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2 years ago

Find the value of each variable in the diagram given that a ∥ b.

Mathematics

1 answer:

Alika [10]2 years ago

4 0

The values are as follows:

z=50

v= 150

x= 100

y=15

w= 50

<h3>What is parallel lines?</h3>

Parallel lines are lines in a plane that are always the same distance apart.

z+130= 180 (Linear pair)

z=50

v+ 30 = 180 (Linear pair)

v= 150

x= 180- 30 - 50 (angle sum property)

x= 100

2y=30 (alternate interior angle)

y=15

w+x+2y=180 (Linear pair)

w+ 100 + 30 = 180

w= 50

Learn more parallel lines here:

brainly.com/question/16701300

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A sine function had an amplitude of 3, period of 6pi, horizontal shift of 3pi/2, & vertical shift of -1.

Simora [160]

Answer: $\bold{y=\dfrac{1}{2}}$

Step-by-step explanation:

f(x) = A sin (Bx - C) + D

amplitude = |A|
period = $\dfrac{2\pi}{B}$
phase shift = $\dfrac{C}{B}$
vertical shift = D

A

amplitude of 3 is given so 3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

B

period of 6π is given so $6\pi=\dfrac{2\pi}{B}\quad \rightarrow \quad B=\dfrac{2\pi}{6\pi}\quad \rightarrow \quad B=\dfrac{1}{3}$

C

$\text{phase shift is given as}\ \dfrac{3\pi}{2}\ \text{so}\ \dfrac{3\pi}{2}=\dfrac{C}{\frac{1}{3}}\quad \rightarrow\quad \dfrac{(\frac{1}{3})3\pi}{2}=C\quad \rightarrow\quad \dfrac{\pi}{2}=C$

D

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

$f(x) = 3\ sin \bigg(\dfrac{1}{3}x - \dfrac{\pi}{2}\bigg) - 1$

Next, solve when x = 2π

$f(2\pi) = 3\ sin \bigg(\dfrac{1}{3}(2\pi) - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{2\pi}{3} - \dfrac{\pi}{2}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{4\pi}{6} - \dfrac{3\pi}{6}\bigg) - 1$

$= 3\ sin \bigg(\dfrac{\pi}{6}\bigg) - 1$

$= 3\ \bigg(\dfrac{1}{2}\bigg) - 1$

$=\dfrac{3}{2}-\dfrac{2}{2}$

$=\dfrac{1}{2}$

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3 years ago

Sean is 27 centimeters shorter than his father who is 2 meters tall. How tall is Sean?

steposvetlana [31]

Height of Sean's Father = 2 m = 200 cm

Now, Height of Sean = 200 - 27 = 173 cm

In short, Your Answer would be: 173 cm

Hope this helps!

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3 years ago

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Helen [10]

Answer:

a^2 +b^2= c^2

Step-by-step explanation:

to prove that a triangle have right angles triangle you have to use the Pythagoras theorem

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2 years ago

5y+3>-7+13 (khan academy)

ladessa [460]

Answer:

y>0.6

Step-by-step explanation:

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5y+3>6

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stiks02 [169]

Answer:

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