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3 years ago

Which statement about the point (2,0) is true?

Mathematics

1 answer:

Maru [420]3 years ago

6 0

Answer:

It is on the x - axis

Step-by-step explanation:

Point (2, 0) lie on the x axis

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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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8 0

2 years ago

jamal calculated that it costs $0.43 per mile and $4.00 per day to operate his car. if jamal drive m miles over d days , which e

DaniilM [7]

Answer:

c = 4(d) + .43(m)

Step-by-step explanation:

We can test this by plugging in numbers for each of the variables. Let's say Jamal drove 5 miles over 2 days.

c = 4(2) + .43(5)

c = 8 + 2.15

c = $10.15

Have a nice day!

4 0

3 years ago

Through: (-1,-1), perp. to x=0

andriy [413]

Answer: negative 1 minus another negitive 1 give you zero/X

Step-by-step explanation:

7 0

4 years ago

Find the midpoint of the segment with these endpoint (4,6),(9,3)

Usimov [2.4K]

Answer:

The midpoint of the segment is (6, 4.5).

Step-by-step explanation:

Midpoint of a segment:

The midpoint of a segment is given by the mean of the coordinates of their endpoints.

Segment with coordinates (3,6) and (9,3).

Mean x-coordinate: (3+9)/2 = 12/2 = 6

Mean y-coordinate: (6+3)/2 = 9/2 = 4.5

The midpoint of the segment is (6, 4.5).

7 0

3 years ago

Is my answer correct?

Yanka [14]

I would have used graph b. Because it shows the decrease more than graph a.

8 0

3 years ago