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2 years ago

11

Find the slope (if defined) of the line that passes through the given points. (-1, 6) and (5, 5)

2 answers:

galben [10]2 years ago

8 0

Answer:

- 1/6

Step-by-step explanation:

Use the following equation to calculate slope between two points:

( Y2 - Y1 ) / ( X2 - X1 )

What's Y2? Y1? X2? X1?

( -1, 6 )

-1 = X1

6 = Y1

( 5, 5 )

5 = X2

5 = Y2

So when we plug in those numbers:

5 - 6 = - 1

5 - (-1) = 6

- 1/6

Naily [24]2 years ago

6 0

The solution for your question is-1/6

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Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

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Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

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Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

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$C = 12cm$

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$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

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Take Square root of both sides

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$B = \sqrt{36.153903093}$

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$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

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Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

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Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

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Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

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