How do you get the variable p alone in the equation 2p-12?

En la figura, la suma de las medidas p + q + r + s =/In the figure, the sum of the measures p + q + r + s =

sertanlavr [38]

Answer:

I think its 300

Step-by-step explanation

This is from my understanding, so I may be a bit wrong.

1. First observe the amount of triangles that form, you have two main triangles and one isosceles triangle that forms in the middle by how these are joined together.

2. Using this idea we will come up with the equations of each triangle that has been formed.

3. We can observe that almost all angles are named with a variable except the one in the middle, being an isosceles we will name the missing variable y.

4. Triangle 1(left side) or T1 equals 180 degrees but what angles form this triangle, these would be p+q+y = 180, T2(right side) = r+s+y = 180

5. After creating these two triangles we notice that we have not taken into account the triangle in the middle, we are given 1 angle of this isosceles. There is a mathematical property which I don't remember the name, but essentially the angle below is the same as the angle above, this being 120 degrees. This will result in T3 = 2y + 120 = 180

6. Solve for y, which gives us y=30, *simple triangle math you know*

7. Finally we fix our equations for p+q+r+s, essentially T1 and T2 will transform into p+q = 180-y and r+s = 180-y, we add them up forming p+q+r+s = 2(180-y)

8. Solve the equation p+q+r+s = 360 - 2y which when adding y becomes p+q+r+s = 360-60 = 300

Notes: when doing these exercises it is important to take into account every triangle, the isosceles triangle is very vital for solving it, as it gives us a way for making an equation that is single handedly dependent on y a constant we can find and use. A good approach for these issues would be writing every piece of information as separate sets and then trying to join them using algebra.

3 0

3 years ago

Judy is pulling on a trunk with a 12-N force. Ike pulls at right angles to Judy. With how much force must Ike pull to make the r

Ratling [72]

To understand the problem, let's first draw a free body diagram of the forces exerted by Judy and Ike on the truck. (Refer to the left side of the attachment).

To solve for the resultant, we just use the tip-to-tail method. This is illustrated on the right side of the attachment.

We can see that the tip-to-tail method forms a right triangle thus we can just apply the Pythagorean theorem in solving for Ike's force.

$20^{2} = 12^{2} + F^{2}$
$400 = 144 + F^{2}$
$256 = F^{2}$
$F = 16.0$

ANSWER: Ike must pull the truck with a force of 16.0 N.