For Question 1: of 8 points)
1 answer:
The two boats' paths cross at the point (3, 6) besides the y-intercept. The substitution method is used to find out the cross point.
<h3>What are the methods for solving two equations?</h3>The methods used for solving two equations are:
- Substitution,
- Elimination,
- Addition/Subtraction, and
- Graphing techniques.
It is given that,
A sailboat with a sick passenger abroad is following a parabolic path. The path is given by the equation,
y = -x² + 4x + 3 ...(i)
A speedboat is trying to catch the sailboat to provide medical aid and is on a path.
That path is given by the linear equation,
y = x + 3 ...(ii)
Substituting equation(ii) in equation(i), we get
x + 3 = -x² + 4x + 3
⇒ x² + x - 4x + 3 - 3 = 0
⇒ x² - 3x = 0
⇒ x(x - 3) = 0
∴ x = 0 or x = 3
Then, finding the y-values:
For x = 0; substituting in equation(i),
y = -(0)² + 4(0) + 3 = 3
For x = 3; substituting in equation(ii),
y = -(3)² + 4(3) + 3 = -9 + 12 + 3 = 6
Thus, for both the boats the cross-out points are (0, 3) and (3, 6).
Since the y-intercept of the path y = x + 3 is 3 at (0, 3), the required point is (3, 6).
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Table is attached below
From the table we can see that the Lemon cost is equal to 35% of the expenses
Let the expense be x, Lemons cost is 70
Lemon cost = 35% * x
70 = 35% * x ( 35% = = 0.35)
70 = 0.35 * x
x =
x= 200, Expense = $200
Given : Profit percentage is 15%= = 0.15
Profit = profit percentage * Expense
Profit = 0.15 * 200 = 30
So profit = $30
