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Roman55 [17]
3 years ago
14

If MN=NQ and MQ=QR=RP, calculate for x​

Mathematics
1 answer:
Akimi4 [234]3 years ago
7 0

Answer:

  • C. 18°

Step-by-step explanation:

  • <em>Refer to attached diagram</em>
<h3>Given </h3>
  • MN = NQ
  • MQ = QR = RP
  • NMR = 3x
  • QMR = x
<h3>To find</h3>
  • Value of x
<h3>Solution</h3>
  • MN = NQ  ⇒ ∠MRN = ∠QMN = 3x+x = 4x
  • MQ = QR ⇒ ∠MRQ = ∠QMR = x

<u>RQP is exterior angle of ΔMQR ⇒ </u>

  • ∠RQP = x + x = 2x

<u>QR = RP ⇒ </u>

  • ∠RPQ = ∠RQP = 2x

<u>∠QRN is exterior angle of ΔQRP ⇒ </u>

  • ∠QRN = 2x + 2x = 4x
  • ∠MRN = ∠QRN - ∠QRM = 4x - x = 3x

<u>∠MRN = ∠NMR = 3x ⇒ </u>

  • NR = MQ

<u>NR = MQ ⇒ </u>

  • ∠NQR = ∠QRN = 4x

<u>We now have a straight angle MQP:</u>

  • ∠MQP = ∠MQN + ∠RQN + ∠RQP
  • 180° = 4x + 4x + 2x
  • 10x = 180°
  • x = 18°

Correct choice is C

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Anthony has to practice his guitar for 1.75 hours each morning and 2.5 hours each evening for the first 4 days this week. How ma
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Step-by-step explanation:

From the above question,

Anthony is practicing 4 days in a week

Hence

The number of hours he practices in the morning for 4 days =

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den301095 [7]

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

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2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

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3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

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Answer:

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