The system has one solution, so it is consistent independent. The graphs intersect at the point (2, 8), which can be checked algebraically.
Complete a table of values for each line.
The point (2, 8) is the solution to the system of equations. Since (2, 8) is the solution to the system of equations, Lucia has 2 dimes
and 8 nickels.
hope it helps :) feel free to ask anymore questions
You didn’t provide any answer choices but you can use my notes to guide you. Hope this helps! :)
Answer: 18
Step-by-step explanation: Well <u><em>percent</em></u> means <em>over 100</em> so we can set up an equation for this problem by reading it from left to right.
<em>What</em> means <em>x</em>, <em>is</em> means <em>equals</em>, <em>30%</em> is <em>30/100</em>, <em>of</em> means <em>times</em> <em>250</em>.
Simplifying on the right side of the equation,
notice that 30/100 reduces to 3/10.
So we have x = 3/10 · 60. Think of the 60 as 60/1 so we can cross-cancel the 60 and 10 to 6 and 1 and we have x = 
or <em>x = 18</em>.
Now let's check our answer back in the original problem to see if it makes sense. We have <em>18 is 30% of 60</em>.
Well we know that 100% of 60 would be 60 so 30% of 60 should be alot less than 60 so 18 seems to make sense as a pretty good answer.
C(x) = 200 - 7x + 0.345x^2
Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.
Range is the set of possible results for c(x), i.e. possible costs.
You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.
You can substitute some values for x to help you, for example:
x y
0 200
1 200 -7 +0.345 = 193.345
2 200 - 14 + .345 (4) = 187.38
3 200 - 21 + .345(9) = 182.105
4 200 - 28 + .345(16) = 177.52
5 200 - 35 + 0.345(25) = 173.625
6 200 - 42 + 0.345(36) = 170.42
10 200 - 70 + 0.345(100) =164.5
11 200 - 77 + 0.345(121) = 164.745
The functions does not have real roots, then the costs never decrease to 0.
The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.
Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.
