For the hypotenuses to be able to lie on the same line:
The tan of angle in both should be the same. That is the two triangles should be similar.
For the first triangle tanθ = 4/10 = 2/5
For the second triangle, tanθ = 12/30 = 6/15 = 2/5
Since both angles in the triangle are the same, hence, the hypotenuses of the two triangles could lie along the same line.
The line of symmetry is x = 8, and it means that it takes 8 seconds to reach the maximum height and 8 more seconds to reach the ground.
Answer:
you need to provide an image
The area of the convex polygon is 43/2 square units
<h3>How to determine the area of the convex polygon?</h3>
The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
![A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%2012%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_1%26x_2%5C%5Cy_1%26y_2%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_2%26x_3%5C%5Cy_2%26y_3%5Cend%7Barray%7D%5Cright%5D%20%2B%20....%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx_n%26x%5C%5Cy_n%26y%5Cend%7Barray%7D%5Cright%5D%20%29)
So, we have:

Evaluate

Remove the absolute bracket

This gives

Hence, the area of the convex polygon is 43/2 square units
Read more about convex polygon at:
brainly.com/question/14522707
#SPJ1
Answer:
180
Step-by-step explanation:
Nightly cost = x
x × 5% = Sales Tax
Total Cost : Percentage
189 : 105%
x : 100%
Cross multiply:
189 × 100% = 105% × x
189 = 1.05x
189 ÷ 1.05 = x
x = 180