18x + 15 - y = 0 5y = 90x + 12 Step By Step and I'll mark you brainliest
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For an amount of 6250 Peso, Hank have the quantities of the following denominations: 2503 bills of 50 peso, 2498 bills of 200 peso and 1249 bills of 500 peso.
<h3>How to apply systems of linear equations in real life equations</h3>
In this question we must translate the statement of the problem into mathematical expressions and then we must solve the resulting system. We need three equations that describe the quantities of 50 peso, 200 peso and 500 peso bills:
<em>y = x - 5</em> (1)
<em>0.5 · y =</em> <em>z</em> (2)
<em>x + y + z = 6250</em> (3)
The solution of the system of <em>linear</em> equations is described below:
<em>x =</em> 2503, <em>y =</em> 2498, <em>z =</em> 1249
For an amount of 6250 Peso, Hank have the quantities of the following denominations: 2503 bills of 50 peso, 2498 bills of 200 peso and 1249 bills of 500 peso.
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<h3>Answer: (-4, 8)</h3>
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Explanation:
The 90 degree counterclockwise rotation rule we use is
the x and y coordinates swap places, and we change the sign of the first coordinate after the swap.
After using that rotation rule, we would go from (8,4) to (-4, 8) which is the final answer.
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Extra info (optional section):
Define the following three points
A = (0,0)
B = (8,4)
C = (-4,8)
Use the slope formula to find that AB and AC have slopes of 1/2 and -2 in that order.
Those slopes multiply to -1, since (1/2)*(-2) = -1. This is a property of any two perpendicular lines as long as neither line is vertical and neither is horizontal. So this is sufficient to prove that the lines are perpendicular. This further means that a 90 degree rotation has taken place.