(a) How could you calculate 23 x 4 on your calculator if the 4 button is broken? (b) How could you calculate 23 x 21 if the 2 bu
1 answer:
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Answer:
Step-by-step explanation:
A lot of math is about matching patterns.
For example, ...
g(x) = f(x -h) +k
means g(x) is the function f(x) translated right by h units and up by k units. This will be true for any expression of f(x).
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In this problem, f(x) = √x. We want to translate it left 6 units (h=-6)*, and up 4 units (k=4).
The notation above means that we will replace x with (x-h) = x+6. and we will add k = 4 to the result.
f(x) = √x
g(x) = f(x+6) +4
g(x) = √(x+6) +4 . . . . . . matches choice D
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* Left is the opposite of right, so left 6 units is the opposite of right 6 units. h=6 for <em>right 6 units</em>, so h=-6 for <em>left 6 units</em>. Then x-h = x-(-6) = x+6.
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<em>Comment on the graph</em>
I find it useful to see a picture with these things. In the attached graphing calculator output, the blue curve is left 6 and up 4 from the red curve. The blue curve is g(x); the red one is f(x).
Interpreting the inequality, it is found that the correct option is given by F.
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- The first equation is of the line.
- The equal sign is present in the inequality, which means that the line is not dashed, which removes option G.
In standard form, the equation of the line is:
Thus it is a decreasing line, which removes options J.
- We are interested in the region on the plane below the line, that is, less than the line, which removes option H.
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- As for the second equation, the normalized equation is:
- Thus, a circle centered at the origin and with radius 2.
- Now, we have to check if the line
, with coefficients
, intersects the circle, of centre
- First, we find the following distance:
- Considering the coefficients of the line and the center of the circle.
- This distance is less than the radius, thus, the line intersects the circle, which removes option K, and states that the correct option is given by F.
A similar problem is given at brainly.com/question/16505684
