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Elden [556K]
3 years ago
12

Is RS perpendicular to DF? Select Yes or No for each statement. R (6, −2), S (−1, 8), D (−1, 11), and F (11 ,4) R (1, 3), S (4,7

), D (3, 9), and F (15, 0) R (−5, −5), S (0, 2), D (8, 3), and F (1, 8)

Mathematics
1 answer:
guajiro [1.7K]3 years ago
3 0

I'll do the first one to get you started.  

Find the slope of the line between R (6,-2) and S (-1,8) to get

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

m = (8-(-2))/(-1-6)

m = (8+2)/(-1-6)

m = 10/(-7)

m = -10/7

The slope of line RS is -10/7

Next, we find the slope of line DF

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

m = (4-11)/(11-(-1))

m = (4-11)/(11+1)

m = -7/12

From here, we multiply the two slope values

(slope of RS)*(slope of DF) = (-10/7)*(-7/12)

(slope of RS)*(slope of DF) = (-10*(-7))/(7*12)

(slope of RS)*(slope of DF) = 10/12

(slope of RS)*(slope of DF) = 5/6

Because the result is not -1, this means we do not have perpendicular lines here. Any pair of perpendicular lines always has their slopes multiply to -1. This is assuming neither line is vertical.

I'll let you do the two other ones. Let me know what you get so I can check your work.

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5 0
3 years ago
The average marks of the first 10 students are 17 and that of the next 15 students is 18. find the mean of 25 students?
Ray Of Light [21]

Answer:

The mean of 25 students is 17.6

Step-by-step explanation:

The formula of the mean (average) is mean (average) = \frac{S}{N} , where S is the sum of the data, and N is the number of the data

∵ The average marks of the first 10 students are 17

- That means the mean is 17 and the number of students is 10

∴ Average = 17

∴ N = 10

∵ Average = \frac{S}{N}

- Substitute average by 17 and N by 10

∴ 17 = \frac{S}{10}

- Multiply both sides by 10

∴ 170 = S

∴ The sum of the marks of the first 10 students is 170

∵ The average of the next 15 students is 18

∴ Average = 18

∴ N = 15

- Substitute average by 18 and N by 15

∴ 18 = \frac{S}{15}

- Multiply both sides by 15

∴ 270 = S

∴ The sum of the marks of the next 15 students is 270

Now to find the mean of 25 students and the two sums and divide the answer by 25

∵ S = 170 + 270

∴ S = 440

∵ N = 25

∴ Mean = \frac{440}{25}

∴ Mean = 17.6

The mean of 25 students is 17.6

3 0
3 years ago
A line passing through which of the following pairs of coordinates represents a proportional relationship? A. (1, 3) and (2, 6)
trasher [3.6K]

Answer:

Answer is A - (1, 3) and (2, 6)

Step-by-step explanation:

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= (1 • 2, 3 • 2)

= (2, 6)

Ratio: 2/2, 6/2

Therefore, the answer is A.  

3 0
3 years ago
Read 2 more answers
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