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3 years ago

What is 4x+3x like terms

Mathematics

2 answers:

nasty-shy [4]3 years ago

6 0

Answer:

Step-by-step explanation:

4x+3x=7x

since both 3 and 4 have the same variable then they could be combined together to get 7x

lapo4ka [179]3 years ago

4 0

Answer:

Step-by-step explanation:

The 4x and the 3x are like terms because they both have a variable of x

Hope this helped

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CAN SOMEONE HELP!!!!

Arisa [49]

Answer:

x int is where the line crosses the x axis. direct variation is proportional, straight line that goes through the origin. slope is the rate of change. y int is where the line crosses the y axis

8 0

3 years ago

Some scientists say, happiness, when measured on a scale of 0 (super unhappy) to 100 (super happy), is a function of the number

ololo11 [35]

Answer:

f(x) = 60-2x

Step-by-step explanation:

Suppose that f(x) = y is a happiness function. It is a function of the number of hours you spend on Instagram per day. That means that the output of the function will be a "happiness score",i.e. the value between 0 and 100, and the variable x will be an output value, the hours spent on Instagram daily.

We know that if we spend 0 hours on Instagram per day the happiness score will be 60, which means that:

f(0) = 60

If we spend 1 hour per day on Instagram our level of happiness will be decreased by 2, i.e. 60-2 = 58. Therefore,

f(1) = 58

If we spend 2 hours on Instagram per day our level of happiness will be decreased even more, i.e. 58-2 = 56. Therefore,

f(2) = 56

Notice that 56 = 60-4 = 60-2*2

If we spend 3 hours on Instagram per day our level of happiness will be decreased even more, i.e. 56-2 = 54. Therefore,

f(3) = 54

Notice that 54 = 60-6 = 60-3*2

Now we can see the pattern from which the level of happiness can be calculated. It is 60 decreased by the number of hours multiplied by 2.

Hence, the "happiness function" is:

f(x) = 60-x*2 = 60-2x, where x is a number of hours spent on Instagram.

7 0

3 years ago

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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2 years ago

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Answer:

TRUE

FALSE

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Step-by-step explanation:

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Step-by-step explanation:

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