Answer:
D is correct Answer. Parallel line on graph means infinity many solutions.
SOLUTION
Consider the property, opposite angle of a cyclic quadrilateral are supplementary
hence
![\angle NMP+\angle NOP=180^0](https://tex.z-dn.net/?f=%5Cangle%20NMP%2B%5Cangle%20NOP%3D180%5E0)
Recall that
![\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cangle%20NMP%3D%5Cangle%20M%3D%288x-24%29%5E0%20%5C%5C%20%5Ctext%7Band%20%7D%20%5C%5C%20%5Cangle%20NOP%3D%5Cangle%20O%3D%284x%29%5E0%20%5Cend%7Bgathered%7D)
Hnece, we have that
![\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cangle%20M%2B%5Cangle%20O%3D180%5E0%28opposite%5Ctext%7B%20angles%20of%20a%20cyclic%20quadrilateral%29%7D%20%5C%5C%20%288x-24%29%5E0%2B4x%5E0%3D180%5E0%20%5Cend%7Bgathered%7D)
Then
![\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%208x-24%2B4x%3D180%20%5C%5C%208x%2B4x-24%3D180%20%5C%5C%2012x-24%3D180%20%5C%5C%20%5Ctext%7BAdd%2024%20t%20o%20both%20sides%20%7D%20%5C%5C%2012x-24%2B24%3D180%2B24%20%5C%5C%2012x%3D204%20%5C%5C%20%5Ctext%7Bdivide%20both%20sides%20by%2012%7D%20%5C%5C%20%5Cfrac%7B12x%7D%7B12%7D%3D%5Cfrac%7B204%7D%7B12%7D%20%5C%5C%20%5Ctext%7BThen%7D%20%5C%5C%20x%3D17%20%5Cend%7Bgathered%7D)
Hence
x=17
Since
![\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cangle%20NOP%3D%284x%29%5E0%20%5C%5C%20%5Ctext%7Bsubstitute%20the%20value%20of%20x%2C%20we%20have%20%7D%20%5C%5C%20%5Cangle%20NOP%3D4%5Ctimes17%3D68%5E0%20%5C%5C%20%5Ctext%7BHence%20%7D%20%5C%5C%20%5Cangle%20NOP%3D68%5E0%20%5Cend%7Bgathered%7D)
Therefore
The measure of angle NOP is 68⁰
Answer; 68⁰ (The fourth Option )
Answer:
Step-by-step explanation:
so S and Y are complementary...that means when added, they equal 90 degrees.
S + Y = 90
S = 4Y - 185
4Y - 185 + Y = 90
5Y - 185 = 90
5Y = 90 + 185
5Y = 275
Y = 275 / 5
Y = 55 <===== angle Y is 55
S + Y = 90
S + 55 = 90
S = 90 - 55
S = 35
The circumference of a circle is PiD, or 2(3.14)(r).
The radius is half the diamater.
Let's solve with the diameter.
18 • 3.14 = 56.52 inches.
I hope this helps!
-4(8-3x)≥6x-8
Expand the left side.
-32+12x≥6x-8
Add 32 to both sides
12x≥6x+24
Subtract 6x.
6x≥24
Divide both sides by 6.
x≥4
Answer: x ≥ 4