Help pls i am being timed on a quiz

Mathematics

1 answer:

Dahasolnce [82]2 years ago

5 0

In analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.

<h3>What is the value of sin∠L?</h3>

Given that angle ONM is a right angled triangle, we can find length of OM using the Pythagorean theorem.

c = √( a² + b² )

OM = √( 4² + 3² )

OM = √( 16 + 9 )

OM = √25

OM = 5

Next, angle OML is also a right angled triangle, we can get the hypotenuse LO.

c = √( a² + b² )

LO = √( OM² + ML² )

LO = √( 5² + 12² )

LO = √( 25 + 144 )

LO = √169

LO = 13

Now, to get sin∠L, we use the mnemonic: SOHCAHTOA

sinθ = opposite / hypotenuse

sin∠L = OM / LO

sin∠L = 5/13

Therefore, in analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.

Learn more about Pythagorean theorem here: brainly.com/question/343682

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Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

lesantik [10]

Answer:

C. Yes, 3.5.

Step-by-step explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality ( $k$ ) is described by the following expression:

$k = \frac{y}{x}$ (1)

Where:

$x$ - Input.

$y$ - Output.

If we know that $(x_{1}, y_{1}) = (13, 45.5)$ , $(x_{2}, y_{2}) = (14, 49)$ and $(x_{3}, y_{3}) = (15, 52.5)$ , then the constants of proportionalities of each ordered pair are, respectively: