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Vikentia [17]
3 years ago
6

When x = 2,what is the value of y for the equation – 3x + 2y = 10?

Mathematics
2 answers:
dexar [7]3 years ago
8 0

Answer:

\huge{ \boxed{ \bold{ \tt{y = 8}}}}

☪ What is the value of y for the equation given below when x = 2 ?

  • -3x + 2y = 10

☪ Step - by - step explanation :

  • \sf{ - 3x + 2y = 10}

plug the value of x ( i.e 2 )

➳ \sf{ - 3 \times 2 + 2y = 10}

Remember : Multiplying or dividing a negative integer by a positive integer gives a negative integer.

➳ \sf{ - 6 + 2y = 10}

Move 6 to right hand side and change it's sign

➳ \sf{2y = 10 + 6}

Add the numbers : 10 and 6

➳ \sf{2y = 16}

Divide both sides by 2

➳ \sf{ \frac{2y}{2}  =  \frac{16}{2}}

➳ \boxed{ \sf{y = 8}}

——————————————————

✏ Now, let's check whether the value of y is 8 or not !

✑ Verification :

\sf{ - 3x + 2y = 10}

→ \sf{ - 3 \times 2 + 2 \times 8 = 10}

→ \sf{ - 6 + 16 = 10}

→ \sf{10 = 10}

L.H.S = R.H.S ( Hence , the value of y is 8 . )

——————————————————

☞ Additional Info :

✒ Sign rules of addition and subtraction of integers:

  • The positive integers are always added and posses the positive ( + ) sign.
  • The negative integers are always added but posses the negative ( - ) sign.
  • The negative and positive integers are always subtracted but posses the sign of the bigger integer.

✒ Sign rules of multiplication and division of integers :

  • Multiplying or dividing positive integers gives a positive integer.
  • Multiplying or dividing positive integer by any negative integer gives a negative integer.
  • Multiplying or dividing a negative integer by a positive integer gives a negative integer.
  • Multiplying or dividing a negative integer by a negative integer gives a positive integer.

✒ Rules for solving an equation :

  • If any equation contains fractions , multiply each term by the LCM of denominators.
  • Remove the brackets , if any.
  • Collect the term with the variable to the left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '.
  • Simplify and get the single term on each side.
  • Divide each side by the coefficient of variable and then get the value of variable.

Hope I helped!

Have a wonderful time ツ

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Cerrena [4.2K]3 years ago
6 0

Answer:

y=x+5

Step-by-step explanation:

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Answer:

(a) See Explanation

(b) \bar x =50 and \sigma_x = 0.8944

(c) The shape is normal

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Step-by-step explanation:

Given

\mu = \$50 -- mean

\sigma = \$20 --- standard deviation

n=500 --- sample size

Solving (a): The reason we can't determine the probability that an amount to access internet by a household will exceed $55.

The question says that a lot of households pay low rates, but the percentage of the households in this category is not given. This means that it is impossible to determine the shape of the distribution.

Hence, the probability cannot be calculated.

Solving (b): Sample mean and Sample standard deviation

The sample mean estimates the population mean

So:

\bar x =\mu

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The sample standard deviation is calculated as thus:

\sigma_x = \frac{\sigma}{\sqrt n}

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\sigma_x = \frac{20}{22.36}

\sigma_x = 0.8944

Solving (c): The shape of the distribution.

We have:

n = 500 --- The sample size

According to Central limit theorem, When the sample size is greater than 30, then the shape of the distribution is normal.

<em>Hence, the shape is normal</em>

Solving (d): P(\bar x \ge 55)

Calculate the test statistic (t)

t = \frac{\bar x - \mu}{\sigma}

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So:

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Referencing the z table, we have:

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