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3 years ago

18/90 in simplest form

2 answers:

7 0

18/90
Divide by the common factor of 18 and 90, 9.
(18/9) / (90/9)
2/10
Divide top and bottom by 2

1/5

Hope this helps :)

Nitella [24]3 years ago

6 0

1/5 because if you divide 18/90 by 2 it is 9/45 thn divide by 9 its 1/5

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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1 year ago

A building is 2ft from a 7 ft fence that surrounds the property. A worker wants to wash a window in the building 11ft from the g

777dan777 [17]

Answer:

Step-by-step explanation:

plug the numbers into the Pythagorean theorem

which is A^2 + B^2 = C^2

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2 years ago

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A cat rescue service found homes for 40 cats in 5 weeks. What was the rate of cats being placed per week? Which ratio is equal t

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A. 8 cats per week. if you simplify 40/5, it equals 8/1

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Terri owns a computer repair shop. Her revenue at the end of last month was $8,000. What is Terri's Run Rate?

Ilia_Sergeevich [38]

Based on the information given Terri's Run Rate is $96,000.

Using this formula

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Where:

Revenue for the Period =$8,000

Number of months in a year=12 months

Let plug in the formula

Run rate=$8,000×12 months

Run rate=$96,000

Inconclusion Terri's Run Rate is $96,000.

Learn more about run rate here:brainly.com/question/16134508

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2 years ago

What is the length of the hypotenuse of the triangle when x = 7? 5x +4 4x

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Answer:

48.01

Step-by-step explanation:

5(7)+4= 39

4(7)=28

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√2305 = 48.01

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