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Juliette [100K]
3 years ago
5

The system of equations shown below is graphed on a coordinate grid:

Mathematics
1 answer:
salantis [7]3 years ago
6 0

3y+x=4

2y-x=6

Solve x+3y=4 for x

Add -3y to both sides

x+3y-3y=4-3y

x=-3y+4

Substitute -3y+4 for x in -x+2y=6

-x+2y=6

-(-3y+4)+2y=6

Simplify both sides of the equation

5y-4=6

Add 4 to both sides

5y-4+4=6+4

5y=10

Divide both sides by 5

5y/5=10/5

y=2

Substitute 2 for y in x=-3y+4

x=-3y+4

x=(-3)(2)+4

x= -6+4

x= -2

Answer : x=-2 and y=2

The answer is A

 it is (-2,2) and lies on both lines


I hope that's help  !

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b) The critical values for this two-sided test are t=±1.711.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>(a) Identify the claim and state  H0  and  Ha. </em>

<em> Which is the correct claim​ below?</em>

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We have an hypothesis test on the difference of two means.

The null and alternative hypothesis are:

H_0: \mu_a-\mu_b=0\\\\H_a: \mu_a-\mu_b\neq 0

The claim of the alternative hypothesis is that the mean annual income is different in County A and County B.

The null hypothesis is that the mean annual income is equal in both counties.

The significance level is α=0.10.

The sample from County A has a mean of S40,400, a s.d. of $8,700 and a sample size of 18 residents.

The sample from County B has a mean of S39,200, a s.d. of $6,000 and a sample size of 8 residents.

The standard error of the difference of means is:

\sigma_d=\sqrt{\frac{\sigma_a^2}{n_a}+\frac{\sigma_b^2}{n_b}}=\sqrt{\frac{8700^2}{18}+\frac{6000^2}{8}}=\sqrt{8705000}=2950

The degrees of freedom are:

df=n_a+n_b-2=18+8-2=24

Then, the test statistic is:

t=\frac{\Delta M-\Delta \mu}{\sigma_d} =\frac{(40,400-39,200)-0}{2950} =\frac{1200}{2950}=0.407

For a statistic t=0.407, and df=24, the P-value is P=0.69. As the P-value is bigger than the significance level, the null hypothesis failed to be rejected.

If we would use the critial value approach, we would have to calculate the critical values for t, for df=24, two sided test and α=0.10.

The critical values, looking in a table, are t=1.711.

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