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melamori03 [73]
3 years ago
13

Factorise the following by taking out a common binomial factor. 7(x - 3) - (x + 3)(x - 3)

Mathematics
2 answers:
g100num [7]3 years ago
7 0

Step-by-step explanation:

7(x - 3) - (x + 3)(x - 3)

(x - 3)(7 - (x + 3))

(x - 3)(7 - x - 3)

(x - 3)(4 - x)

zvonat [6]3 years ago
7 0

Answer:

(x - 3)(4 - x).

Step-by-step explanation:

The common binomial factor is (x - 3) so we have:

7(x - 3) - (x + 3)(x - 3)

= (x - 3)( 7 - (x + 3))

= (x - 3)(4 - x)

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<u>Step-by-step explanation:</u>

It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0).  Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ cos\ \dfrac{\theta}{2}

It is given that sin θ = -\dfrac{7}{25}  ⇒  y = -7 & hyp = 25

Use Pythagorean Theorem to find "x":

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cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}

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