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3 years ago

How do u solve this?

Mathematics

2 answers:

kolbaska11 [484]3 years ago

7 0

Answer:

You can solve this by substitution method

substitute the value of Y from 2nd equation in the first thet will give you the value of X and once your find the value of X you can substitute that value in any of the equation and get the answer

kompoz [17]3 years ago

6 0

Answer:

x = - 27/8 and

y = - 97/8

Step-by-step explanation:

3x-2=y

3x - 2 = 1/3x - 11

3x - 1/3x = -11 + 2

8/3x = - 9

x = (-9) / (8/3)

x = - 27/8

Substitution:

3(-27/8)- 2 = y

81/8 - 2 = y

y = - 97/8

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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

Trina had 50 eggs. After using some of her eggs to make 12 batches of brownies, she has 14 eggs remaining. How many eggs did Tri

Alexeev081 [22]

Step-by-step explanation:

eggs used : 50-12= 38 eggs

$\frac{38 \: eggs}{12 \: batches} = 3.1667eggs \: per \: batch$

8 0

3 years ago

9 ft 8 ft 5 ft 13 ft What is the area of this figure?

Vlad1618 [11]

Answer:

D. 98 ft.^2

Step-by-step explanation:

A= b*h

=13*8

=104 ft.^2

Because there is a piece missing, we know it must be under 104 ft.^2. They didn't give us enough information to find the complete area of the missing triangle, so I used the process of elimination. With the responses given and this information, we can assume that the answer is 98 ft.^2.

8 0

3 years ago

Geela makes orange paint with 5 parts yellow to

Oxana [17]

Answer:

Geela would need 9 yellow parts

Explanation:

Originally, the Geela needed more yellow than red and the difference was 4 parts.

6-2=4 parts

4 parts + 5 parts of yellow = 9 yellow parts.

3 0

3 years ago

Ella and kate play basketball last year ella scored 16 points per game kates total points for the season were 22 less than Ellis

KatRina [158]

Alright, lets get started.

Ella and kate played basketball last year.

In each game, Ella scored 16 points.

We have not given the number of games played.

So, lets suppose there are n games played last year.

So, total points of Ella will be = number of games * each game score

total points of Ella will be = n * 16 = 16 n

Kates total points for the season are 22 less than Elli's points

Means , Kates total points = 16 n - 22

This expression is similar with expression given 16 z - 22 (which is give in question)

It means z = n , means variable z means total games played in last year. : Answer

Hope it will help :)

4 0

3 years ago