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3 years ago

11

The steps below show the incomplete solution to find the value of y for the equation 4y − 2y − 4 = −1 + 13: Step 1: 4y − 2y − 4

= −1 + 13 Step 2: 4y − 2y − 4 = 12 Step 3: 2y − 4 = 12 Which of these is most likely the next step? 2y = 3 2y = 8 2y = 16 2y = 18

1 answer:

Maurinko [17]3 years ago

3 0

Answer:

You stopped at 2y-4=12

If we add same number to both sides the equation will remain true. For example if we have 5=5, and we add 7 to both sides, we get 12=12 which is also true. Now let's do this with our equation. Add 4 to both sides(to have only y on the left side). We get 2y=16, hence y=8.

Answer. 2y=16

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Step-by-step explanation:

Consider point A as Pine Knob fire tower and Point B as Colt Station fire tower. So the distance between both towers that is AB is 30 km.

Now both fire tower are located at a bearing of N65°E. That is at point A from north, Colt station fire tower is located at an angle of 65° towards east.

From ranger on Pine knob tower, fire spotted makes bearing of N80°E. That is at point A from north fire is located at an angle of 80° towards east.

Similarly, from ranger on Pine knob tower, fire spotted makes bearing of S70°E. That is at point B from south fire is located at an angle of 70° towards east.

Now calculate $\theta_{1}=\angle BAC$ and $\theta_{2}=\angle ABD$ as follows,

For $\theta_{1}=\angle BAC$

$\angle XAC=\angle XAB+\angle BAC$

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For $\theta_{2}=\angle ABD$

By using alternate angle property,

$\ angle XAB =\angle ABD=65\degree$

Refer attachment 1.

From diagram consider the triangle ABC. To find the third angle that is \angle BAC can be calculated by using angle sum property of triangle.

$\angle BAC+\angle ABC+\angle BCA=180\degree$

$\therefore15\degree +135\degree +\angle BCA=180\degree$

$\therefore \angle BCA=30\degree$

Refer attachment 2.

Sine rule for the $\Delta ABC$ can be applied as follows,

$\ddfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

Substituting the values,

$\dfrac{\sin 15}{a}=\dfrac{\sin 135}{b}=\dfrac{\sin 30}{30}$

Now distance AC and BC can be calculated as follows,

For distance AC,

$\dfrac{\sin 135}{b}=\dfrac{\sin 30}{30}$

Cross multiplying,

$30\times\sin 135=b\times\sin 30$

$\dfrac{30\times \sin 135}{\sin 30}=b$

$b=42.43\:km$

The distance of fire from Pine Knob fire tower is 42.43 km

For distance BC,

$\dfrac{\sin 15}{a}=\dfrac{\sin 135}{42.43}$

Cross multiplying,

$42.43\times\sin 15=a\times\sin 135$

$\dfrac{42.43\times \sin 15}{\sin 135}=a$

$a=15.53\:km$

The distance of fire from Pine Knob fire tower is 15.53 km

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