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Nat2105 [25]
2 years ago
15

Which type of transformation is described by (x, y) (x+2, y+3)

Mathematics
1 answer:
Readme [11.4K]2 years ago
3 0
This is a translation. It moves two to the right and three up.
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Step-by-step explanation:

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What is the product of (3x-9) and 6x^2-2x+5? Write your answer in standard form.
jolli1 [7]

Answer:

  • The product of 3x-9 and 6x^2-2x+5 is 18x^3 -60x^2 + 33x - 45
  • No, they are not equal

Step-by-step explanation:

a. Given

3x-9 and 6x^2-2x+5

Required

Product

The solution is as follows

First, put both expression in different brackets

(3x-9)(6x^2-2x+5)

Expand (6x^2-2x+5) bracket by (3x-9)

To do that. we first multiply (6x^2-2x+5) by 3x then by -9. This is done as follows

3x (6x^2-2x+5) - 9(6x^2-2x+5)

Now, we proceed to opening the bracket

(3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)

(18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)

Open both brackets

18x^3 -6x^2+ 15x -54x^2 + 18x -45

Collect like terms

18x^3 -6x^2 -54x^2 + 15x  + 18x -45

18x^3 -60x^2 + 33x - 45

Hence, the product of 3x-9 and 6x^2-2x+5 is 18x^3 -60x^2 + 33x - 45

b. Given

  • 3x-9 and 6x^2-2x+5
  • 9x-3 and 6x^2-2x+5

Required

Are their products equal?

To check if they are equal or not, we find the product of both and compare the solutions

We've already solved for 3x-9 and 6x^2-2x+5 in the (a) part of this exercise, so we move to the product of 9x-3 and 6x^2-2x+5

The solution is as follows

First, put both expression in different brackets

(9x-3)(6x^2-2x+5)

Expand (6x^2-2x+5) bracket by (9x-3)

To do that. we first multiply (6x^2-2x+5) by 9x then by -3. This is done as follows

9x (6x^2-2x+5) - 3(6x^2-2x+5)

Now, we proceed to opening the bracket

(9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)

(54x^3  - 18x^2+ 45x) - (18x^2 - 6x +15)

Open both brackets

54x^3  - 18x^2+ 45x -18x^2 + 6x -15

Collect like terms

54x^3  - 18x^2 -18x^2 + 45x  + 6x -15

54x^3  - 36x^2 + 51x  -15

Now, we compare both answers

Is

18x^3 -60x^2 + 33x - 45

equal to

54x^3  - 36x^2 + 51x  -15

No, they're not.

Reason is that, for both expressions to be equal, we must have the same expression after expanding both of them

7 0
3 years ago
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