Answer: The team won 100 games and losses 28 games
Step-by-step explanation:
Let the number of games won denoted by x and the games lost is denoted by y .
Given : A minor league baseball team plays 128 games in a season.
Team won 16 more than three times as many games as they lost.
Then, the system of equations, we have
We can rewrite equation (2) as
Now, Eliminate equation (3) from (1), we get
Substitute the value of y in (2), we get
Hence, the team won 100 games and losses 28 games.
Answer:
The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
xy = -8
∵ A = 0 , B = 1 , C = 0
∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0
∴ B² - 4AC > 0
∴ The graph is hyperbola
* The equation xy = -8
∵ We have term xy that means we rotated the graph about
the origin by angle Ф
∵ Ф = π/4
∴ We rotated the x-axis and the y-axis by angle π/4
* That means the point (x' , y') it was point (x , y)
- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ
∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)
∴ x' = x/√2 - y/√2 = (x - y)/√2
∴ y' = x/√2 + y/√2 = (x + y)/√2
* Lets substitute x' and y' in the 1st answer
∵ (x')² - (y')² - 16 = 0
∴
(
* Lets open the bracket
∴
* Lets add the like terms
∴
* Simplify the fraction
∴ -2xy - 16 = 0
* Divide the equation by -2
∴ xy + 8 = 0
∴ xy = -8 ⇒ our equation
∴ Answer (a) is our answer
∴ The answer is hyperbola; (x')² - (y')² - 16 = 0
* Look at the graph:
- The black is the equation (x')² - (y')² - 16 = 0
- The purple is the equation xy = -8
- The red line is x'
- The blue line is y'
Answer:
Step-by-step explanation:
We are asked the equation of the graph which passes through the points at (0,5) and (-3,-4).
Now, we know that the equation of a straight line passing through the points () and (
) is given by
.
So, in our case () ≡ (0,5) and (
) ≡ (-3,-4)
Therefore, the equation of the straight line will be
⇒
⇒ (Answer)