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2 years ago

The sum of two consecutive even integers is 186. What are the two numbers?

Mathematics

2 answers:

ozzi2 years ago

6 0

Answer: 92 and 94

Step-by-step explanation:

x = first number

x + 2 = second number

x + x + 2 = 186

simplify

2x + 2 = 186

subtract 2 from both sides

2x = 184

divide both sides by 2

x = 92

92 + 2 = 94

The numbers are 92 and 94.

andrew11 [14]2 years ago

5 0

Make sure you read through the problem carefully so that you recognize that we are dealing with consecutive even integers here.

Any 2 consecutive even integers can be represented as x + x + 2.

So we can represent our integers as follows.

X ⇒ first integer

X + 2 ⇒ second integer

Since their sum is 168, our equation reads x + x + 2 = 186.

Simplifying on the left side gives us 2x + 2 = 186.

Now subtract 2 from both sides to get 2x = 184.

Now divide both sides by 2 and we find that x = 92.

If x = 92, then x + 2 will be 92 + 2 or 94.

So our two consecutive integers are 92 and 94.

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If B is the midpoint of AC, AB=x+6 and AC=5x-6, then what is BC?

nikklg [1K]

If B is the midpoint of AC, then AB=BC. It is also BC=AC-AB

AB = x + 6

AC = 5x - 6

BC = (5x - 6) - (x + 6)

We can kinda use distributive property, like this:

BC = 5x - 6 -x - 6

Combine like terms:

BC = 4x - 12

To verify, we can add AB and BC to see if their sum is equal to AC.

(x + 6) + (4x - 12) = 5x - 6

If we are correct, this equation will be true.

x + 6 + 4x - 12 = 5x - 6

Combine like terms:

6 + 5x - 12 = 5x - 6

5x - 6 = 5x - 6

It's correct!

BC = 4x - 12. Final Answer.

Let me know if you have any questions about this! :)

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2 years ago

Jake completed a marathon race in 3 hours and 12 minutes. What would be Jake's running time as a decimal?

VikaD [51]

$\text{Given that Jake completed a marathon race in 3 hours and 12 minutes.}\\
\\
\text{we need to find this time in decimals. so we will convert 12 minutes into hours}\\
\\
\text{We know that there are 60 minutes in 1 hour. }\\
\\
\text{so in 1 minute there will be}=\frac{1}{60 }\text{ hour}$

$\text{hence in 12 minutes we have}=\frac{1}{60}\times 12=\frac{1}{5}=0.2 \text{ hours}\\
\\
\text{hence the Jake's running time is}=3\text{hours + 12 minute}\\
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=3\text{ hours}+0.2 \text{ hours}\\
\\
=3.2 \text{ hours}$

Hence, Jake's running time in decimal is: 3.2 hours

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2 years ago

The graphs of functions f(x) and g(x) = f(x) + k are shown below:

Nataly [62]

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gives us a slope equation of:
$m= \frac{4-0}{2-0}$ and the slope is 2. Using the point (0, 0) to write the equation of the line for f(x) looks like this in the slope-intercept form of the equation:
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Step-by-step explanation:

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