<h3>
Answer: Choice A. (7,4)</h3>
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Explanation:
Use the slope and given point to find the y intercept
y = mx+b
8 = (-2/3)*(1) + b
8 = -2/3 + b
8 + 2/3 = b
24/3 + 2/3 = b
26/3 = b
b = 26/3
The equation of the line is y = (-2/3)x + 26/3
To confirm this, plug in x = 1 and we should get y = 8, due to the point (1,8)
y = (-2/3)x + 26/3
y = (-2/3)*1 + 26/3
y = -2/3 + 26/3
y = (-2+26)/3
y = 24/3
y = 8
So that verifies we have the correct equation.
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Next, go through each answer choice to see if the x coordinate of the point leads to the y coordinate.
If we try x = 7, then,
y = (-2/3)x + 26/3
y = (-2/3)(7) + 26/3
y = -14/3 + 26/3
y = (-14+26)/3
y = 12/3
y = 4
This shows that (7,4) is on the line. Choice A is the answer
That rules out choice B.
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If we tried x = -5, then,
y = (-2/3)x + 26/3
y = (-2/3)(-5) + 26/3
y = 10/3 + 26/3
y = 36/3
y = 12
meaning that (-5,12) is on the line. That rules out choices C and D.
Refer to the graph below. It visually confirms that of the four answer choices, only point A is on the line. I used GeoGebra to make the graph.
Volume = 20,670 inches cubed
Surface Area = 3915 inches squared
Step-by-step explanation:
The denominator of the first term is a difference of squares, such that
4<em>a</em> ² - <em>b</em> ² = (2<em>a</em>)² - <em>b</em> ² = (2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)
So you can write the fractions as
(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)/(2<em>a</em> + <em>b</em>)
Multiply through the second fraction by 2<em>a</em> - <em>b</em> to get a common denominator:
(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)²/((2<em>a</em> + <em>b</em>) (2<em>a</em> - <em>b</em>))
((4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²) / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))
Expand the numerator:
(4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²
(4<em>a</em> ² + <em>b</em> ²) - (4<em>a</em> ² - 4<em>ab</em> + <em>b</em> ²)
4<em>ab</em>
<em />
So the original expression reduces to
4<em>ab</em> / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))
or
4<em>ab</em> / (4<em>a</em> ² - <em>b</em> ²)
upon condensing the denominator again.
If it was 23 degrees below zero it would be -23 degrees
