4 years ago

Can someone plz help me https://brainly.com/question/20958557

Mathematics

1 answer:

Lunna [17]4 years ago

4 0

Answer:

I will do my best :)

Step-by-step explanation:

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Find two consecutive positive even integers such that the square of the first decreased by 64 equals 3 times the second.

IRINA_888 [86]

Answer:

10 and 12

Step-by-step explanation:

let the consecutive even integers be n and n + 2 , then

n² - 64 = 3(n + 2) ← distribute parenthesis

n² - 64 = 3n + 6 ( subtract 3n + 6 from both sides )

n² - 3n - 70 = 0 ← in standard form

(n - 10)(n + 7) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 7 = 0 ⇒ n = - 7

Since n must be a positive even integer then n = 10 and n + 2 = 10 + 2 = 12

The 2 numbers are 10 and 12

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3 years ago

How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half dollar, and a on

tekilochka [14]

Answer:

A person can select 3 coins from a box containing 6 different coins in 120 different ways.

Step-by-step explanation:

Total choices = n = 6

no. of selections to be made = r = 3

The order of selection of coins matter so we will use permutation here.

Using the formula of Permutation:

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

We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.

Order of coin is important means that if we select 3 coins in these two orders:

--> nickel - dime - quarter

--> dime - quarter - nickel

They will count as two different cases.

Calculating the no. of ways 3 coins can be selected from 6 coins.

nPr = $\frac{n!}{(n-r)!}$ = $\frac{6!}{(6-3)!}$

nPr = 120

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3 years ago