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Harlamova29_29 [7]
3 years ago
11

Analyze the diagram below and answer the question that follows.

Mathematics
1 answer:
Anna35 [415]3 years ago
7 0

Answer:

The right statement is sin(J) = cos(L) ⇒ answer D

Step-by-step explanation:

* Lets describe the figure

- LKJ is a right triangle, where K is a right angle

∵ m∠K = 90°

∵ LJ is opposite to angle K

∴ LJ is the hypotenuse

∵ LJ = 219

∵ KJ = 178

- By using Pythagoras Theorem

∵ (LJ)² = (LK)² + (KJ)²

∴ (219)² = (LK)² + (178)² ⇒ subtract (178)² from both sides

∴ (LK)² = (219)² - (178)²

∴ (LK)² = 16277

∴ LK = √16277 = 127.58

* Lets revise how to find the trigonometry function

# sin Ф = opposite/hypotenuse

# cos Ф = adjacent/hypotenuse

# tan Ф = opposite/adjacent

∵ LK is the opposite side to angle J

∵ LJ is the hypotenuse

∵ sin(J) = LK/LJ

∵ LK = 127.58 , LJ = 219

∴ sin(J) = 127.58/219 = 0.583

∵ LK is the adjacent side to angle L

∵ LJ is the hypotenuse

∵ cos(L) = LK/LJ

∵ LK = 127.58 , LJ = 219

∴ cos(L) = 127.58/219 = 0.583

∴ sin(J) = cos(L)

* The right statement is sin(J) = cos(L)

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What are the transformations to this quadratic function y= (x+4) power of 2 - 8
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Answer:

Horizontal shift of 4 units to the left.

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Step-by-step explanation:

Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:

The vertex form of the quadratic function is y = a(x - h)² + k

Where:

The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).

The axis of symmetry occurs at <em>x = h</em>.

<em>a</em> =  determines whether the graph opens up or down, and makes the graph wider or narrower.

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<em>k</em> = determines how far up or down the parent function is translated.

Going back to your quadratic function,

          y = (x + 4)² - 8

  • The vertex occrs at (-4, -8)
  • a is assumed to have a value of 1.
  • Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.  
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p = principal
r = rate, change to a decimal
n = number of times it is compounded per year
t = time in years
A = 10,000(1 + .055/12)^(12*(44/12))
Since the time is in months and the formulas is in years, I put the (44/12) to represent the time. This will actually simplify to 44.
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