Given the functions f(x) = 7x + 13 and g(x) = x2 + 2, which of the following functions represents f[g(x)] correctly?
1 answer:
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Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.
Step-by-step explanation:
The right angle triangle ABC representing the scenario is shown in the attached photo.
Angle A is alternate to the angle of depression, hence, they are the same.
The height of the lighthouse represents the opposite side of the right angle triangle. The distance, x of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine x, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/x
x = 57/Tan 11.1 = 57/0.1962
x = 290.5 feet to the nearest tenth.
81 a² - 25 is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
Step-by-step explanation:
The difference of two squares is a binomial of two terms each term is a square and the sign between the two terms is (-), its factorization is the product of two identical binomials with different middle signs
- a² - b² is a difference of two squares
- a² - b² = (a + b)(a - b)
∵ The binomial is 81 a² - 25
∵ = 9
∵ = a
∴
∵ = 5
∵ = z³
∴
- The two terms have square root
∵ The sign between them is (-)
∴ 81 a² - 25 is a difference of two squares
∵ Its factorization is two identical brackets with different
middle signs
∵ 81 a² = 9a × 9a
∵ 25 = 5z³ × 5z³
- The terms of the two brackets are 9a and 5z³
∴ 81 a² - 25 = (9a + 5z³)(9a - 5z³)
81 a² - 25 is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
Learn more:
You can learn more about the difference of two squares in brainly.com/question/1414397
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