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4 years ago

The sum of 5 consecutive integers is 110, what is the fourth number in this sequence?

Mathematics

1 answer:

Xelga [282]4 years ago

5 0

The answer is: " 23 " .

→ The fourth number in the sequence is: " 23 " .

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Explanation:

To solve:

" x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

in which:

"x" = The first number in these sequence;

"(x + 1 )" = the second number in the sequence;

"(x + 2)" = the third number in the sequence;

"(x + 3)" = the fourth number in the sequence;

"(x + 4)" = the fifth number in the sequence;

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Solve for the "fourth number in the sequence" ; or: "(x + 3)" ;

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Given: " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

↔ " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;

→ Solve for "x" ;

→ then, solve for "(x + 3)" ;

→ which is the fourth number in this sequence;

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→ " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;

"5x + 1 + 2 + 3 + 4= 110 " ;

" 5x + 10 = 110 " ;

Solve for "x" :

Subtract "10" from EACH SIDE of the equation; as follows:

" 5x + 10 - 10 = 110 - 10 " ;

to get :

" 5x = 100 " ;

Now, divide EACH SIDE of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" ; as follows:

5x / 5 = 100 / 5 ;

to get:

" x = 20 " .

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Now, to find the fourth number in the sequence:

→ " (x + 3) " ;

→ Substitute "20" for "x" ;

" x + 3 = 20 + 3 = 23" ;

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The answer is: " 23 " .

The fourth number in the sequence is: " 23 " .

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Let us check our work:

If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then: "24" is the "fifth number" .

As such: "22" is the "third number" ; "21" is the "second number" ; and "20" is the "first number" . Is this consistent with: "x = 20" as the "first number" ? Yes!

Thus, "20 + 21 + 22 + 23 + 25 = ? 110 ? ? ;

→ 20 + 21 = 41 ;

→ 41 + 22 = 63 ;

→ 63 + 23 = 86 ;

→ 86 + 24 = 110 . Yes!

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Hope this answer is helpful!

Best wishes in your academic pursuits—

and within the "Brainly" community!

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Fantom [35]

Answer:

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$y = 3 - 6 \sin {}^{} (2x + \frac{\pi}{2} )$

Standard Form of Sinusoid is

$y = - 6 \sin(2x + \frac{\pi}{2} ) + 3$

Which corresponds to

$y = a \sin(b(x + c)) + d$

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

$y = - 6(2(x + \frac{\pi}{4} )) + 3$

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

$\frac{2\pi}{ |b| }$

$\frac{2\pi}{ |2| } = \pi$

So the period is pi radians.

b. Amplitude is

$| - 6| = 6$

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that rule, our range is [6+3, -6+3]= [9,-3] So our range is [-3,9].

D. Plug in 0 for x.

$3 - 6 \sin((2(0) + \frac{\pi}{2} )$