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3 years ago

What coordinate pair is the solution for the given system? Equation 1: 4x ? 2y = 4 Equation 2: 2x + y = 6

Mathematics

1 answer:

Mars2501 [29]3 years ago

4 0

Answer: The answer is (2, 2).

Step-by-step explanation: The given system of equations is

$4x-2y=4,\\\\2x+y=6.$

We are to find the co-ordinate pair that is the solution for the above system of equation.

Multiplying the second equation by 2 and adding to the first equation, we have

$4x+4x=4+12\\\\\Rightarrow 8x=16\\\\\Rightarrow x=2,$

and

$y=6-2\times 2=6-4=2.$

Thus, the co-ordinate pair is (2, 2).

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3 years ago

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter

Digiron [165]

Answer:

at least 5

Step-by-step explanation:

If the question was similar to the one given below

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

The answer would be as follows

If we use 3 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get

4C2= 6 ways to use these letters and the comma

If we use 4 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get

5C2= 10 ways to use these letters and the comma

If we use 5 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get

6C2= 15 ways to use these letters and the comma

We need the least number of the alphabets to assign codes to 12 participants.

So the least number of alphabets is 5 because it can give codes to at least to 12 people .

Pair of alphabets + distinct letter ≥ 12

5 + 1 ≥ 12

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3 0

3 years ago

Take your time! :) Not important, but I would like to know, I'm writing flashcards so I can remember when I start back in school

Sav [38]

Answer:

The LCM of two numbers is the least common multiple. You want to find the least possible number that is divisible by the two numbers. So, you can list the factors of the two numbers. If there are factors that are repeated, put the repeated factors to the side. With the remaining factors, multiply the factors by each other and the repeated factors.

For example, let's try to find the least common multiple between 10 and 15.

Factors of 10: 2 * 5

Factors of 15: 3 * 5

The repeated factor is 5.

2 and 3 are left over. 2 * 3 = 6. 6 * 5 = 30. So, that is the least common multiple.

The GCF of two numbers is the greatest common factor. You want to find the greatest factor that is included in both numbers. So, again, you can list the factors of the two numbers and find the greatest factor that is repeated between the two numbers.

For example, let's try to find the greatest common factor between 30 and 45.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 45: 1, 3, 5, 9, 15, 45

Between the two numbers, shared factors are 1, 3, 5, and 15. So, the greatest common factor is 15.

Hope this helps!

5 0

4 years ago