Answer: PR=14.5.
Step-by-step explanation:
1. If the area of PQR is 50, then (QR*PQ)/2=50, so QR*PQ=100 (the area of a triangle is the base*height/2).
2, The tangent of an angle is (the opposite side)/(the adjacent side). So, the tangent of angle P=QR/PQ. Angle P is 36 degrees, and the tangent of 36 degrees is 0.726542528. We can substitute this into the equation we found to get 0.726542528=QR/PQ.
3. Using the equations we found in Steps 1 and 2, we can create a system of equations:
We can solve this system of equations to get PQ=11.7319 and QR=8.52375.
4. Using Pythagorean theorem, we can say that PR^2=QR^2+PQ^2. If we substitute the values of PQ and QR into the equation, we can come to the conclusion that PR=14.5014410206, which simplifies to PR=14.5.
Answer:
System of equations:
3.5c + 5a = 377
c + a = 85
Solved:
(53, 32)
Step-by-step explanation:
32 children's tickets were sold and 53 adults tickets were sold.
We can solve this by setting up 2 equations. We can use any letters like. For now, I'll use x and y.
So now we know that x - y = 0.7 and x + y = 1.
Now we can eliminate one of the letters by adding or subtracting one equation from the other. I am going to eliminate y by adding the two together (the y and the -y cancel).
This gives us 2x = 1.7, and so x = 1.7 ÷ 2 = 0.85
Finally, we can substitute x for 0.85 back into one of the original equations to figure out what y equals. I'm going to use x + y = 1.
So now we have 0.85 + y = 1, so y = 1 - 0.85 = 0.15
The numbers, therefore, are 0.85 and 0.15 (you can check by using the other equation).
Hope this helps!
Answer:
continually look to expand and invest.
Step-by-step explanation:
Capital resources are general used for the production of other goods and services. If there are excessive capital resources in an economy, the company will plan to produce more goods and services using the available resources. The number of employees will also increase. However, there won't be plans for more investment or expansion.
