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dimaraw [331]
3 years ago
11

Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment i

n the ratio of 5:3.
Mathematics
1 answer:
olga2289 [7]3 years ago
4 0

Answer:

B ( 5 , 3/4 )

Step-by-step explanation:

Solution:-

We are given two points in the cartesian coordinate system as:

                    A ( -5 , 2 )              C ( 11, 0 )

The point B lies on the line segment from A to C. The ratio of segment given is:

                               AB / BC = 5 / 3

To solve such type of problems. We will use vector equation of line AC.

To form a vector equation of line representing AC. We will first determine the direction vector ( d ) that is parallel to the line AC as follows:

                  d = OC - OA

                  d = < 11, 0 > - < -5,2 >

                  d = < 16 , -2 >

The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point C is expressed as:

                 < x , y > = OA + t*d

                 < x , y > = < -5, 2 > + t* < 16 , - 2 >  

The above equation satisfies all the points that lies on the line AC. To determine the coordinates of ( B ). We will plug in the appropriate value of parameter ( t ) and evaluate. We are given the ratio 5:3.

So point B is 5/8 th the magnitude of the distance AC from A. Hence, t = 5/8 as follows:

                < x , y > = < -5 , 2 > + ( 5/8 ) * < 16 , -2 >

                < x , y > = < -5 , 2 > + < 10 , -5/4 >

                < x , y > = < 5 , 3/4 >   ... Answer

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3 years ago
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Ksenya-84 [330]

I'll show you how to do one of the equations and one of the inequalities. All the others are done exactly in the same way: you'll only have to change the numbers, and it will be a good exercise.

Equations

Let's take the first equality as an example: we have

|x-2|=5

By definition, the absolute value of a number is the positive version of that number: if the number is already positive the absolute value doesn't change it; if a number is negative the absolute value changes its sign.

So, if the absolute value of a number is 5, than that number was already 5, or it was -5, and the absolute value changed it to positive 5.

So, the solutions are given by

|x-2|=5 \iff x-2=5 \lor x-2 = -5 \iff x=7 \lor x=-3

Inequalities

Again, we'll use the first one as example. We have

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By the same logic as before, the absolute value of a number is greater than 7 if the number is already greater than 7, or if it is smaller than -7. For example, we have |-10|=10>7.

So, we have

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Instead, if we have an inequality with the "less than" sign, we have for example

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4 0
3 years ago
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77julia77 [94]

Answer:

B

Step-by-step explanation:

This is quite a trial and error question.

Given from the table

$1 cost of item = $0.08 tax on item

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$10 cost of item = ($0.08x10) tax on item = $0.80 tax on item

The only one that is different is the incorrect value therefore $0.64 is the incorrect one.

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Dima020 [189]
I believe it’s 11>r/9. I may be wrong.
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kodGreya [7K]
26.38

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