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3 years ago

Which of the following expression is equivalent to 6x2−13x−28

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

5 0

Answer:

I, III and IV

Step-by-step explanation:

Required

Determine equivalent expressions to $6x^2 - 13x - 28$

To do this, we simplify each of the given options.

$I.\ 6x2+8x-21x-28$

Simplify like terms

$6x2+8x-21x-28$

$= 6x2-13x-28$

This is equivalent to the given expression

$II.\ 2x(3x + 4) + 7x(3x - 4)$

Open Bracket

$2x(3x + 4) + 7x(3x - 4)$

$2x*3x + 2x*4 + 7x*3x - 7x*4$

$6x^2 + 8x - 21x^2 - 28x$

Collect Like Terms

$6x^2 - 21x^2 + 8x - 28x$

$-15x^2 - 20x$

This is not equivalent to the given expression

$III.\ 2x(3x+4)-7(3x+4)$

Open Bracket

$2x(3x+4)-7(3x+4)$

$2x*3x + 2x*4 - 7*3x - 7*4$

$6x^2 + 8x - 21x - 28$

Simplify Like Terms

$6x^2 -13x - 28$

This is equivalent to the given expression

$IV.\ (3x + 4)(2x-7)$

Open Brackets

$3x * 2x - 3x * 7 + 4*2x-4*7$

$6x^2 - 21x+ 8x-21$

Simplify like terms

$6x^2 -13x-21$

This is equivalent to the given expression

Hence: I, III and IV are equivalent to the given expression

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y is isolated in both equations, thus you may set the expressions (-2x + 9) and (4x - 3) equal to each other and solve for x.

-2x + 9 = 4x - 3

Subtract 9 from both sides.

-2x + 9 - 9 = 4x - 3 - 9

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Subtract 4x from both sides.

-2x - 4x = 4x - 12 - 4x

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Divide both sides by -6.

-6x/-6 = -12/-6

x = 2

Substitute 2 for x into one of the original equations to find y.

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y = 4(2) - 3 (substitute)

y = 8 - 3 (multiply)

y = 5 (subtract)

Plug x- and y-values into original equations to check work.

5 = -2(2) + 9

5 = - 4 + 9

5 = 5

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Answer:

x = 2 and y = 5; (2, 5).

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Given:

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The highest common factor (HCF) of A and B

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