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Triss [41]
4 years ago
10

Given: quadrilateral ABCD inscribed in a circle Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary

Mathematics
1 answer:
kari74 [83]4 years ago
8 0

Answer:

Step-by-step explanation:

Given that quadrilateral ABCD inscribed in a circle

We have angle A and C are lying on either side of the centre.

If O is the centre, we get

AOC will be 2A (as per subtended arc theorem)

Similarly AOC major arc would be 2C

Since 2A+2C = 360(angle around a point)

dividing by 2, we get A+C =180

Or A and C are supplementary

Similarly we can prove B and D are supplementary.

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Give two examples that show how using parentheses can change the order in which operations are performed in an expression
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Yes, parentheses can change the order in which operations are performed in an expression.

Let us understand this with two examples.

First example.

Let us suppose we have to simplify the expression

2\cdot (5-3)\\
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In this expression we have evaluated subtraction first instead of multiply.

Second example.

Let us suppose we have to simplify the expression

(5\cdot 2)- 3\\
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Therefore, from above two examples we can see that  parentheses can change the order in which operations are performed in an expression.

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Find the 17 th term of each sequence. a₁₆ = 1/5, d= 1/2
Dmitry [639]

7/10 is 17th term of sequence a₁₆ = 1/5, d= 1/2.

Given the 16th term and the common difference, we add the common difference from the 16th term to determine the 17th term:

a₁₇ =  a₁₆ + d

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<h3>How to solve an equation?</h3>

To solve linear equations, utilize the steps that are provided below.

  1. Remove parentheses from each side of the equation and combine similar terms to make it simpler.
  2. To separate the variable term on one side of the equation, use addition or subtraction.
  3. To find the variable, use division or multiplication.
  4. The common denominator can be multiplied by each side of the equation to eliminate fractions.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

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