : The equation of elliptical path of Earth as
Comparing the equation with the general equation, we get
(h,k) as (-2.5,0)
a = 
b = 
We have the Sun located at the coordinate (0,0).
Hence, the distance between Sun and Earth in July = 149.5 + 2.5 =152
∴ Earth's distance from the Sun in July is 152 million kilometers.
Answer: the shaded region = 69.66mm^2
Explanation:
Assume shaded region is X
Then :
X + Area of circle = area of square
X = area of square - area of circle
Find area of square:
Side length = 18mm
Area = 18 x 18 = 324
Find area of circle:
Side length of a square = the diameter of the circle = 18mm
And r(radius) = d/2 = 18/2 = 9
Area = pi x 9^2 = 254.34
Now find X
X = 324 - 254.34 = 69.66
