A) Complete the table of values for y = x^2 - 4x
1 answer:
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<h3>Answer: Choice B) x = 65, y = 10</h3>
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Work Shown:
The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so
(2x-y)+60 = 180
2x-y = 180-60 ... subtract 60 from both sides
2x-y = 120 ... call this equation 1
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Similarly, (2x+y) and 40 also combine to 180
(2x+y) + 40 = 180
2x+y = 180-40 ... subtract 40 from both sides
2x+y = 140 ... call this equation 2
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Line up equation 1 and equation 2. Then add straight down
That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.
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If x = 65, then,
2x-y = 120
2(65)-y = 120
130 - y = 120
-y = 120-130
-y = -10
y = 10
or
2x+y = 140
2(65)+y = 140
130+y = 140
y = 140-130
y = 10
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Either way end up with x = 65 and y = 10
<h3>Answer:</h3>
ellipse
<h3>Explanation:</h3>Written in general form, the equation is ...
... x² +2y² -4y = 0
The coefficients of the squared terms are the same sign, and of different values, so the equation is of an ellipse.
These are the other possibilities that can be determined from the coefficients of the squared terms.
- Same sign, same value: circle.
- Opposite sign: hyperbola.
- Only one squared term: parabola.
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Of course, your handy graphing calculator can show you the graph, making it easy for you to determine the conic section that is described.