30-60-90 special right triangles

Mathematics

1 answer:

Mazyrski [523]3 years ago

6 0

So so the sides are x, x√3, 2x

here is an attachemtnt don't mind the one on the left

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Solve the system of equations

insens350 [35]

Answer:

x = 3, y = 1 is the solution of the given system.

Step-by-step explanation:

Here, the given system of equations is:

y = -x + 4 ...... (1)

y = x - 2 .......... (2)

Now, to find the solution of the system, SUBSTITUTE the value of y from equation (1) in to the equation (2). We get ,

y = x - 2 ⇒ -x + 4 = x - 2 ( as from (1), y = -x + 4)

or, -x -x = -2 -4

or, - 2 x = -6 ⇒ x = 6/2 = 3

or, x = 3

⇒ y = x - 2 = 3 - 2 = 1

⇒ y = 1

Hence, x = 3, y = 1 is the solution of the given system.

5 0

3 years ago

Quadrilateral ABCD is inscribed in this circle.

Sunny_sXe [5.5K]

Answer: $m\angle A=116\°$

Step-by-step explanation:

The missing figure is attached.

For this exercise it is important to remember that, by definition, the opposite interior angles of an inscribed quadrilateral are supplementary, which means that their sum is 180 degrees.

Based on this, you can identify that the angle D and the angle B are opposite and, therefore, supplementary.

Knowing that, you can write the following equation:

$x+28\°=180\°$

Now you must solve for "x" in order to find its value. This is:

$x=180\°-28\°\\\\x=152\°$

Then:

$m\angle D=152\°$

You know that:

$m\angle A=(x-36)\°$

Therefore, since you know the value of "x", you can substitute it into $m\angle A=(x-36)\°$ and then you must evaluate, in order to find the measure of the angle A. This is:

$m\angle A=152\°-36\°\\\\m\angle A=116\°$