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2 years ago

4x-11y=68 ; 6x+5y=-27 by elimination

Mathematics

1 answer:

zimovet [89]2 years ago

4 0

Answer:

$x=\frac{1}{2}\\\\y=-6$

Step-by-step explanation:

Given the following system of equations:

$\left \{ {{4x-11y=68} \atop {6x+5y=-27}} \right.$

In order to solve the system of equations using the Elimination Method, you can follow these steps:

- Multiply the first equation by -6 and the secondd equation by 4.

- Add both equations.

- Solve for "y".

Then:

$\left \{ {{-24x+66y=-408} \atop {24x+20y=-108}} \right\\.........................\\86y=300\\\\y=\frac{-516}{86}\\\\y=-6$

- Substitute the value of "y" into one of the original equations and solve for "x":

$6x+5(-6)=-27\\\\6x=-27+30\\\\x=\frac{3}{6}\\\\x=\frac{1}{2}$

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Answer:

1. x = -4y ---> y = (-1/4)x

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2. y = -2x + 4

3. y = (1/3)x - 1

Step-by-step explanation:

1. Re-write your equation so that x is on the right and y is on the left:

x = -4y ---> y = (-1/4)x

slope = -1/4. y-intercept = (0,0)

2. y-intercept = (0,4) ----> P1

x-intercrpt = (2,0) ----> P2

slope m = (y2 - y1) / (x2 - x1)

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therefore, y - y1 = mx - x1 ---> y - 4 = -2x

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2 years ago

−7x−50≤−1 AND−6x+70>−2

fgiga [73]

Answer:

$-7\geq x$ and $[-7,12)$ in interval notation.

Step-by-step explanation:

We have been given a compound inequality $-7x-50\leq -1\text{ and }-6x+70>-2$ . We are supposed to find the solution of our given inequality.

First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.

$-7x-50\leq -1$

$-7x-50+50\leq -1+50$

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Dividing by negative number, flip the inequality sign:

$\frac{-7x}{-7}\geq \frac{49}{-7}$

$x\geq -7$

$-6x+70>-2$

$-6x+70-70>-2-70$

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Dividing by negative number, flip the inequality sign:

$\frac{-6x}{-6}$

$x$

Upon merging both intervals, we will get:

$-7\geq x$

Therefore, the solution for our given inequality would be $-7\geq x$ and $[-7,12)$ in interval notation.

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The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability tha

kozerog [31]

Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

$\mu = 3500 \times 0.0004 = 1.4$

The probability that 2 or fewer cars will be stolen is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466$

$P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452$

$P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417$

Then:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335$

0.8335 = 83.35% probability that 2 or fewer will be stolen.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ1

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1 year ago