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3 years ago

Use special right triangle properties to solve for the missing sides.

Mathematics

1 answer:

stiv31 [10]3 years ago

5 0

Answer:

cos30=12/x

√3/2=12/x

x=12×2/√3=24√3/3=8√3

sin30=y/x

1/2=y/8√3

1/2×8√3=y

y=4√3

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Ilya [14]

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Answer:

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Step-by-step explanation:

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3 years ago

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Sliva [168]

Answer:

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Step-by-step explanation:

Parent function:

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Transformations:

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$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

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$\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}$

$\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}$

If the parent function is shifted ¹/₄ unit up:

$\implies g(x)=x^2+\dfrac{1}{4}$

If the parent function is shifted ¹/₄ unit down:

$\implies g(x)=x^2-\dfrac{1}{4}$

If the parent function is compressed vertically by a factor of ¹/₄:

$\implies g(x)=\dfrac{1}{4}x^2$

If the parent function is stretched horizontally by a factor of ¹/₂:

$\implies g(x)=\left(\dfrac{1}{2}x\right)^2$

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

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