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devlian [24]
3 years ago
9

what is the smallest of 3 consecutive positive integers if the product of smaller two interfere is 5 less than 5 times the large

r?
Mathematics
1 answer:
Lady_Fox [76]3 years ago
8 0

Answer:

Two options:

5,6, and 7

-1,0,and 1

Step-by-step explanation:

Three consecutive natural numbers can be represented as n, n+1, and n+2.

The product of the smaller two would be n(n+1). The less than 5 times the larger is 5(n+2)-5.

Set them equal and solve by factoring:

n(n+1) = 5(n+2) -5\\n^2+n = 5n+10 -5\\n^2+n = 5n+5\\n^2 -4n-5=0\\(n-5)(n+1)=0

Set each factor equal to 0.

n-5==0 so n=5.

n+1=0 so n=-1.

This means the 3 consecutive numbers would be 5,6, and 7

OR

-1, 0 or 1.

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3 years ago
Find the values of x and y
zhuklara [117]

You can use a tangent:

tangent=\dfrac{opposite}{adjacent}

We have opposite = 17 and adjacent = x.

\tan30^o=\dfrac{\sqrt3}{3}

substitute:

\dfrac{17}{x}=\dfrac{\sqrt3}{3}       cross multiply

x\sqrt3=(3)(17)     multiply both sides by √3

x(\sqrt3)(\sqrt3)=51\sqrt3

3x=51\sqrt3      divide both sides by 3

x=17\sqrt3

Use the Pythagorean theorem:

y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34

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Other method.

30^o-60^o-90^o triangle.

The sides are in the ratio 1:2:\sqrt3\to17:y:x

Therefore

17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3

 


4 0
3 years ago
Find the length between (1, 3) and (5, 6)
ipn [44]

Answer:

5

Step-by-step explanation:

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3 years ago
In △EKL, m∠K = 90º, m∠E = 25º, EK = 3 cm, KH - altitude. Find EH.
laiz [17]

Answer:

EH = 3.31

Step-by-step explanation:

We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.

Where,

EK = Base = 3

KH = perpendicular altitude

EH = Hypotenuse

m<K = 90

m<E = 25

We know that

cosθ = Base/ Hypotenuse

cos 25 = 3/ EH

EH = 3/cos25

EH = 3.31

Perpendicular alitutude can also be calculated by using the formula for tanθ.

3 0
2 years ago
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