X = 12 , just solved it right now :)
a = 4, b = -21, c = -18
to keep from getting "mixed up", evaluate the discriminant first ...
b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729
sqrt(729) = 27
x = (21 +/- 27)/8
x = -3/4, x = 6
since the discriminant is a perfect square, the original quadratic will factor ...
4x<sup>2</sup> - 21x - 18 = 0
(4x + 3)(x - 6) = 0
x = -3/4, x = 6
Answer: Black
Step-by-step explanation: I feel like the higher the line is on the graph, the farther they have moved, so since the black line is the lowest, it might be Noah.
Hope this helps!
Answer:
16 apples.
Step-by-step explanation:


Price of apples, Px=$4
Price of tomatoes, Py=$3
Ratio of their Marginal Utilities



Since Natalie’s income is $320
320 = xPx+yPy

Since x=16, Natalie will consume 16 apples.
Answer:
y=4
Step-by-step explanation:
4y+3=19
=4y=19-3
=y=16/4=4