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3 years ago

Which best explains how you know that P(2, 7) is on the same line as Q(7, 4) and R(12, 1)?

Mathematics

1 answer:

Helen [10]3 years ago

4 0

Answer:

See explanation below

Step-by-step explanation:

The best explanation is noticing that in order to get from the point R (12, 1) to the point Q (7, 4) we move 5 units to the left and 3 units up. And to go from point Q (7, 4) to point P (2, 7) we do exactly the same: move 5 units to the left and 3 units up. That means that these points are all connected via the same rate of change: - 3/5, which is in fact the slope of the line the three points belong to.

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Help please explanation as detailed as you can make it but easy to understand

Doss [256]

Answer:

tan(x) = (√6)/2

Step-by-step explanation:

The tangent identity is ...

tan = sin/cos

<h3>Substitution</h3>

Substituting the given values of sine and cosine, we have ...

$\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}$

<h3>Simplification</h3>

At this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.

We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...

$\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}$

The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.

<em>Additional comment</em>

If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)

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1 year ago