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timurjin [86]
1 year ago
10

On a coordinates plane, a line passes through ( - 2 , 3 ) and ( 2 , 6 ). Which of the followings lies on the same line.

Mathematics
1 answer:
Dahasolnce [82]1 year ago
4 0

By direct comparison and definition of <em>line</em> segment  we notice that the point (x, y) = (- 6, 0) lies on the <em>line</em> segment <u>AB</u> as each <u>AP</u> is a multiple of former. (Correct choice: C)

<h3>What point lies on a line segment?</h3>

According to linear algebra, a point lies in a <em>line</em> segment if its vector is a multiple of the vector that generates the <em>line</em> segment itself, that is:

<u>AB</u> = k · <u>AP</u>        (1)

The vector that generates the <em>line</em> segment is:

<u>AB</u> = (2, 6) - (- 2, 3)

<u>AB</u> = (4, 3)

And the vectors related to each point are:

Case A

<u>AP</u> = (- 2, 12) - (- 2, 3)

<u>AP</u> = (0, 9)

Case B

<u>AP</u> = (6, 12) - (- 2, 3)

<u>AP</u> = (8, 9)

Case C

<u>AP</u> = (- 6, 0) - (- 2, 3)

<u>AP</u> = (- 4, - 3)

Case D

<u>AP</u> = (- 6, 6) - (- 2, 3)

<u>AP</u> = (- 4, 3)

By direct comparison and definition of <em>line</em> segment  we notice that the point (x, y) = (- 6, 0) lies on the <em>line</em> segment <u>AB</u> as each <u>AP</u> is a multiple of former. (Correct choice: C)

To learn more more on line segments: brainly.com/question/25727583

#SPJ1

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-13x=90-2y <br> -6x=48-2y
Kisachek [45]

While it's pretty obvious to most of us that


-13x=90-2y

-6x=48-2y


is a system of linear equations, it'd be well to include that info plus the instructions "solve this system of linear equations."


Subtract the 2nd equation from the first:


-13x=90-2y

+6x=-48+2y

-----------------------

-7x = 42. Then x = -42/7, or x = 6.


Now subst. 6 for x in either one of the given equations. Suppose we use the 2nd equation:


-6x=48-2y


Then -6(6)=48-2y, or -36 = 48 - 2y, or 2y = 48+ 36 = 84. Then y = 42.


The solution is (6, 42).

3 0
2 years ago
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 9 sin(xy), (0, 8)
malfutka [58]

Answer:

The magnitude is  \Delta f(0,8)  =  72

The  direction  is  i i.e toward the x-axis

Step-by-step explanation:

From the question we are told that

   The function is  f(x, y) =  9sin(xy) \ \ \

    The point considered is  (0,8 )

Generally the maximum rate of change of f at the given point and the direction is mathematically represented as

            \Delta f(x,y) =  [\frac{\delta  f(x,y)}{\delta x } i + \frac{\delta  f(x,y)}{\delta y } j  ]

             \Delta f(x,y) =  [\frac{\delta  (9sin(xy))}{\delta x} i  + \frac{\delta  (9sin(xy))}{\delta y} i   ]

            \Delta f(x,y) = [9y cos (x,y) i +  9xcos (x,y) j]

At  (0,8 )

            \Delta  f (0,8) =  [9(8) cos(0* 8)i  + 9(8) sin(0* 8)j  ]

            \Delta  f (0,8) = 72 i

3 0
2 years ago
3 increased by the product of 4 and a number is equal to the same number decreased by 6. What is the number
nasty-shy [4]

Answer:

1

Step-by-step explanation:


8 0
3 years ago
Suppose that the waiting time for an elevator at a local shopping mall is uniformly distributed from 0 to 90 seconds.
Nady [450]

Answer:

1/3

Step-by-step explanation:

60-90 is 30 numbers, right? So it is 30/90, or 1/3

7 0
3 years ago
Please help! 10 points, thank you
Tpy6a [65]

Answer:

261.5 ft^2

Step-by-step explanation:

Surface Area of a rectangular prism = Length x Width x Height

= 8.5ft x 6ft x 5.5ft

= 261.5 ft

5 0
3 years ago
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