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3 years ago

WILL MARK BRAINLYIST IF CORRECT!

Mathematics

2 answers:

Nady [450]3 years ago

6 0

Your answer will be C

Damm [24]3 years ago

3 0

Answer:

itsssssssssssssssssss C

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Question : In the given figure , ∆ APB and ∆ AQC are equilateral triangles. Prove that PC = BQ.

lorasvet [3.4K]

Answer:

See Below.

Step-by-step explanation:

We are given that ΔAPB and ΔAQC are equilateral triangles.

And we want to prove that PC = BQ.

Since ΔAPB and ΔAQC are equilateral triangles, this means that:

$PA\cong AB\cong BP\text{ and } QA\cong AC\cong CQ$

Likewise:

$\angle P\cong \angle PAB\cong \angle ABP\cong Q\cong \angle QAC\cong\angle ACQ$

Since they all measure 60°.

Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:

$m\angle PAC=m\angle PAB+m\angle BAC$

Likewise:

$m\angle QAB=m\angle QAC+m\angle BAC$

Since ∠QAC ≅ ∠PAB:

$m\angle PAC=m\angle QAC+m\angle BAC$

And by substitution:

$m\angle PAC=m\angle QAB$

Thus:

$\angle PAC\cong \angle QAB$

Then by SAS Congruence:

$\Delta PAC\cong \Delta BAQ$

And by CPCTC:

$PC\cong BQ$

5 0

2 years ago

Read 2 more answers

How do you express sin x + cos x in terms of sine only?

frez [133]

Answer:

$\sin x + \sqrt{1-\sin^2x}$

Step-by-step explanation:

Given: sin x + cos x

To change the given trigonometry expression in term of sine only.

Trigonometry identity:-

$\sin^2x+\cos^2x=1$
$\cos x=\sqrt{1-\sin^2x}$

Expression: $\sin x+\cos x$

We get rid of cos x from expression and write as sine form.

Expression: $\sin x + \sqrt{1-\sin^2x}$ $\because \cos x=\sqrt{1-\sin^2x}$

Hence, The final expression is only sine function.

4 0

3 years ago

Angles A = 60, B = 2x, C = 3x and D = 25 are 4 angles on a straight, what 3 points is the value of angle B?*

iragen [17]

Answer:

B = 38°

Step-by-step explanation:

A straight angle is 180°. If your four angles total a straight angle, then ...

60 +2x +3x +25 = 180

95 = 5x . . . . . . subtract 85

x = 19 . . . . . . divide by 5

2x = 38 . . . . . angle B is 38°

4 0

1 year ago

What are the solutions to the quadratic equation below? x^2+34x-72=0

Annette [7]

Answer:

( x + 36 ) ( x - 2 ) = 0

Step-by-step explanation:

x^2 + 36x - 2x -72 = 0

x ( x + 36 ) - 2 ( x + 36 ) = 0

( x + 36 ) ( x - 2 ) = 0

7 0

3 years ago

The weight of one serving of trail mix is 2.5 ounces. How many servings are there in 22.5 ounces of trail mix?

Verdich [7]

Answer:

9 servings

There should be an answer to that. Answer: There are 9 servings. step- by- step Explanation: We would first divide 22.5/2.5. This will give us the amount of time 2.5 will go into 22.5, providing us with the amount of servings

Step-by-step explanation:

7 0

2 years ago