Answer:

Step-by-step explanation:
To calculate the lenght of the diagonal d across the square, we can assume that the square it is compound of two right triangles. So, we can resolve this exercise using The Pythagorean Theorem.
<em>The Pythagorean theorem</em> states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.
If in a right triangle there are legs of length a and b, and the measure of the hypotenuse is c, then the following relation is fulfilled:
a is the height, b is the base, and c is
the hypotenuse.
To obtain the value of the hypotenuse

To find the value of the lenght of the diagonal d across the square, we have:
Where a = b = 20
Substituting the values

Round the answer to 2 decimal places

Answer:
<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>
<u>Our system of equations:</u>
<u>x + y = 12</u>
<u>7x + 12y = 104</u>
Correct statement and question:
Alejandro loves to go to the movies. He goes both at night and during the day. The cost of a matinee is 7 dollars. The cost of an evening show is 12 dollars.
Alejandro went to see a total of 12 movies and spent $ 104. How many of each type of movie did he attend? Write a system of equations.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Step 1:
Let x to represent the number of matinee shows Alejandro went to.
Let y to represent the number of evening shows Alejandro went to.
Now, let's write our system of equations:
x + y = 12
7x + 12y = 104
*********************
x = 12 - y
*********************
7 (12 - y) + 12y = 104
84 - 7y + 12y = 104
5y = 104 - 84
5y = 20
y = 20/5
<u>y = 4 ⇒ x = 12 - 4 = 8</u>
<u>Alejandro went to 8 matinee shows and 4 evening shows.</u>
Given:
The system of equations is:
Line A: 
Line B: 
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Equating (i) and (ii), we get



Divide both sides by 2.

Substituting
in (i), we get
The solution of system of equations is (-4,-8).
Now verify the solution by substituting
in the given equations.


This statement is true.
Similarly,



This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
18xy + 24y = 6y(3x + 8)
The common factor is 6y