Answer: a
Step-by-step explanation:
We are give that:
y = 3x^2 - 8x -2
Thus, y is given in terms of x. We will use this to substitute in the second equation and get the values of x as follows:
2x - y = 5
2x - (3x^2 - 8x -2) = 5
2x - 3x^2 + 8x + 2 -5 = 0
-3x^2 + 10x - 3 = 0
(x-3) (3x-1) = 0
either x = 3
or x = 1/3
Now, we will use the calculated values of x to find y as follows:
At x=3: y = 3x^2 - 8x - 2 = 3(3)^2 - 8(3) - 2 = 1
At x=1/3 : y = 3x^2 - 8x - 2 = 3(1/3)^2 - 8(1/3) - 2 = -13/3
Based on the above calculations, the solution sets of the system of equations given are either (3,1) or (1/3 , -13/3)
Answer:
695 feet.
Step-by-step explanation:
Please find the attachment.
Let x represent distance between ship and base of statue.
We have been given that the Statue of Liberty is approximately 305 feet tall. The angle of elevation of a ship to the top of the statue is 23.7 degrees. We are asked to find the distance between ship and base of statue.
We can see that angle of elevation forms a right triangle with base of statue and ship.
Now, we will use tangent to solve for x as:
![\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%3D%5Cfrac%7B%5Ctext%7BOpposite%7D%7D%7B%5Ctext%7BAdjacent%7D%7D)
![\text{tan}(23.7^{\circ})=\frac{305}{x}](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%2823.7%5E%7B%5Ccirc%7D%29%3D%5Cfrac%7B305%7D%7Bx%7D)
![x=\frac{305}{\text{tan}(23.7^{\circ})}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B305%7D%7B%5Ctext%7Btan%7D%2823.7%5E%7B%5Ccirc%7D%29%7D)
![x=\frac{305}{0.438969309852}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B305%7D%7B0.438969309852%7D)
![x=694.80939\approx 695](https://tex.z-dn.net/?f=x%3D694.80939%5Capprox%20695)
Therefore, the ship is approximately 695 feet away from the base of statue.
Answer:12x-157-5.2x
Step-by-step explanation:Like this or you want us to solve it lol