Solve the system of equations. y = 9x y= 2x+56

Mathematics

1 answer:

nadya68 [22]3 years ago

5 0

Answer:

(8, 72)

Step-by-step explanation:

Here we have two separate equations for y: y = 9x and y = 2x + 56.

Equating these equations eliminates y temporarily; we get:

9x = 2x + 56, or 7x = 56. Dividing both sides by 7 results in x = 8.

Then, by the first equation, y = 9(8) = 72.

The solution is (8, 72).

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The ratio of the measure of the acute angle in a right triangle is 1/2 . Find the measures of the two angles

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30° and 60°.

<h3>Further explanation</h3>

We will solve the problem of the measures of angles in the triangle.

Recall this condition:

The acute angle ⇒ an angle of less than 90°.
The right angle ⇒ an angle of exactly 90°.
A right triangle ⇒ a triangle in which one angle is a right angle.
The interior angles ⇒ the angles inside a triangle.
All the interior angles in a triangle , i.e., $\boxed{ \ \angle A + \angle B + \angle C = 180^0 \ }$

<u>Given that:</u>

The ratio of the measure of the acute angle in a right triangle is ¹/₂.

<u>Question:</u>

Find the measures of the two angles.

<u>The Process:</u>

We call it the triangle ABC. An interior angle inside is a right angle, e.g., ∠A = 90°.

From the ratio of two other acute angles, i.e., 1: 2, we call it ∠B = x and ∠C = 2x.

Let's arrange the three angles in ABC triangle as follows:

$\boxed{ \ 90^0 + x + 2x = 180^0 \ }$

Both sides subtracted by 90°.

$\boxed{ \ x + 2x = 180^0 - 90^0 \ }$

$\boxed{ \ 3x = 90^0 \ }$

Both sides divided by 3.

We get $\boxed{ \ x = 30^0 \ }$

We substitute the value of x back into B and C.

$\boxed{\boxed{ \ \angle B = x\ } \rightarrow \boxed{ \ \angle B = 30^0 \ }} \\\boxed{\boxed{ \ \angle C = 2x\ } \rightarrow \boxed{ \ \angle C = 60^0 \ }}$