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3 years ago

Which Graph shows a system of equations with a solution at (2,-1)

Mathematics

2 answers:

zimovet [89]3 years ago

8 0

The one with the U shape going up, and the red line is tilting to the left that last picture

hjlf3 years ago

3 0

Answer:

its the 4 one with the parabola facing down and red line going through the y intercept -3

Step-by-step explanation:

a solution is the point of interception between 2 lines

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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

Find angles a, b and c? Please help.

laiz [17]

Answer:

B=112 degrees A=68 degrees and C=68 degrees

Step-by-step explanation:

the opposite angle of the 112-degree angle is the angle on the top left of the page, this means both of the angles are the same. You can then tell that that angle is the same as the one across from it because it shows on the page. You can then figure out the opposite angle which is B so that means angle B is equal to 112 degrees. To figure out angle A you can just do 180 minus the angle B which is 112 degrees. You now know angle A which is 68 degrees, now to find the angle C you just have to notise that angle C is the opposite angle of angle A. This means that algle C is also 68 degrees.

8 0

3 years ago

Read 2 more answers

Someone please help

Anna71 [15]

9514 1404 393

Answer:

622

Step-by-step explanation:

The n-th term of an arithmetic sequence is given by the formula ...

an = a1 +d(n -1)

where a1 is the first term (6), and d is the common difference (14-6=8).

Then the 78th term is ...

a78 = 6 + 8(78 -1) = 6 + 616 = 622

The 78th term is 622.

5 0

3 years ago

If m angle 3 = 73 degrees, m angle FDE. What does this mean? It’s question #7. And how do I do it?

nadezda [96]

Answer:

Step-by-step explanation:

8 0

4 years ago

Is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same populati

olganol [36]

The distribution of the values obtained from a simple random sample of size n from the same population is incorrect.

<h3>What is sampling distribution?</h3>

The sampling distribution of a statistic of size n is the distribution of the values obtained from a simple random sample of size n from the same population.

The sampling distribution is the process of getting a sample through simple random techniques from the sample population.

So, it is incorrect that the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

Learn more about sampling distribution here:

brainly.com/question/3663642

#SPJ1

8 0

2 years ago