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3 years ago

Find the equation of the line between the points (10, – 5) and ( - 2,0).

Mathematics

1 answer:

Natali5045456 [20]3 years ago

3 0

Answer <u>(assuming it can be in slope-intercept form)</u>:

$y = -\frac{5}{12} x-\frac{5}{6}$

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}$

Thus, the slope of the line is $-\frac{5}{12}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute values for $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{12}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

$y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}$

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Principal Philippi use a random sample of 20 student records to determine how far in miles students live from the school the res

nexus9112 [7]

Take 3 4 5 3 4 5 6 5 4 3 2 3 4 5 6 4 8 4 3 2 and add them all together

=83

Now you divide 83 by the number of terms in the sample set, which is 20.

83/20 = 4.15

For rounding to the nearest tenth, look at the hundredths space, which is 5. Since it is 5 or higher, round the tenths up one.

final answer= 4.2

6 0

3 years ago

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Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that comput

Andrej [43]

Answer:

a)There is a 4.88% probability that none is concerned that employers are monitoring phone calls.

b)There is a 7.89% probability that all are concerned that employers are monitoring phone calls.

c)There is a 37.23% probability that exactly two are concerned that employers are monitoring phone calls.

Step-by-step explanation:

The binomial probability is the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).

It is given by the following formula:

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

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 a success.

In this problem, a success is being concerned that employers are monitoring phone calls.

53% of adults are concerned that employers are monitoring phone calls, so $p = 0.53$

(a) Out of four adults, none is concerned that employers are monitoring phone calls.

Four adults, so $n = 4$ .

Is the probability of 0 successes, so x = 0.

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

$P = C_{4,0}.(0.53)^{0}.(0.47)^{4}$

$P = 0.0488$

There is a 4.88% probability that none is concerned that employers are monitoring phone calls.

(b) Out of four adults, all are concerned that employers are monitoring phone calls.

Four adults, so $n = 4$ .

Is the probability of 4 successes, so x = 4.

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

$P = C_{4,0}.(0.53)^{4}.(0.47)^{0}$

$P = 0.0789$

There is a 7.89% probability that all are concerned that employers are monitoring phone calls.

(c) Out of four adults, exactly two are concerned that employers are monitoring phone calls.

Four adults, so $n = 4$ .

Is the probability of 4 successes, so x = 2.

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

$P = C_{4,2}.(0.53)^{2}.(0.47)^{2}$

$P = 0.3723$

There is a 37.23% probability that exactly two are concerned that employers are monitoring phone calls.

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3 years ago

The distance between two points is 6_/6.One endpoint is (4,-1). It is known that the y-coordinate of the other endpoint is 9.

babunello [35]

The x-coordinate of the given endpoint will be " $x = 4 \pm 2\sqrt{29}$ ".

According to the question,

The end points are:

$(x_1,y_1) = (4,-1)$
$(x_2, y_2) = (x,9)$

Distance,

$6\sqrt{6}$

As we know,

The distance formula,

→ $Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

By substituting the values, we get

→ $6\sqrt{6} = \sqrt{(x-4)^2+(9+1)^2}$

→ $216= (x-4)^2+100$

→ $(x-4)^2 = 116$

→ $x-4 = \pm \sqrt{116}$

→ $x-4=\pm 2\sqrt{29}$

→ $x = 4 \pm 2\sqrt{29}$

Thus the above answer is right.

Learn more:

brainly.com/question/18310956

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2 years ago

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Dafna1 [17]

Formula for the Conditional Probability is:
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3 years ago

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