Shakeva buys a car for $41.9K. Her state charges a 5% sales tax, $27 for registration, $19 for a new title certificate, and $45
1 answer:
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Answer:
The first option .
Step-by-step explanation:
To have exactly 2 real and two non real solutions, the degree of the polynomial must be a degree 4. Degree is the highest exponent value in the polynomial and is also the number of solutions to the polynomial. This polynomial ha 2 real+2 non real= 4 solutions and must be . This eliminates the bottom two solutions.
In order to have two real and two non real solutions, the polynomial must factor. If it factors all the way like
This means x=0, 10, -10 are real solutions to the polynomial. It has no non real solutions. This eliminates this answer choice.
Only answer choice 1 meets the requirement.
The explanation for this is one of my favorite pieces of mathematical reasoning. First, let's thing about distance; what's the shortest distance between two points? <em>A straight line</em>. If we just drew a straight line between A and B, though, we'd be missing a crucial element of the original problem: we also need to pass through a point on the line (the "river"). Here's where the mathemagic comes in.
If we take the point B and <em>reflect it over the line</em>, creating the point B' (see picture 1), we can draw a line straight from A to B' that passes through a point on the line. Notice the symmetry here; the distance from the intersection point to B' is<em> the same as its distance to B</em>. So, if we reflect that segment back up, we'll have a path to B, and because it came from of the line segment AB', we know that it's <em>the shortest possible distance that includes a point on the line</em>.
If we apply this same process to our picture, we see that the line segment AB' crosses the line at the point (1, 1)
