9514 1404 393
Answer:
2 nickels, 9 dimes
Step-by-step explanation:
When there are a number of overlapping shaded areas on the graph, I find it convenient to use the reverse of the inequalities. That makes the <em>unshaded</em> area the solution space. Here, the vertices of the triangular solution space are ...
(2, 9), (2, 13), (6, 9)
Any of the grid points within (or on) this triangle is a possible solution. One of them is (2, 9) corresponding to 2 nickels and 9 dimes.
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Three solutions are shown:
(x, y) = (2, 9), (3, 10), (4, 11)
A median intersects at the midpoint of the opposite length. The midpoint is:
x,m = (4+-2)/2 = 1
y,m = (-1+7)/2 = 3
The midpoint is at (1,3). With this point and point R(9,9), the equation would be:
y = mx + b, where
m = (9 - 3)/(9 - 1) = 0.75
b is the y-intercept
Substituting any point,
3 = 0.75(1)+b
b = 2.25
Thus, the equation for the median is:
y = 0.75x + 2.25
-8/5 is a rational number because in order to be a rational number it must be able to be written as a fraction. -8/5 is a fraction; therefore, the negative does not affect it.
Let's translate it into an equation and then solve...
7/x = 7.35
x * 7/x = 7.35 * x
7 = 7.35x
7/7.35 = x
.9524 = x
So 7 divided by .9524 (rounded to the nearest ten thousandth) equals 7.35
