ANSWER:
For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.
For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.
![132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39](https://tex.z-dn.net/?f=132%20%3D%20x%20%2B%20%283x-24%29%5C%5C132%20%3D%204x%20-%2024%5C%5C156%3D4x%5C%5Cx%3D39)
The m∡B = 39°
The correct answers are:
(D) a<span>b ll cd
(F) a</span><span>b and cd are coplanar
Explanation:
The symbol for parallel is " </span>ll ". Therefore, if we translate the given sentence, <span>ab and cd are parallel, into the Mathematical terms, we can write it as:
</span>
ab ll cd (Option D)
Where ab = line
cd = line
Furthermore, the lines ab and cd are coplanar because they form the plane. In other words, you can say that the lines ab and cd lie on the same plane. (Option F)
Hence the correct answers are:
(D) ab ll cd
(F) ab and cd are coplanar
Answer:
2nd one from the left.
Step-by-step explanation:
it has the same angle measures.
Answer:
The ships are 66 meters apart.
Step-by-step explanation:
For the sake of convenience, let us label ships A and B
As shown in the figure, the distances to the ships from right triangles.
The distance to the ship A is
and it is given by
![tan (61^o)= \dfrac{50}{d_1}](https://tex.z-dn.net/?f=tan%20%2861%5Eo%29%3D%20%5Cdfrac%7B50%7D%7Bd_1%7D)
![d_1=\dfrac{50}{tan (61^o)}](https://tex.z-dn.net/?f=d_1%3D%5Cdfrac%7B50%7D%7Btan%20%2861%5Eo%29%7D)
![\boxed{d_1= 27.71m}](https://tex.z-dn.net/?f=%5Cboxed%7Bd_1%3D%2027.71m%7D)
And the distance to the ship B is
and is given by
![tan (28^o)= \dfrac{50}{d_2}](https://tex.z-dn.net/?f=tan%20%2828%5Eo%29%3D%20%5Cdfrac%7B50%7D%7Bd_2%7D)
![d_2=\dfrac{50}{tan (28^o)}](https://tex.z-dn.net/?f=d_2%3D%5Cdfrac%7B50%7D%7Btan%20%2828%5Eo%29%7D)
![\boxed{ d_2=94.04m}](https://tex.z-dn.net/?f=%5Cboxed%7B%20d_2%3D94.04m%7D)
Therefore, the distance
between the ships A and B is
![d= d_2-d_1=94.04-27.7\\\\\boxed{d=66m}](https://tex.z-dn.net/?f=d%3D%20d_2-d_1%3D94.04-27.7%5C%5C%5C%5C%5Cboxed%7Bd%3D66m%7D)
In other words, the ships are 66 meters apart.
Answer:
Step-by-step explanation:
- Number of dimes = d, each d = 10 c
- Number of quarters = q, each q = 25 c
- Total = $2 = 200 c
<u>Equations according the given:</u>
<u>Solve for q by substitution:</u>
- 10(q + 6) + 25q = 200
- 10q + 60 + 25q = 200
- 35q = 140
- q = 140/35
- q = 4
<u>Find the value of d:</u>
Nathaniel has 10 dimes and 4 quarters