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2 years ago

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

Mathematics

1 answer:

IRINA_888 [86]2 years ago

8 0

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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The dishwasher Marlin wants costs $720. This week only, the dishwasher is discounted by 25%. Marlin must pay 6% sales tax. Which

Mkey [24]

Answer:

C, both methods save the same amount of money

Step-by-step explanation:

First, we need to calculate what each answer choice will equal.

For A, it asks us to add the sales tax and then take the discount off. So, to find out what the sales tax is equal to, we multiply 720 x 0.06 (because 6% is equal to 0.06).

720 x 0.06 = 43.2

Add the sales tax to the original amount and you get 763.2.

Now we take the discount, which is 25% or 1/4.

1/4 of 763.2 is 190.8.

Subtract the discount from the price and you get 572.4.

For B, it says to take the discount first and then add the sales tax.

25% = 1/4, so 1/4 of 720 is equal to 180.

Subtract 180 from 720, and you get 540.

Now add the sales tax.

540 x 0.06 = 32.4.

540 + 32.4 = 572.4.

The answer is C, both methods save the same amount of money!

7 0

2 years ago

Simplify 2/3(30d-15) Can someone please explain distributive property with fractions?

Oksana_A [137]

Answer:

You do 2/3 times 30d minus 2/3 times 15. That will give you 20d - 10

Step-by-step explanation:

(2/3x30d) - (2/3x15) = 20d - 10

7 0

2 years ago

Can someone help me with part c?

Black_prince [1.1K]

I don't understand it sorry

5 0

2 years ago

The sum of two polynomials is -yz to the second power-3z to the second power-4y+4. If one of the polynomials is y-4yz to the sec

balu736 [363]

Answer:

- 5yz^2 - 3z^2 - 5y + 7

Step-by-step explanation:

The polynomial is:

$-yz^2-3z^2-4y+4$ ( 1 )

this polynomial is the result of the sum of two polynomials, one of them given by

$y-4yz^2-3$ ( 2 )

if you find to know what is the other polynomial, you can take the difference between the polynomial (1) and (2). It is necessary to take the difference between simmilar terms, as follow:

- yz^2 - 3z^2 - 4y + 4

- (4yz^2 + y - 3 )

- yz^2 - 3z^2 - 4y + 4

- 4yz^2 - y + 3

- 5yz^2 - 3z^2 - 5y + 7

hence the other polynomial is - 5yz^2 - 3z^2 - 5y + 7

5 0

3 years ago

Help please!?!?! Urgent ?!HELP!?

shtirl [24]

Answer:

key is 18

exit tag is 15

lock is 14

key*tag*lock = 3780

Step-by-step explanation:

54/3 is 18 so each key is 18

48-key = 30 so each tag is 15 since 15+15 = 30

18*15*14=3780

6 0

2 years ago