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3 years ago

How to find it is related to the opposite angle in a cyclic quadrilateral is equal to 180 degeres

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

Answer: The measure of ∠BEF=110°.

Step-by-step explanation:

Given: In cyclic quadrilateral ABCD, ∠C = 110°

Then, ∠A+∠C=180° [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ ∠A+ 110°=180°

⇒ ∠A = 180° - 110°

⇒ ∠A = 70°

In cyclic quadrilateral ABEF,

∠A+∠E=180° [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ 70° + ∠E=180°

⇒∠E=110°

Hence, the measure of ∠BEF=110°.

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Evaluate the expressions. 8!-6!, 7!-5!, and 12!/8! BRAINLIST 5 min left plz hurry

nordsb [41]

Answer:

The evaluated expressions are $8!-6!=39600$ , $7!-5!=4920$ and $\frac{12!}{8!}=11880$

Step-by-step explanation:

The factorial of a positive integer n is the product of all positive integers less than or equal to n:

$n!=n\times (n-1)\times (n-2)\times (n-3)\times ...\times 3\times 2\times 1$

The factorial of n is denoted by n!

Now to find the expressions 8!-6!, 7!-5!, and 12!/8! :

Given expression is 8!-6!:

$8!-6!=[8\times (8-1)\times (8-2)\times (8-3)\times (8-4)\times (8-5)\times (8-6)\times (8-7)]- [6\times (6-1)\times (6-2)\times (6-3)\times (6-4)\times (6-5)]$ (By using factorial of n formula)

$=[8\times 7\times 6\times 5\times 4\times 3\times 2\times 1]- [6\times 5\times 4\times 3\times 2\times 1]$

$=[6\times 5\times 4\times 3\times 2\times 1][(8\times 7)-1]$

$=[720][56-1]$

$=[720][55]$

$=39600$

Therefore $8!-6!=39600$

Given expression is 7!-5! :

$7!-5!=[7\times (7-1)\times (7-2)\times (7-3)\times (7-4)\times (7-5)\times (7-6)]-[5\times (5-1)\times (5-2)\times (5-3)\times (5-4)]$ (By using factorial of n formula)

$=[7\times 6\times 5\times 4\times 3\times 2\times 1]- [5\times 4\times 3\times 2\times 1]$

$=[5\times 4\times 3\times 2\times 1][(7\times 6)-1]$

$=[120][42-1]$

$=[120][41]$

$=4920$

Therefore $7!-5!=4920$

Given expression is $\frac{12!}{8!}$

$\frac{12!}{8!}=\frac{12\times (12-1)\times (12-2)\times (12-3)\times (12-4)\times (12-5)\times (12-6)\times(12-7)\times (12-8)\times (12-9)\times (12-10) \times(12-11)}{8\times (8-1)\times (8-2)\times (8-3)\times (8-4)\times(8-5)\times (8-6)\times (8-7)}$ (By using factorial of n formula)

$=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times4\times 3\times 2\times 1}{8\times 7\times 6\times 5\times4\times 3\times 2\times 1}$

$=12\times 11\times 10\times 9$

$=11880$

Therefore $\frac{12!}{8!}=11880$

4 0

3 years ago

Please help me:( I've been stuck on this for so long

Contact [7]

Answer:\

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Step-by-step explanation:

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3 years ago

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Find the area of the figure

Pani-rosa [81]

Answer:

42.12cm²

Step-by-step explanation:

Firs well have to find the hypotenuse of the big and small right angled triangles because it is the length of the long and short diagonals which is needed in solving

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Using Pythagoras theorem

let the length be x

x²=10²+6²

x²=100+36

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x=√136

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Using Pythagoras theorem

let the length be y

y²=6²+4²

y²=36+16

y²=52

√y²=√52

y=√52

y=7.2

Now to find the total area of the shape which is a kite

Formula=

1/2 x D1 x D2

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$\frac{1}{2} \times 11.7 \times 7.2 \\ = \frac{11.7 \times 7.2}{2} \\ = \frac{84.24}{2} \\ = 42.12 {cm}^{2}$

<h2><em>OladipoSeun</em><em>♡˖꒰ᵕ༚ᵕ⑅꒱</em></h2>

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3 years ago

What is 1 1/3 + 5 1/6

jolli1 [7]

Answer:

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Step-by-step explanation:

11/3 + 5 1/6

change 5 1/6 into improper fraction (5 x 6 + 1) = 31/6

11/3 + 31/6

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3 goes into 6 two times therefore, 2 x 3 = 6 & 2 x 11 = 22

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Now change back to proper fraction. How many times does 6 go into 53?

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Hope this helps!

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3 years ago