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2 years ago

What is

Mathematics

1 answer:

arsen [322]2 years ago

8 0

9514 1404 393

Answer:

B. 17°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relations between angles and sides. Here, the relevant relation is ...

Sin = Opposite/Hypotenuse

sin(N) = PQ/PN

sin(N) = 4/14

N = arcsin(4/14) ≈ 16.6° . . . . use the inverse function to find the angle

N ≈ 17°

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Evgesh-ka [11]

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This can be re-written as:

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$\begin{gathered} -3(3a+4)\text{ = 3}\times5 \\ -3(3a+4)=\text{ 15} \\ \text{Expand the bracket} \\ -9a\text{ - 12 = 15} \\ \text{Collect like terms} \\ -9a\text{ = 15 + 12} \\ -9a\text{ = 27} \\ \text{Divide both sides by -9} \\ \frac{-9a}{-9}=\frac{27}{-9} \\ a\text{ = -3} \end{gathered}$

To verify if the solution is correct, substitute a = -3 into the question given. If the Right Hand Side equals the Left Hand Side, then the solution is correct.

$\begin{gathered} 4-\frac{3(3a+4)}{5}=\text{ 7} \\ \text{Substitute a = }-3 \\ 4\text{ - }\frac{3(3(-3)+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-9+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-5)}{5}\text{ = 7} \\ 4\text{ - }\frac{-15}{5}=\text{ 7} \\ 4-(-3)=7 \\ 4+3=7 \\ 7=7 \end{gathered}$

Since the Left Hand Side = Right Hand Side = 7, the solution a = -3 is correct

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