The difference of the squares of two positive consecutive even integers is 84. Find the integers.

Answers

Answer 1

Answer:

The two integers are 20 and 22.

Step-by-step explanation:

Let x be the first integer.

[tex](x+2)^{2}-x^{2} = 84\\x^{2} +4x+4-x^{2} = 84\\4x = 80\\x = 20[/tex]

Answer 2

Applying the difference of squares, and solving the equation, it is found that the numbers are 20 and 22.

----------------------

The two consecutive even integers are: n and n + 2.The difference of the squares is given by:

[tex]D_s = (n+2)^2 - n^2[/tex]

Expanding the difference:

[tex]D_s = n^2 + 4n + 4 - n^2[/tex]

[tex]D_s = 4n + 4[/tex]

----------------------

The difference is 84, thus:

[tex]D_s = 84[/tex]

Now, we solve for n.

[tex]4n + 4 = 84[/tex]

[tex]4n = 80[/tex]

[tex]n = \frac{80}{4}[/tex]

[tex]n = 20[/tex]

----------------------

Thus, the numbers are: [tex]n = 20[/tex] and [tex]n + 2 = 20 + 2 = 22[/tex]

A similar problem is given at https://brainly.com/question/5453470


Related Questions

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Answers

the standard form is 4.19•10^-3

What is the value of x?
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Answers

Answer:

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Step-by-step explanation:

So add +2 both sides that cancels 2 and that makes it -11.00 now divide it by -5 and x is by itself

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Step-by-step explanation:

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I’m pretty sure it would look something like this.

FREE 100 POINT GIVEAWAY PLS READ DOWN BELOW TO ENTER(YOU CAN ENTER IN THE COMMENTS TOO)
I'm going to be doing two random question (you can only answer each once) and ill post the giveaway so you can get your points- if the answer box is full then u can answer in the comment section too this time you must get both question right;)

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Answers

Answer:

I think like 16.9 fluid ounces

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Step-by-step explanation:

Answer:

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4x^2-21x-18=0
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Answers

a = 4, b = -21, c = -18

to keep from getting "mixed up", evaluate the discriminant first ...

b<sup>2</sup> - 4ac = (-21)<sup>2</sup> - 4(4)(-18) = 729

sqrt(729) = 27

x = (21 +/- 27)/8

x = -3/4, x = 6

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(4x + 3)(x - 6) = 0

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Answer:

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Step-by-step explanation:

b/c it is 6 wanted amount out of 13 total amount

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Answers

Answer:

A -19

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Step-by-step explanation:

Answer:

1.= -19 2. -35  3. -180    4.  -81

Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Since 180 is double 90 divide 45 by 2 and you'll get 24.5

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Answer 4^2+4=20 Explanation x^2+x=? so 4^2(4x4=16)+ 4 = 20

Y0UR M0MWY 100KS L1KE TH1$

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Answer:

I'm confused to what this means

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Answer:

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Step-by-step explanation:

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A line that crosses others in the same plane might be referred to as a transversal. The most common usage of this term is in cases where the crossed lines are parallel or nearly so.

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Answers

Answer: $9.20

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Answer:

$1.20

Step-by-step explanation:

He has to leave 100% of the cost which is $5.50 + 2.50 or $8.00.

He wants to leave 115% of the $8 he has to leave.

So you set it up like

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Then you solve for x

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So he will leave $9.20.

It then asks for just how much the tip is that he will leave so

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3

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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gil borrows $8000 for college expenses. he will pay a total of $2280 back in interest after 6 years. what was his interest rate

Answers

Answer:

R = 41.8129%/year

Equation:

r = (1/t)(A/P - 1)

Calculation:

Solving our equation:

r = (1/6)((8000/2280) - 1) = 0.41812865

r = 0.41812865

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Step-by-step explanation:

Answer:

I believe it is 4.75 %

Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation: took the quiz

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A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.

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