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34kurt
3 years ago
14

The sum of 6 consecutive even number is 126. what is the fourth number in the sequence

Mathematics
1 answer:
bulgar [2K]3 years ago
5 0

let's start off by keeping in mind that, if you multiply any integer by 2, regardless of what that integer is, you will always get an EVEN integer, say 13 * 2 = 26, or 18 * 2 = 36 and so on.

let' see a few consecutive even integers

2, 4, 6, 8, 10, 12 , 14..............

notice, to get another one from any of them, we can simply hop back or forwards twice, namely  8 ± 2, gives us 6 and 10.

so let's use for our first even integer say "2a".

that simply means our next even integer can just be 2a + 2

and we add 2 again and so on to get all 6 even integers.

now, we know they add sum up to 126.


\bf \stackrel{1st}{(2a)}+\stackrel{2nd}{(2a+2)}+\stackrel{3rd}{(2a+4)}+\stackrel{4th}{(2a+6)}+\stackrel{5th}{(2a+8)}+\stackrel{6th}{(2a+10)}~~=~~126
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
12a+30=126\implies 12a=96\implies a=\cfrac{96}{12}\implies \boxed{a=8}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\stackrel{4th}{2(8)+6}\implies 22

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if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles and the measure of angle 3 is 56 degree
dimulka [17.4K]

Answer:

34º

Step-by-step explanation: so basically you know a complementary angle is 2 angles that make a straight line and a vertical angle crosses which means 2 angles are congruent to each other so I drew a line that bisected the angle by drawing a line that cut through the right angle and i extended a line down from the right angle so now I have a vertical angle and a complementary so from here I labeled each angle <1 <2 <3  If I know angle 3 is 56º then I know 56 plus __ equals 90º I then subtracted 56 from 90 and I got 34 and since I am trying to figure out what angle 1 is I know that angle 1 and 2 are vertical angles therefore I know they are congruent to each other so <1 = 34º

6 0
3 years ago
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y + 1 = 0?
Bezzdna [24]

Answer:

The answer is

<h2>4x + y - 6 = 0</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

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y = - 4x - 1

Comparing with the above formula

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Since the lines are parallel their slope are also the same

That's

Slope of the parallel line is also - 4

Equation of the line using point ( 1 , 2) is

y - 2 = -4(x - 1)

y - 2 = - 4x + 4

4x + y - 2 - 4

We have the final answer as

<h3>4x + y - 6 = 0</h3>

Hope this helps you

7 0
3 years ago
Help me find the answer
solmaris [256]
I possibly think it is c that is what I got
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3 years ago
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loris [4]
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3 0
3 years ago
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I want the 17 <br> No the answer only the name of the fraction
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n is equal to 15 because 15 divided by 5 is 3. therefore, 3 = 15/5.

5 0
3 years ago
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