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3 years ago

Solve the following system of equations 2x + y = 3 X = 2y - 1

Mathematics

1 answer:

pishuonlain [190]3 years ago

7 0

Answer:

x = 1 , y = 1

Step-by-step explanation:

Solve the following system:

{2 x + y = 3 | (equation 1)

x = 2 y - 1 | (equation 2)

Express the system in standard form:

{2 x + y = 3 | (equation 1)

x - 2 y = -1 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + y = 3 | (equation 1)

0 x - (5 y)/2 = (-5)/2 | (equation 2)

Multiply equation 2 by -2/5:

{2 x + y = 3 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract equation 2 from equation 1:

{2 x+0 y = 2 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 2:

{x+0 y = 1 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = 1 , y = 1

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3 years ago

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3 years ago

2) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen

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The mean of the discrete probability distribution is of 1.28.

<h3>What is the mean of a discrete distribution?</h3>

The expected value of a discrete distribution is given by the <u>sum of each outcome multiplied by it's respective probability</u>.

Then, considering the given distribution, the mean is given by:

E(X) = 0(0.13) + 1(0.61) + 2(0.15) + 3(0.07) + 4(0.04) = 1.28.

More can be learned about the mean of a discrete probability distribution at brainly.com/question/24855677

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2 years ago

a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.

spin [16.1K]

Answer:

$\huge\boxed{7.79 \ \text{feet}}$

Step-by-step explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

| \

x | \ 9

| \

|_____\

4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that $a^2+b^2=c^2$ , where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

$a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79$

Hope this helped!

7 0

3 years ago