<h2>
Hello!</h2>
The answer is:
The length of "x" is equal to 4 units.
<h2>
Why?</h2>
To solve the problem and find the length of x, we need to remember the alternate angles rule. The alternate angles rule establish that alternate angles will be also equal.
So, for the triangles, we have:
The angle((α)) formed between the base (2.5) and the hypotenuse (5) of the big triangle is equal to the angle(α) formed between the base (2) and the hypotenuse (x) of the small triangle. It also means that the triangles are similar since they have congruent angles(α) and proportional sides (SAS).
We are given:
First triangle,
Second triangle,
So, using the cosine identity, we have:
Therefore, we have that the hypotenuse of the second triangle (x) is equal to 4 units.
Hence, the length of "x" is equal to 4 units.
Have a nice day!
Step-by-step explanation:
<u>A</u><u>B</u><u>C</u><u>D</u><u>E</u><u>F</u><u>G</u><u>H</u><u>I</u><u>J</u><u>K</u><u>L</u><u>M</u><u>O</u><u>P</u><u>Q</u><u>R</u><u>S</u><u>T</u><u>U</u><u>V</u><u>W</u><u>X</u><u>Y</u><u>Z</u>
Answer:
![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
Step-by-step explanation:
Let the total number of batteries produced daily be represented by x.
7/8 of the batteries are packaged immediately.
So the total number of packaged batteries = ![\[\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
Remaining batteries = ![\[x-\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5Bx-%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity= ![\[\frac{2}{3} * \frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
Remaining batteries are faulty.
So the total number of faulty batteries = ![\[\frac{x}{8} - \frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%20-%20%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
= ![\[\frac{3x - 2x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B3x%20-%202x%7D%7B24%7D%5C%5D)
= ![\[\frac{x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%5C%5D)
So the faction of batteries which are faulty =
= ![\[\frac{x}{24} \div x\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%20%5Cdiv%20x%5C%5D)
=
A. (-1,-2)
Because:
x + y = -3
-1 + (-2) = -3
-3 = -3
x - y = 1
-1 - (-2) = 1
-1 + 2 = 1
1 = 1
That is:
Forty-five thousand, five hundred seventy-two.
~Deceptiøn
