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fomenos
3 years ago
7

What is the solution of the system of linear equations? y = 3x - 2 y - 2 = x

Mathematics
1 answer:
iris [78.8K]3 years ago
6 0

Answer:

x = 2 y = 4

Step-by-step explanation:

y = 3x - 2

x = y - 2

Plug in the equation of x into the first equation and solve for y.

y = 3x - 2

y = 3(y - 2) - 2 Multiply out

y = 3y - 6 - 2

y = 3y - 8     Add 8 to each side

y + 8 = 3y - 8 + 8      8 cancels on the right

y + 8 = 3y          Subtract y from each side

y - y + 8 = 3y - y       The y on the left cancels

8 = 2y      Divide each side by 2

8/2 = 2y/2   2 on the right cancels because 2/2 = 1

8/2 = y

4 = y  

Now plug your answer into the 2nd equation given to solve for x.

x = y - 2

x = 4 - 2

x = 2

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Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (pop
creativ13 [48]

Answer:

Alternative hypothesis:\mu_1 -\mu_2 \neq 0

Or in the alternative way would be:

 Alternative hypothesis:\mu_1 \neq \mu_2

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "The means for the two groups (American Idol and 60 Minutes) is the same". So we want to check if we have significant differences between the two means, so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:\mu_1 -\mu_2 = 0

This null hypothesis can be expressed like this:

Null hypothesis:\mu_1 = \mu_2

Alternative hypothesis:\mu_1 -\mu_2 \neq 0

Or in the alternative way would be:

Alternative hypothesis:\mu_1 \neq \mu_2

4 0
3 years ago
X–2 1/2=6 3/4. X=?<br><br> x – 3.23 = 0.77. X=?
Over [174]

Answer:

x= 105/4

x=4

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Estimate the quotient to the tenths place. Then find the quotient. Round to the nearest thousandth 3)1.066 The estimate is The q
riadik2000 [5.3K]

Answer:

Estimate = 0.4

Quotient = 0.355 ---> Approximated to nearest thousandth

Step-by-step explanation:

Question like this is better answered using attachment;

See Attachment

When 1.066 is divided by 3,

The quotient is 0.3553......

When estimating to tenths,

We stop the quotient at 0.35 then round it up.

This gives 0.4

When estimating to nearest thousandth,

We stop the quotient at 0.3553 then round it up;

This gives 0.355

7 0
3 years ago
Find the largest positive integer that will divide 542, 436, 398 leaving reminders 7, 11, 15 respectively
saveliy_v [14]

Answer:

17

Step-by-step explanation:

Here in this question for finding the numbers that will divide 398, 436 and 542 leaving remainder 7, 11 and 15 respectively we have to first subtract the remainder of the following. By this step we find the highest common factor of the numbers.

And then the required number is the HCF of the following numbers that are formed when the remainder are subtracted from them.

Clearly, the required number is the HCF of the numbers 398−7=391,436−11=425, and, 542−15=527

We will find the HCF of 391, 425 and 527 by prime factorization method.

391=17×23425=52×17527=17×31

Hence, HCF of 391, 4250 and 527 is 17 because the greatest common factor from all the numbers is 17 only.

So we can say that the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.

Note: - whenever we face such a type of question the key concept for solving this question is whenever in the question it is asking about the largest number it divides. You should always think about the highest common factor i.e. HCF. we have to subtract remainder because you have to find a factor that means it should be perfectly divisible so to make divisible we subtract remainder. because remainder is the extra number so on subtracting remainder it becomes divisible.

8 0
3 years ago
What is the answer to -26-(-49)?
Radda [10]

Answer:

23

Step-by-step explanation:

-26-(-49)=-26+49=23

7 0
3 years ago
Read 2 more answers
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