Answer:
Step-by-step explanation:
Given
Required
Eliminate a
Multiply the first equation by -4
Add to the second equation
Solve brackets
Open bracket
At this point, a has been eliminated;
From the list of given options, the option that answers the question is
Answer:
The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
Step-by-step explanation:
Here is the complete question
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
y=35x; y=-0.05(x-400)²+9,492
what does the solution of the system represent in this context?
Solution
The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .
So, 35x = -0.05(x-400)² + 9,492.
Expanding the right side, we have
35x = -0.05(x² - 800x + 160000) + 9492
35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492
35x = -0.05x² +40x - 8000 + 9492
35x = -0.05x² +40x + 1492
Collecting all the terms to the left side, we have
0.05x² - 40x - 1492 + 35x = 0
0.05x² - 5x -1492 = 0
Using the quadratic formula,
We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.
The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
We confirm that by plugging in x = 229.83 in both equations.
y = 35x = 35(229.83) = 8044.05 ≅ 8044.1
y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1
La diferencia entre los ángulos <em>AOB</em> y <em>COD</em> del sistema de tres ángulos <em>consecutivos</em> es igual a 25°.
La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.
<h3>Cómo analizar tres ángulos consecutivos</h3>
Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.
De acuerdo con el enunciado, tenemos las siguientes condiciones:
∠AOB + ∠BOC = 125° (1)
∠BOC + ∠COD = 100° (2)
Por (1) y (2) tenemos las siguiente identidad:
∠AOB - 25° = ∠COD
∠AOB - ∠COD = 25°
La diferencia entre los ángulos <em>AOB</em> y <em>COD</em> del sistema de tres ángulos <em>consecutivos</em> es igual a 25°.
En el segundo caso, tenemos el siguiente sistema:
∠AOB = ∠BOC + ∠COD (3)
∠AOB + ∠BOC - ∠COD = 40° (4)
Por (3) y (4) tenemos la siguiente identidad:
2 · ∠BOC = 40°
∠BOC = 20°
La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.
Para aprender más sobre ángulos, invitamos cordialmente a ver esta pregunta verificada: brainly.com/question/21209282