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Volgvan
2 years ago
7

Solve the following: 3x + 7 = 5x - 1 X =

Mathematics
1 answer:
dexar [7]2 years ago
7 0

Answer:

x= 4

Step-by-step explanation:

3x + 7 = 5x - 1

combine the like numbers: add 1 to the other side, isolating 5x

3x + 8 = 5x

Subtract 3x from 5x, isolating 8

8 = 2x

divide

4 = x

Check if it works

3(4) + 7 = 5(4) - 1

19 = 19

Yes, it is correct

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<h3><u>We are given:</u></h3>

The initial points:             T(2 , 3)      U(5, 4)       V(2, 0)

The transformed points: T'(-1, 2)       U'(2,3)          V'(-1, -1)

<h3><u>Identifying the Transformation rule:</u></h3>

Since all these points will follow the same rule, we will take a pair of initial and transformed points and compare them

T(2, 3) → T'(-1, 2)

We can see that these points are not reflected across the y-axis

<u>Checking if they have a dilation of 0.25 about the origin:</u>

Dilation of 0.25 about the origin basically means if the Initial x and y coordinates are multiplied by 0.25 to form the transformed points

So, if the points have a dilation of 0.25:

x (initial) * 0.25 = x(final)

2*0.25 = -1

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Hence, there is no dilution of 0.25

<u>Checking if the given points are translated:</u>

To check this, we will take 2 pairs of initial and transformed points

T(2,3) →  T'(-1,2)

U(5,4) → U'(2,3)

To check if there is transformation, we need to check if the difference between the x and y coordinates of initial and transformed points is equal

<u>Change in coordinates of T:</u>

x-coordinates:

x(final) - x(initial) = x(change)

x(change) = -1 - (2)

x(change) = -3

y-coordinates:

y(change) = y(final) - y(initial)

y(change) = 2 - (3)

y(change) = -1

<u>Change in coordinates of U:</u>

x-coordinates:

x(change) = x(final) - x(initial)

x(change) = 2 - 5

x(change) = -3

y-coordinates:

y(change) = y(final) - y(initial)

y(change) = 3 - 4

y(change) = -1

Since there is the same change in x and y coordinates of the initial and transformed points, we know that Translation took place

Since the change in x is -3 and the change in y is -1, the translation will look like:

(x-3 , y-1)

Which is also option d.

Hence, option d is the correct answer

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3 years ago
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Answer:

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