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2 years ago

Consider the following points on cartesian plane. A (1;2) BC3; 1) and CG-3; 4) prove that Points A, B and C are collinear.

Mathematics

1 answer:

Arlecino [84]2 years ago

5 0

Step-by-step explanation:

Collinear points have the same gradient

find the gradient(slope) between AB first

$= \frac{1 - 2}{3 - 1} \\ = \frac{ - 1}{2}$

Find the one for BC

$= \frac{4 - 1}{ - 3 - 3} \\ = \frac{3}{ - 6} \\ = \frac{ - 1}{2}$

Find the gradient between AC now

$= \frac{4 - 2}{ - 3 - 1} \\ = \frac{2}{ - 4} \\ = \frac{ - 1}{2}$

YOUR LAST STATEMENT NOW WILL BE

POINTS A,B AND C ARE COLLINEAR SINCE THE GRADIENTS BETWEEN THEM IS THE SAME!!!

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The perimeter of a Balcony is 26 ft it is 4 ft wide how long is it?

Dmitrij [34]

Answer:

30ft

Step-by-step explanation:

if you add 26 and 4, you'll get an answer of 40

8 0

3 years ago

The data below are the monthly average high temperatures for New York City. What is the five-number summary? 40, 40, 48, 61, 72,

yawa3891 [41]

Answer:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77

Step-by-step explanation:

The first step is to write the temperatures in crescent order:

40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84,

The sample minimum is the lowest value = 40

The sample maximum is the highest value = 84.

Since there are 12 numbers, the sample median is the average between the 6th and 7th terms:

$M = \frac{61+65}{2}\\ M=63$

The first quartile is the average between the 3rd and 4th terms:

$Q_1 = \frac{42+48}{2}\\ Q_1=45$

The third quartile is the average between the 9th and 10th terms:

$Q_3 = \frac{76+78}{2}\\ Q_3=77$

Therefore, the answer is:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77

8 0

3 years ago

Write an expression for the sequence of operations described below.

Murrr4er [49]

Answer:

8+s+n

Step-by-step explanation:

Add s to 8=8+s

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3 0

3 years ago

PLEEZZ

jonny [76]

4 < 4(6y - 12) - 2y |use distributive property

4 < (4)(6y) + (4)(-12) - 2y

4 < 24y - 48 - 2y |add 48 to both sides

52 < 26y |divide both sides by 26

2 < y → y > 2

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4x + 3 < 3x + 6 |subtract 3 from both sides

4x < 3x + 3 |subtract 3x from both sides

x < 3

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-5r + 6 ≤ -5(r + 2) |use distributive property

-5r + 6 ≤ (-5)(r) + (-5)(2)

-5r + 6 ≤ -5r - 10 |add 5r to both sides

6 ≤ -10 FALSE

No solution

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-2(6 + s) ≥ -15 - 2s |use distributive property

(-2)(6) + (-2)(s) ≥ -15 - 2s

-12 - 2s ≥ -15 - 2s |add 2s to both sides

-12 ≥ -15 TRUE

All real numbers

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3s + 6 ≤ -5(s + 2) |use distributive property

3s + 6 ≤ (-5)(s) + (-5)(2)

3s + 6 ≤ -5s - 10 |subtract 6 from both sides

3s ≤ -5s - 16 |add 5s to both sides

8s ≤ -16 |divide both sides by 8

s ≤ -2

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4/3 s - 3 ?

4 0

3 years ago

Find the volume for the regular pyramid. V =

mylen [45]

The volume is given by:
V = L * Apb * h
Where,
L: side of the base
Apb: apothema of the base
h: height
Substituting we have:
V = (4) * ((root (3) / 2) * 4) * (6)
Rewriting we have:
V = (4) * ((root (3) / 2) * 4) * (6)
V = 96 * (root (3) / 2)
V = 48 * root (3)
Answer:
V = 48 * root (3)

7 0

3 years ago

Read 2 more answers

Consider the following points on cartesian plane. A (1;2) BC3; 1) and CG-3; 4) prove that Points A, B and C are collinear. ​

Consider the following points on cartesian plane. A (1;2) BC3; 1) and CG-3; 4) prove that Points A, B and C are collinear.