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Juli2301 [7.4K]
3 years ago
6

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th

e left of the line is shaded.
Which linear inequality is represented by the graph?

Mathematics
2 answers:
Grace [21]3 years ago
6 1

Answer:

the correct answer is y>2x+(3/4) and (2,5)

hope this helps

(p.s:Please mark me as brainlyest)

Step-by-step explanation:

I just took the test on E2020

miss Akunina [59]3 years ago
4 0

Answer:

y> \frac{2}{3}x+3

Step-by-step explanation:

we have the points

(-3,1) and (0,3)

step 1

Find the slope m of the line

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{3-1}{0+3}

m=\frac{2}{3}

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{2}{3}

b=3 ----> the y-intercept is the point (0,3)

substitute the values

y=\frac{2}{3}x+3

step 3

Find the equation of the inequality

we know that

The slope is positive

Everything to the left of the line is shaded ( The inequality is of the form y > ax+b or y ≥ ax+b)

Is a dashed line (The inequality is of the form y > ax+ b or y < ax+b)

therefore

The equation of the inequality is of the form y > ax+b

The inequality is

y> \frac{2}{3}x+3

see the attached figure to better understand the problem

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Find the midpoint of the segment with the following endpoints.<br> (8,5) and (0, -1)
Karo-lina-s [1.5K]

Answer:

(4,2)

Step-by-step explanation:

Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)

6 0
3 years ago
A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen
noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

n = 5, p = 0.93

Calculate P(at least one valve opens).

This is P(X \geq 1)

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

So

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

P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807

Finally

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193

There is a 99.99998% probability that at least one valve opens.

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3 years ago
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Sqrt(pow(width,2) + pow(length ,2)
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