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kipiarov [429]
3 years ago
5

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
8 0

Answer:

y =  x² - 8x + 17

Step-by-step explanation:

Recall this formula:

y = a(x-h)² + k

Original equation was y = x², which in this form looks like

y = 1(x - 0)² + 0

If the shape of the graph didn't change, that means that a (the compressor/intensifier) stayed the same (a - value) meaning we can write the equation as..

y = (x-h)² + k

Remember, (h, k) is the vertex, which looking from your graph is at (4, 1)

y = (x - 4)² + 1

y = x^2- 8x + 16+1

y = x² - 8x + 17

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Verify sine law by taking triangle in 4 quadrant<br>Explain with figure.<br>​
Ksivusya [100]

Proof of the Law of Sines

The Law of Sines states that for any triangle ABC, with sides a,b,c (see below)

a

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=

b

 sin  B

=

c

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For more see Law of Sines.

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 sin  B =

h

c

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b

or

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Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

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Using a similar method it can be shown that in this case

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- Q.E.D

Obtuse Triangles

The proof above requires that we draw two altitudes of the triangle. In the case of obtuse triangles, two of the altitudes are outside the triangle, so we need a slightly different proof. It uses one interior altitude as above, but also one exterior altitude.

First the interior altitude. This is the same as the proof for acute triangles above.

Draw the altitude h from the vertex A of the triangle

 sin  B =

h

c

      a n d          sin  C =

h

b

or

h = c  sin  B       a n d         h = b  sin  C

Since they are both equal to h

c  sin  B = b  sin  C

Dividing through by sinB and then sinC

c

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=

b

 sin  B

Draw the second altitude h from B. This requires extending the side b:

The angles BAC and BAK are supplementary, so the sine of both are the same.

(see Supplementary angles trig identities)

Angle A is BAC, so

 sin  A =

h

c

or

h = c  sin  A

In the larger triangle CBK

 sin  C =

h

a

or

h = a  sin  C

From (6) and (7) since they are both equal to h

c  sin  A = a  sin  C

Dividing through by sinA then sinC:

a

 sin  A

=

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Combining (4) and (9):

a

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2 years ago
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Step-by-step explanation:

3 0
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I hope this can help u

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mrs_skeptik [129]
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