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2 years ago

What is the solution of the system? 5x + 2y = 9 4x - 3y = 44

Mathematics

1 answer:

Lady bird [3.3K]2 years ago

6 0

Hello!

$\large\boxed{5, -8}$

5x + 2y = 9

4x - 3y = 44

We can eliminate y by multiplying both expressions in order to have the y coefficients equal.

The LCM (least common multiple) of 2 and 3 is 6, so we can multiply each accordingly:

3(5x + 2y = 9)

2(4x - 3y = 44)

Distribute:

15x + 6y = 27

8x - 6y = 88

Cancel using addition:

15x + 6y = 27

8x - 6y = 88

------------------

23x = 115

Divide:

x = 5.

Plug in this value of x into an equation to solve for y:

5(5) + 2y = 9

25 + 2y = 9

2y = -16

y = -8

The solution of the system is:

(5, -8).

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3 years ago

Read 2 more answers

Mitch has a swimming pool in his backyard. The rectangular swimming pool has a volume of 243 m cubed. The length of the pool is

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81 $m^{3}$

Step-by-step explanation:

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2 years ago

g Use the information below for questions 1 through 5. A San Francisco-based tech firm is able to keep 80% of its new employees

meriva

Answer:

0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they survive the first year, or they do not. The probability of an employee surviving the first year is independent of other employees. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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This means that $p = 0.8$

Q1. What is the chance that two randomly sampled new employees will both be able to survive their first year

This is P(X = 2) when n = 2. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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0.64 = 64% probability that two randomly sampled new employees will both be able to survive their first year

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2 years ago