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mrs_skeptik [129]
3 years ago
7

The product of two consecutive even integers is 2208. What is their sum?

Mathematics
1 answer:
Katena32 [7]3 years ago
6 0

Answer:

±94

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

  • Standard Form: ax² + bx + c = 0
  • Solving Quadratic Equations
  • Consecutive Integers

Step-by-step explanation:

<u>Step 1: Define</u>

<em>x</em>  (1st consecutive term)

<em>x + 2</em> (2nd consecutive term)

<u>Step 2: Set up equation</u>

x(x + 2) = 2208

<u>Step 3: Solve for </u><em><u>x</u></em>

  1. Distribute <em>x</em>:                                   x² + 2x = 2208
  2. Rewrite in Standard Form:           x² + 2x - 2208 = 0
  3. Factor quadratic:                          (x - 46)(x + 48) = 0
  4. Find roots:                                     x = -48, 46

<u>Step 4: Identify Consecutive Integers</u>

<em>Possibility 1: x = -48</em>

1st Consecutive Even Term: -48

2nd Consecutive Even Term: -48 + 2 = -46

<em />

<em>Possibility 2: x = 46</em>

1st Consecutive Even Term: 46

2nd Consecutive Even Term: 46 + 2 = 48

<u>Step 5: Find sums</u>

<em>Possibility 1: x = -48</em>

-48 + -46 = -94

<em>Possibility 2: x = 46</em>

46 + 48 = 94

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3х - 30 = у<br> 7y - 6 = 3х
mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3<em>x</em> – 30 = <em>y</em>  and the second is 7<em>y</em> – 6 = 3<em>x</em>

As I look, I see 3 ways to use substitution to solve this:

  1. substitute 7<em>y</em> – 6 for 3<em>x</em>
  2. substitute 3<em>x</em> – 30 for <em>y</em>
  3. solve 3<em>x</em> – 30 = <em>y</em> for 3<em>x</em> and make it equal to 7<em>y</em> – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

<u>Method 1</u>:

3<em>x</em> – 30 = <em>y</em>

7<em>y</em> – 6 = 3<em>x</em>  — initial system of equations

7<em>y</em> – 6 – 30 = <em>y</em>  — substitute 7<em>y</em> – 6 for 3<em>x</em>

<u>7</u><u><em>y</em></u> – 6 – 30 = <u><em>y</em></u>  — marking like terms, bold for constants, <u>underlined</u> for variables

7<em>y</em> – 36 = <em>y</em>  — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract <em>y</em> from both sides, divide by 6 OR subtract 7<em>y</em> from both sides and divide by –6 . For the sake of time, I'm subtracting 7<em>y</em>, though I don't like dealing with negatives.

7<em>y</em> – 7<em>y</em> – 36 = <em>y</em> – 7<em>y</em>  — subtract 7<em>y</em> from both sides

–36 = –6<em>y</em>  — simplify

–36 ÷ –6 = –6<em>y</em> ÷ –6  — divide by –6 on both sides

<em>y</em> = 6  — simplify

Again, we can diverge here: substitute <em>y</em> into 3<em>x</em> – 30 = <em>y</em> or substitute <em>y</em> into 7<em>y</em> – 6 = 3<em>x</em>

I'm going to choose 3<em>x</em> – 30 = <em>y</em> but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3<em>x</em> – 30 = <em>y</em>  — initial equation

3<em>x</em> – 30 = 6  — substitute 6 for <em>y</em>

3<em>x</em> – 30 + 30 = 6 + 30  — add 30 to both sides to isolate 3<em>x</em>

3<em>x</em> = 36  — simplify the expression

3<em>x</em> ÷ 3 = 36 ÷ 3  — divide both sides by 3 to isolate <em>x</em>

<em>x</em> = 12  — simplify

So, we have <em>x</em> = 12 and <em>y</em> = 6 . We know they work for 3<em>x</em> – 30 = <em>y</em>  but not if they work for 7<em>y</em> – 6 = 3<em>x</em> . Let's substitute those in to see if (12, 6) really is the solution point.

7<em>y</em> – 6 = 3<em>x</em>  — original equation

7(6) – 6 ≟ 3(12)  — substitute 6 for <em>y</em> and 12 for <em>x</em>

42 – 6 ≟ 36  — simplify by multiplying

36 = 36 ✔  — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0
3 years ago
Can a triangle be drawn with side lengths 8.4 inches, 9.2 inches, and 17 inches?
sasho [114]

Answer:

yes

Step-by-step explanation:

based on the triangle inequality theorem, add the two smallest numbers together (8.4,9.2) to get 17.6 which is bigger than 17

3 0
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2(6 – x) – (9x + 2) = 4 + 8(x – 4)
Crank

Answer:

1.526

Step-by-step explanation:

12-2x-9x-2 = 4+8x-32

-11x+10 = 8x-28

-19x = -29

x = 1.526

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What is the answer to this question with work I need it ASAS
PtichkaEL [24]

The answer is 7 3/4 inches.

I noticed the word "train" in the problem and I knew I had to help you! :)

6 0
2 years ago
What is the length of DE?
Andrew [12]

Answer:

The length of DE is 5 because they are similar triangle .

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