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natta225 [31]
2 years ago
7

The graph of the function f(x) = log2x is shown.

Mathematics
1 answer:
jekas [21]2 years ago
7 0

The domain of the function g(x) = 2 log₂(x - 4) + 3 will be (4, ∞). Then the correct option is A.

<h3>What are domain and range?</h3>

The domain means all the possible values of x and the range means all the possible values of y.

The graph of the function f(x) = log₂x is shown.

Function g is defined as g(x) = 2f(x - 4) + 3.

Then the function g(x) will be

g(x) = 2 log₂(x - 4) + 3

Then the domain of the function g(x) will be (4, ∞).

Then the correct option is A.

More about the domain and range link is given below.

brainly.com/question/12208715

#SPJ1

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Convert (-6, -6) from Cartesian coordinates to polar coordinates. Round the length to the nearest 0.01 Express the
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Answer:

  (8.49; 225°)

Step-by-step explanation:

The angle is a 3rd-quadrant angle. The reference angle will be ...

  arctan(-6/-6) = 45°

In the 3rd quadrant, the angle is 45° +180° = 225°.

The magnitude of the vector to the point is its distance from the origin:

  √((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49

The polar coordinates can be written as (8.49; 225°).

_____

<em>Additional comment</em>

My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.

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Answer:

If the given lengths of 7 cm, 24 cm, and 25 cm for the sides of a triangle satisfy the equation of the Pythagorean Theorem, then, yes, the given side lengths are those of a right triangle. Let's see if they are:

The well-known equation of the famous Pythagorean Theorem is:

a² + b² = c², which says that for a right triangle, the sum of the squares of the lengths of the two shorter sides of the triangle is equal to the square of the length of the longest side called the hypotenuse, where a and b are the lengths of the two shorter sides (also called the "legs") and c is the length of the hypotenuse (the side opposite the right angle).

We're given that a = 7 cm and b = 24 cm and that c = 25 cm. Substituting these values into the equation of the Pythagorean Theorem, we get:

a² + b² = c²

(7 cm)² + (24 cm)² = (25 cm)²

(7 cm)(7 cm) + (24 cm)(24 cm) = (25 cm)(25 cm)

49 cm² + 576 cm² = 625 cm²

625 cm² = 625 cm²

As we can see, the equation of the Pythagorean Theorem is satisfied, i.e., made a true statement, by the given lengths; therefore, if these three lengths, 7 cm, 24 cm, and 25 cm, are the lengths of the sides of a triangle, then the triangle is indeed a right triangle.

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