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Sophie [7]
2 years ago
12

A positive integer squared plus 3 times it’s consecutive integer is equal to 43

Mathematics
2 answers:
Jobisdone [24]2 years ago
5 0

Answer:

5

Step-by-step explanation:

let positive integer be x

x² + 3(x+1)=43

x²+3x+3-43=0

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x+8) - 5(x+8)=0

(x-5)(x+8)=0

x-5=0 or x+8=0

x=5. or x=-8

but the question says positive integer,

therefore, x=5

Eduardwww [97]2 years ago
3 0

Answer:

the integer is 5

Step-by-step explanation:

x^2+3(x+1)=43

x^2+3x+3=43

x^2+3x+(9/4)=43-3+(9/4)

(x+(3/2))^2=42 1/4

x+(3/2)=sqrt(42 1/4)

x+(3/2)=6 1/2

x=(6 1/2)-(3/2)

x=5

check:

5^2+3(6)=43

25+18=43

43=43

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Answer: 12,972,960

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Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways

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The 3rd has a choice among 12 ways

The 4th has a choice among 11 ways

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The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways

But the 3 (that formed one group) could seat among themselves in 3!

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5 0
3 years ago
The diagram shows a sector of a circle radius 10cm
Yuki888 [10]

Answer:

\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}

Step-by-step explanation:

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\text{Radius = 10 cm}

\text{Perimeter of the sector = 10 + arc length + 10  }

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\text{arc length   = (sector angle/ 360 ) * perimeter of the circle}

\text{Perimeter of a circle }=2\pi r

\text{sector angle} = 135

\text{arc length}   =  (135/ 360 ) * 2\pi (10)

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\text{Using  }\pi =3.14

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\text{Perimeter of the sector = 20  + 23.55}

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\text{perimeter of the sector  = 43.6  cm }

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