Answer:
The ball reached its maximum height of (
) in (
).
Step-by-step explanation:
This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.
The first step in completing the square is to group the quadratic and linear term:
Now factor out the coefficient of the quadratic term:
After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:
Now take the balancing term out of the parenthesis:
Simplify:
The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:
Answer:
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
<h3>
Answer: 25w+200 > 750</h3>
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Explanation:
He starts off with 200 cards. Then he adds on 25w more cards for each week (w). Overall, he'll have 200+25w cards
We can think of it like this:
- After 1 week, he adds on 25*1 = 25 cards
- After 2 weeks, he adds on 25*2 = 50 cards total
- After 3 weeks, he adds on 25*3 = 75 cards total
- After 4 weeks, he adds on 25*4 = 100 cards total, and so on.
- After w weeks, he adds on 25w cards total
So that's another way to see where the 25w comes from.
The expression 200+25w is the same as 25w+200. This is because we can add two numbers in any order.
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Since he wants to know when he'll have more than 750 cards, this means we set 25w+200 greater than 750.
That's how we get to the answer of 25w+200 > 750
Notice how there isn't a line under the inequality sign. We aren't using the "greater than or equal to" symbol here. We want to know when the cards gets over 750, but we don't want to know when it's equal to 750.
Area = 4.5 x 4.5 = 20.25 in²
Perimeter = 4 x 4.5 = 18 in
Answer:
2As and 1E
Step-by-step explanation:
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