Model the unknown number situation by writing an algebraic expression.

HELP A line passes through two points with coordinates (6,-8) and (-3,7).

FromTheMoon [43]

Answer:

Step-by-step explanation:

<u>Equation of the Line</u>

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the points (6,-8) and (-3,7), thus:

$\displaystyle y+8=\frac{7+8}{-3-6}(x-6)$

$\displaystyle y+8=\frac{15}{-9}(x-6)$

Simplifying:

$\displaystyle y+8=-\frac{5}{3}(x-6)$

Multiplying by 3:

$3(y+8)=-5(x-6)$

$3y+24=-5x+30$

Moving all the variables to the left side:

3y + 5x = 30 - 24

3y + 5x = 6

4 0

2 years ago

Why it is not possible for two lines to be parallel and perpendicular?

max2010maxim [7]

Parallel lines have the same slope. for example, the two lines y = 6x + 3 and
y = 6x - 5 are parallel because they have the same slope, 6x.

the slopes of perpendicular lines are opposite reciprocals, which means that you would flip the numbers of the fraction and make it negative. for example, the opposite reciprocal of -3x is 1/3x.

also, parallel lines never intersect, whereas perpendicular lines intersect at a 90 degree angle.

therefore, it isnt possible for two lines to be both parallel and perpendicular.

7 0

2 years ago

The probability of rain on the last day of July is 95 % . If the probability remains constant for the first seven days of August

8090 [49]

The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516

<h3>The probability that it rains at most 2 days</h3>

The given parameters are:

Number of days, n = 7
Probability that it rains, p = 95%
Number of days it rains, x = 2 (at most)

The probability that it rains at most 2 days is represented as:

P(x ≤ 2) = P(0) + P(1) + P(2)

Each probability is calculated as:

$P(x) = ^nC_x * p^x * (1 - p)^{n - x}$

So, we have:

$P(0) = ^7C_0 * (92\%)^0 * (1 - 92\%)^{7 - 0} = 0.00000002097$

$P(1) = ^7C_1 * (92\%)^1 * (1 - 92\%)^{7 - 1} = 0.00000168821$

$P(2) = ^7C_2 * (92\%)^2 * (1 - 92\%)^{7 - 2} = 0.00005824315$

So, we have:

P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315

P(x ≤ 2) = 0.00005995233

Hence, the probability that it rains at most 2 days is 0.00005995233

This is calculated as:

Mean = np

So, we have:

Mean = 7 * 92%

Evaluate

Mean = 6.44

Hence, the mean is 6.44

<h3>The standard deviation</h3>

This is calculated as:

σ = √np(1 - p)

So, we have:

σ = √7 * 92%(1 - 92%)

Evaluate

σ = 0.718

Hence, the standard deviation is 0.718

<h3>The variance</h3>

We have:

σ = 0.718

Square both sides

σ² = 0.718²

Evaluate

σ² = 0.516

This represents the variance

Hence, the variance is 0.516

Read more about normal distribution at:

brainly.com/question/4079902

#SPJ1

7 0

1 year ago

It took gigi 1 hour and 20 minutes to complete a bicycle race It took Johnny twice as long because he got a flat tire. How many

Brrunno [24]

180 minutes, also 2 hours and 40 minutes

8 0

3 years ago

The first 32 whole numbers are evenly spaced around the circumference of a circle. Which number will be opposite of 26?

Ludmilka [50]

Answer:

"10"

Step-by-step explanation:

This is rather thinking "pictorially". Picture it.

You can match it with a round clock that has numbers 1 - 12 written on it.

So,

32 and 16 would be opposite of each other [top and bottom]. And, 1 - 15 would be on right side and 17 - 31 would be on left side.

Now,

Going counter-clockwise from 32, 26 would be the 6th number. Going counter-clockwise from 16, 10 would be the 6th number.

Hence, they would be opposite of each other.

10 would be opposite of 26

6 0

3 years ago