Answer:
Step-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
<u>Find the equation of the function f(x), use the points on the graph:</u>
- c = 5 as the y-intercept is (0, 5)
- a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
- a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4
<u>The function is:</u>
Find the equation of g(x)
<u>Find the slope of g(x):</u>
- m = (1 - 7)/(-1 + 4) = -2
<u>Use (-4, 7) to find its equation:</u>
- y - 7 = -2(x + 4)
- y = -2x + 7 - 8
- y = -2x - 1
<h3>See the required comparison below</h3>
<u>The y-intercepts:</u>
- f(x) ⇒ 5,
- g(x) ⇒ -1
- -5 < - 1
<u>Values at x = 3:</u>
- f(3) = -3² + 4(3) + 5 = 8
- g(3) = -2(3) - 1 = - 7
- 8 > 7
<u>Average rate of change in the interval [2,5]:</u>
- f(x) ⇒ (0 - 9)/(5 - 2) = -3
- g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
- -3 < -2
<u>Max of function in the interval [-5, 5];</u>
- f(x) ⇒ 9, vertex of the function
- g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
- 9 = 9
There are 30 players in the tournament
Step-by-step explanation:
as in the attachment, i have named the lines by letters for easiness
If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:

You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.

This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is: 
So we can plug our dimensions into the formula: 
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.
PERIMETER
The formula for the perimeter of a rectangle is: 
We can plug our dimensions into the formula: 
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.