Solve the equation of x+6-4x=3

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Mars2501 [29]

Answer:

Step-by-step explanation:

1) y = 2x ----------(I)

x + y = 6 -----------(II)

Plug in y =2x in equation (II)

x + 2x = 6 {Add like terms}

3x = 6

x = 6/3

x = 2

Plugin x = 2 in (I)

y = 2*2

y = 4

Check:

LHS = x +y

= 2 + 4

= 6 = RHS

2)5x + 10y = 3 ------------(I)

x = (-1/2) y ------------(II)

Substitute x = (-1/2)y in (I)

$5*\frac{-1}{2}y + 10y = 3\\\\\frac{-5}{2}y+ \frac{10*2}{1*2}y = 3\\\\\frac{-5}{2}y+\frac{20}{2}y=3\\\\\frac{-5+20}{2}y = 3\\\\\frac{15}{2}y=3\\\\ y = 3*\frac{2}{15}\\\\ y = \frac{2}{5}$

Substitute y = (2/5) in equation (II)

$x = \frac{-1}{2}*\frac{2}{5}\\\\x = \frac{-1}{5}$

Check:

Substitute x and y value in equation (I)

$LHS = 5*\frac{-1}{5}+10*\frac{2}{5}\\\\ = -1 + 2*2\\\\ = -1 + 4\\ = 3 = RHS$

3) y - x = 3x + 2

y = 3x + 2 + x

y = 4x + 2 ---------------(I)

2x + 2y = 14 - y

2x + 2y +y = 14

2x + 3y = 14 ------------------(II)

Substitute y = 4x + 2 in equation (II)

2x + 3(4x +2) = 14

2x + 3*4x + 3*2 = 14

2x + 12x + 6 = 14

14x + 6 = 14

14x = 14 - 6

14x = 8

x = 8/14

x = 4/7

Substitute 'x' value in (I)

$y = 4*\frac{4}{7} +2\\\\y = \frac{16}{7}+2\\\\y= \frac{16}{7}+\frac{2*7}{1*7}\\\\y=\frac{16}{7}+\frac{14}{7}\\\\y=\frac{30}{7}$

Check:

 $LHS = 2x + 3y\\\\ = 2*\frac{4}{7}+3*\frac{30}{7}\\\\ = \frac{8}{7}+\frac{90}{7}\\\\=\frac{8+90}{7}\\\\=\frac{98}{7}\\\\=14 = RHS$ 

6 0

3 years ago

What is a mean median and mode

Anarel [89]

Answer:

Mean, median, and mode are three kinds of "averages".

Step-by-step explanation:

Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so I'll add and then divide:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.

The median is the middle value, so first I'll have to rewrite the list in numerical order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

The mode is the number that is repeated more often than any other, so 13 is the mode.

The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15

median: 14

mode: 13

range: 8

4 0

3 years ago

What is the median of the data set 27, 36, 16, 31, 8

BabaBlast [244]

Hey!

----------------------------------------------------

Solution:

Median is the middle number in a data set.

~Arrange from least to greatest

27, 36, 16, 31, 8 → 8, 16, 27, 31, 36

~Find the median

8, 16, 27, 31, 36

----------------------------------------------------

Answer:

$\large\boxed{27~is~the~median!}$

----------------------------------------------------

Hope This Helped! Good Luck!

3 0

3 years ago

5/6-3/8=please help me

Yakvenalex [24]

$\frac{5}{6}-\frac{3}{8}=\\
\frac{20}{24}-\frac{9}{24}=\\
\frac{11}{24}$

8 0

4 years ago

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A. We are interested in determining wh

mafiozo [28]

Answer:

a. 1.44

Step-by-step explanation:

We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.

At the null hypothesis, it is tested if the proportion is of at most 40%, that is:

$H_0: p \leq 0.4$

At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:

$H_1: p > 0.4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that $p = 0.4, \sigma = \sqrt{0.4*0.6}$

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.

This means that:

$n = 200, X = \frac{90}{200} = 0.45$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}$

$z = 1.44$

Thus the correct answer is given by option a.

8 0

3 years ago