217 ÷ 19 with remainder

Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable

Let us use the elimination method with your problem

∵ 3x + 2y = 4 ⇒ (1)

∵ 3x + 6y = -24 ⇒ (2)

- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs

∵ -3x - 2y = -4 ⇒ (3)

- Add equations (2) and (3)

∴ 4y = -28

- Divide both sides by 4

∴ y = -7

Substitute value of y in equations (1) OR (2) to find x

∵ 3x + 2(-7) = 4

∴ 3x - 14 = 4

- Add 14 for both sides

∴ 3x = 18

- Divide both sides by 3

∴ x = 6

The solution of the system of equations is (6 , -7)

<em>I hope this explanation help you</em>

Learn more:

You can learn more about the system of linear equations in brainly.com/question/6075514

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3 0

3 years ago

According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System i

lozanna [386]

Answer:

a

The null hypothesis is $H_o : \mu = 32.48$

The alternative hypothesis is $H_a : \mu < 32.48$

b

$t = -1.504$

c

There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

Step-by-step explanation:

From the question we are told that

The mean price of is $\mu = \$ 32.48$

The sample size is n = 56

The sample mean is $\= x = \$30.15$

The standard deviation is $\sigma = \$12$

The null hypothesis is $H_o : \mu = 32.48$

The alternative hypothesis is $H_a : \mu < 32.48$

Generally the test statistic is mathematically represented as

$t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }$

=> $t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }$

=> $t = -1.504$

Generally the p-value is mathematically represented as

$p-value = P (t < -1.504 )$

From the z-table

$P(t < -1.504) = 0.066291$

So

$p-value = 0.066291$

From the value we obtain we see that

$p -value > \alpha$

Then we fail to reject the null hypothesis

Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48

3 0

3 years ago

217 ÷ 19 with remainder​

217 ÷ 19 with remainder