Answer:
The sample is large enough, representative of the entire population, and chosen randomly so the conclusion is valid.
Answer:
straight angle
Step-by-step explanation:
Answer:
Step-by-step explanation:
If lines OA and OC trisect angle NOD, then
By angle addition postulate:
If line OB bisects ange NOD, then
Angle AOB is 20 degrees less than angle NOA, then
By angle addition postulate,
Thus,
and
<h3>
Answer:</h3>
none of the above
(the <em>first choice</em> will probably be marked correct, though it is not)
<h3>
Step-by-step explanation:</h3>
You can find the inverse function by solving for y:
x = f(y)
x = √(y -5)
x² = y -5
x² + 5 = y
Then ...
f^-1(x) = x² + 5 . . . . . matches the equation in the first selection
We note that the original function f(x) is a function by virtue of the fact that only the positive square root is of interest. That is, the <em>range</em> of the function f(x) is y ≥ 0. Then the inverse function will have the <em>domain</em> x ≥ 0.
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The offered choices seem to put restrictions on the <em>range</em> (y-values) of the inverse function. There is no need. The range is automatically restricted by the values the inverse function can generate (y ≥ 5). What is needed is a restriction on the <em>domain</em>, which must be x ≥ 0.
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<em>Comment on the graph</em>
The inverse of a function is the mirror image of that function reflected across the line y=x. That line is shown in dashed orange. The original function f(x) is shown in red.
The offered choice #1 for the inverse function f^-1(x) is shown in blue. As you can see, for negative values of x, there is no corresponding branch of the square root function f(x). In order to properly define the inverse function, we must make it look like the portion of the blue curve that is overlaid with purple dots. That is, we must restrict the domain of the inverse function to x ≥ 0. (The values of the inverse function will always satisfy y ≥ 5, whether we have properly restricted its domain or not.)
We can see that the 33 degrees corresponds to angle A (parallel lines) meaning they’re equal.
This means that 33 + 2x = 5x (5x is the exterior angle, so the other two interior angles’ sum must equal to it)
3x = 33
x = 11