The quadratic function h(t) = −16t² + 84t + 72, shows that the person throws the ball from on top of a 72 feet building at a velocity of 84 feet/second.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
The quadratic function h(t) = −16t² + 84t + 72, shows that the person throws the ball from on top of a 72 feet building at a velocity of 84 feet/second.
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The main idea here is to "translate" the words into maths.
First we need to identify the unknowns and label these.
We need to know the number if dimes and the number of quarters. So lets say
x: number of dimes
y: number of quarters
Now lets write equations from the written problem.
We know that there are 36 coind total, thus:
x + y = 36
We also know that the coins total 5.85 dollars, but it is better to count in cents, that is 585 cents.
x are the number of dimes, their value is x*10
y are quarters with value of y*25
thus:
10x+25y=585
We have two equations and two unknowns now, that needs to be solved to get the answer.
x + y = 36
10x+25y=585
Answer:
x = 3/8
Step-by-step explanation:
<h3>
Answer: -7 < x < 17</h3>
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Explanation:
Plug in the lower bound of the domain, which is x = -3
f(x) = 3x+2
f(-3) = 3(-3)+2
f(-3) = -9+2
f(-3) = -7
If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.
If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.
The range of f(x) is -7 < y < 17
Recall that the domain and range swap places when going from the original function f(x) to the inverse 
This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.
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In short, we found the range of f(x) is -7 < y < 17.
That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.
Answer:
The answer would be 5/6.
Step-by-step explanation: