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zhuklara [117]
3 years ago
12

The Oxy coordinate plane for two parallel lines a and a' has the equations 2x - 3y-1 = 0 and 2x - 3y + 5 = 0. respectively. Whic

h vector translation to convert a to a'
Mathematics
1 answer:
Andru [333]3 years ago
7 0

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x,  (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x,  (2/3)*x - 1/3) = (x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

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jeyben [28]

Answer:

Step-by-step explanation:

As x = 0 is a zero, (x + 0) is a factor.

Dividing the equation by (x + 0) leaves x² - 9x + 20.

Factoring this polynomial

x² - 9x + 20 = (x - 4)(x - 5)

x - 4 = 0

x = 4

x - 5 = 0

x = 5

The zeros are at 0, 4, and 5.

Which can be verified by using a plotting calculator.

3 0
2 years ago
Read 2 more answers
Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (-7,3) and (-8,-9).
Illusion [34]

Answer:

  12x -y = -87

Step-by-step explanation:

You can start with the 2-point form of the equation of a line and manipulate it to give you the standard form.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (-9 -3)/(-8 -(-7))(x -(-7)) +3

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  y = 12x +84 +3

  -12x +y = 87 . . . . . subtract the x-term

  12x -y = -87 . . . . . . make the leading coefficient positive (per standard form)

3 0
3 years ago
Our of the four runners: Alex, Ben, Curtis, and Dan, the oldest came in second place. Alex ran the distance faster than Curtis,
Alexus [3.1K]

Considering the situation described, the classification of the runners is given as follows:

Dan - Ben - Alex - Curtis.

<h3>What is the classification of the runners?</h3>

The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.

Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:

Dan - Ben - Alex - Curtis.

A similar problem, in which a situation is interpreted, is given at brainly.com/question/5660603

#SPJ1

5 0
1 year ago
How can I solve this?
jok3333 [9.3K]

The 3 inside angles need to equal 180 degrees.

Angle K is given as 48 degrees.

Angle M would be 90 degrees.

Angle J = 180 - 90 - 48 = 42

Angle J = 42 degrees

3 0
2 years ago
Find the distance between the two points to the nearest tenth. (0,-5) and (-4,2) 5 5.3 5.2 5.6
zubka84 [21]
Sqr (x2 - x1)^2 + (y2 - y1)^2
Sqr (-4-0)^2 + (2+5)^2
Sqr (16) + 49 = sqr 65
I got around 8.
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7 0
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