Answer:
No, the maximum height that the balloon can reach is 9ft.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
The function h(x) =-0.5(x-4)² +9, is a Quadratic Function in the Vertex form.
Vertex form: f (x) = a(x - h) 2 + k
Where:
- (h, k) is the vertex of the parabola-
- h is the horizontal shift (how far left, or right, the graph has shifted from x = 0).
- k represents the vertical shift (how far up, or down, the graph has shifted from y = 0).
In this case a = -0.5, it means that the parabola opens downward and has a maximum point at the vertex.
So, the maximum height that the balloon can reach is k=9ft.
9 ∠ 12
The balloon will not hit the ceiling 12 ft above the pool.
Feel free to ask for more if needed or if you did not understand something.
<span>1. Let t = time in years, with t = 0 representing the year 2005. Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school. Create the two functions to represent the situation.
f(t) = 85 + 18t </span>⇒ y = 85 + 18x<span>
g(t) = 95 + 15t </span>⇒ y = 95 + 15x
y = y
85 + 18x = 95 + 15x
18x - 15x = 95 - 85
3x = 10
x = 10/3
x = 3 1/3
y = 85 +18(10/3) = 85 + 180/3 = 85 + 60 = 145
y = 95 + 15(10/3) = 95 + 150/3 = 95 + 50 = 145
x = 10/3 or 3 1/3
y = 145
Answer:
Step-by-step explanation:
Neutron: has mass and no charge
Protons: has mass and a positive charge
Answer:
These fractions are already in simplest form.
Step-by-step explanation:
(x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15 as there is no remaider.
<h3>What is a factor of a polynomial?</h3>
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial function f(x) = x³ - x² - 17x -15.
If (x - 5) is it's factor then f(5) = 0.
∴ f(x) = x³ - x² - 17x -15.
f(5) = 5³ - 5² - 17(5) - 15.
f(5) = 125 - 25 - 85 - 15.
f(5) = 0.
So, the remainder is zero hence (x - 5) is a factor of the polynomial function f(x) = x³ - x² - 17x -15.
learn more about factor of a polynomial here :
brainly.com/question/26354419
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