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zimovet [89]
3 years ago
11

Q8 Q3.) Solve the system by the substitution method.

Mathematics
1 answer:
inn [45]3 years ago
3 0
Recall that (x+y)^2=x^2+2xy+y^2. So we can add twice the first equation to the second one to get

x^2+y^2+2xy=10+2\cdot3\iff(x+y)^2=16\implies x+y=\pm4

Since xy=3, we have y=\dfrac3x (x\neq0) so

x+y=x+\dfrac3x=\pm4\implies x^2\mp4x+3=0

If x+y=4, then

x^2-4x+3=(x-3)(x-1)=0\implies x=3,x=1\implies y=1,y=3

If x+y=-4, then

x^2+4x+3=(x+1)(x+3)=0\implies x=-1,x=-3\implies y=-3,y=-1

So the solution set is

(x,y)\in\{(-3,1),(1,3),(-1,-3),(-3,-1)\}
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Help please which expression could NOT be used to find the quotiend of 1,377 and 9
topjm [15]

Answer:

C

Step-by-step explanation:


7 0
2 years ago
Find x and IJ is HK is an altitude of triangle HIJ
ss7ja [257]
3x+3=90
subtract 3 from both sides
3x=87
divide both sides by 3
x=29

To find IJ, plug in the x value
x+8+x-9
29+8+29-9
57=IJ
4 0
2 years ago
There are 3 3/4 cookies. if there is 1/4 of a cookie in each bag, how many bags are there?
Svetlanka [38]

Answer:

15 bags

Step-by-step explanation:

3 = 12/4

3 3/4 = 3+3/4 = 12/4 + 3/4 = (12+3)/4 = 15/4

(15/4) ÷ (1/4) = 15

5 0
2 years ago
Consider the following hypothesis test:
Gnom [1K]

Answer:

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

H_0: \mu\leq50\\\\H_a:\mu> 50

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22

The null hypothesis is rejected, as z>zc and falls in the rejection region.

8 0
3 years ago
Please help!!<br> Picture shown!
Anestetic [448]

Answer:

3x - 6y = -12

x - 2y = -8

3x - 6y = -12

-3x +6y= 24

no solutions

inconsistent

5 0
2 years ago
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