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Answer: f(2) is 3.
Step-by-step explanation:
f(2) just means "what is the vale of the function, f, when x = 2? Look for x=2 and read the y value where the line crosses x=2, in this case, the y value is 3. So f(2) = 3.
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[One could also determine the equation for the line. Provided below.]
The slope is -(1/2) and the y-intercept is 4:
y = -(1/2)x + 4
For x=2,
y = -(1/2)*(2) + 4
y = 3
y(2) = 3
Answer: 
a = 2 and b = 3
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Explanation:
Let's expand out 
to get the following:
The x term here is 2ax
Compare this to the x term of 
and we see that
--------------
The constant term of 
is the 
portion since it doesn't have the variable x attached to it.
Compare this with the 7 of which is also the constant.
Equate the two items, plug in a = 2 and solve for b.
Therefore,
Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
Answer:
Third option. -2
Step-by-step explanation:
the y change is -2
the x change is +1
slope is change in y/ change in x. So it would be -2/1 or -2
