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SOVA2 [1]
3 years ago
6

If the sum of six consecutive even integers is 390 what is the smallest of the six integers

Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0
The answer is 60 but im going to explain it down below if you want to know how to do it :)

first because we dont know the values of the 6 numbers we have to lay it out like this.
x
x+2
x+4
x+6
x+8
x+10
-------- (then we add it together)
6x+30 = 390 (the sum of the 6 numbers)

using this equation we find out what x is 

so we do 390-30 to find what 6x is, which is 360
because now we know that 6x=360, we divide 360 by 6 to find out what x is
360 divided by 6 =60..... x = 60

so now we know that the smallest integer is 60
to check the answer we could add the 6 numbers which are:
60+62+64+66+68+70=390 :)

so the smallest integer is 60

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Find the missing lengths: LK=15 and KH=9, find KI and HI.
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Answer:

KI=11.25 and HI=6.75

Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

base^2+perpendicular^2=hypotenuse^2

Use Pythagoras in triangle HKL

LH^2+KH^2=LK^2

(LH)^2+9^2=15^2

(LH)^2+81=225

(LH)^2=144

Taking square root on both sides.

LH=12

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

(KI)^2+15^2=(12+x)^2

(KI)^2+225=x^2+24x+144

(KI)^2=x^2+24x+144-225

(KI)^2=x^2+24x-81...(1)

Use Pythagoras theorem in ΔHKI,

(KI)^2=x^2+9^2

(KI)^2=x^2+81...(2)

From (1) and (2) we get

x^2+81=x^2+24x-81

24x=162

x=\dfrac{162}{24}=6.75

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

(KI)^2=(6.75)^2+81

(KI)^2=126.5625

Taking square root on both sides.

KI=\sqrt{126.5625}

KI=11.25

Hence, the measure of KI is 11.25 units.

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Step-by-step explanation:

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A rectangular lawn is 2 m longer than it is wide.
PtichkaEL [24]

Let's breadth be x

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ATQ

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\\ \sf\longmapsto 4x^2+8x=84

\\ \sf\longmapsto (2x)^2+2(2x)(2)=84

\\ \sf\longmapsto (2x)^2+2(2x)(2)+2^2=2^2+84

\\ \sf\longmapsto (2x+2)^2=88

\\ \sf\longmapsto 2x+2=\pm\sqrt{88}

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\\ \sf\longmapsto 2x+2\approx 9.7

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Now

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\\ \sf\longmapsto Perimeter=19.2m

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\\ \sf\longmapsto \dfrac{19.2}{13}

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hypotenuse =

\sqrt{a {}^{2} + b {}^{2}  }

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