Answer:
Option b. ![4y=x+1](https://tex.z-dn.net/?f=4y%3Dx%2B1)
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
we have the points
(7,2) and (-1,0)
substitute the given values in the formula
![m=\frac{0-2}{-1-7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B0-2%7D%7B-1-7%7D)
![m=\frac{-2}{-8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-2%7D%7B-8%7D)
![m=\frac{2}{8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B8%7D)
simplify
![m=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B4%7D)
step 2
Find the equation of the line in point slope form
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B4%7D)
![point\ (-1,0)](https://tex.z-dn.net/?f=point%5C%20%28-1%2C0%29)
substitute
![y-0=\frac{1}{4}(x+1)](https://tex.z-dn.net/?f=y-0%3D%5Cfrac%7B1%7D%7B4%7D%28x%2B1%29)
![y=\frac{1}{4}x+\frac{1}{4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7Dx%2B%5Cfrac%7B1%7D%7B4%7D)
Multiply by 4 both sides
![4y=x+1](https://tex.z-dn.net/?f=4y%3Dx%2B1)
The answer would be the first one
2=m/2−7
Simplify both sides of the equation.
2=m/2−7
2=1/2m+−7
2=1/2m−7
Flip the equation.
1/2m−7=2
Add 7 to both sides.
1/2m−7+7=2+7
1/2m=9
Multiply both sides by 2.
2*(1/2m)=(2)*(9)
m=18
64x2.40 = 153.6
64x1.90 = 121.6
add 153.6 to 121.6
275.2
The horizontal distance from the base of the skyscraper to the ship is 870 feet.
Data;
- Angle of Depression = 45°
- Observation Deck = 870 feet
<h3>Horizontal Distance </h3>
To calculate the horizontal distance from the base of the skyscraper, we can use trigonometric ratio SOHCAHTOA here;
Since we have the value of angle and opposite, we can calculate the adjacent using tangent of the angle.
![Tan \theta = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=Tan%20%5Ctheta%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Let's substitute the values and solve
![Tan 45 = \frac{870}{x} \\x = \frac{870}{tan 45} \\x = 870 ft](https://tex.z-dn.net/?f=Tan%2045%20%3D%20%5Cfrac%7B870%7D%7Bx%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B870%7D%7Btan%2045%7D%20%5C%5Cx%20%3D%20870%20ft)
The horizontal distance from the base of the skyscraper to the ship is 870 feet.
Learn more on trigonometric ratio here;
brainly.com/question/11967894