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3 years ago

What is the value of x? A.54 B.–16 C.126 D.16

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

8 0

Since the angles are vertical they are also congruent. Therefore x equals 16

sergij07 [2.7K]3 years ago

6 0

Answer: Choice D) 16

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Work Shown:

The two angles are vertical angles. They are congruent or equal in measure.

8x - 2 = 7x + 14
8x - 2+2 = 7x + 14+2 ... add 2 to both sides
8x = 7x + 16
8x - 7x = 7x + 16 - 7x ... subtract 7x from both sides
x = 16

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how many ways are there to win the jackpot? how many ways are there to match 5 of 6 numbers? how many ways are there to match 4

musickatia [10]

The number of ways to match 5 of 6 numbers is 6 ways

The number of ways to match 4 of 6 numbers is 15 ways

The number of ways to match 3 of 6 numbers is 20 ways

To calculate number of ways to match 5 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C5=\frac{6!}{(6-5)! . 5!}$

$6C5=\frac{6!}{(1)! . 5!}$

$6C5=\frac{6.5.4.3.2.1}{1.5.4.3.2.1}$

$6C5=\frac{6}{1}$

$6C5= 6 \ ways$

∴ 6 ways are to match 5 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C4=\frac{6!}{(6-4)! . 4!}$

$6C4=\frac{6!}{(2)! . 4!}$

$6C4=\frac{6.5.4.3.2.1}{2.1.4.3.2.1}$

$6C4=\frac{30}{2}$

$6C4= 15 \ ways$

∴ 15 ways are to match 4 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

$nCr =\frac{n!}{(n - r)! . r !}$

$6C3=\frac{6!}{(6-3)! . 3!}$

$6C3=\frac{6!}{(3)! . 3!}$

$6C3=\frac{6.5.4.3.2.1}{3.2.1.3.2.1}$

$6C3=\frac{120}{6}$

$6C3= 20 \ ways$

∴ 20 ways are to match 3 of 6 numbers

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