Answer:
9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;
(x - 2)²/2² - (y + 3)²/3² = 1
Step-by-step explanation:
The standard form of a hyperbola is given as follows;
(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1
The given equation is presented as follows;
9·x² - 36·x = 4·y² + 24·y + 36
By completing the square, we get;
(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)
(3·x - 6)² - 36 = (2·y + 6)²
(3·x - 6)² - (2·y + 6)² = 36
(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1
(3·x - 6)²/6² - (2·y + 6)²/6² = 1
3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1
(x - 2)²/2² - (y + 3)²/3² = 1
The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.
The answer is 12 1/2 or 12.5
Answer:
Movie: $4.25
Video Game: $5.25
Step-by-step explanation:
For this problem, we can use system of equations to solve for the rental costs of the movies and video games. Let's use x for movies and y for video games.
Equation 1
5x+3y=37
Equation 2
2x+6y=40
To start, we can use elimination to solve for x and y. Let's cancel out y. To do so, we have to multiply the first equation by 2 to get the y equal.
10x+6y=74
Now that the y are equal, we can subtract both equations.
8x=34
x=4.25
The movie rental cost is $4.25.
Now that we know x, we can plug in to find y.
2(4.25)+6y=40
8.5+6y=40
6y=31.5
y=5.25
The rental cost for video games is $5.25.
The answer is ‘y=30’
i don’t really know how to explain it but multiply the first top number’-4x’ with all of the bottom numbers. Multiply the first number at the bottom ‘-10’ by all the numbers at the top.
-40x-20y=-140
-40x+28y=-100
-
____________
-8y=240
— ——
-8 -8
y=30
15 inches
the formula for the area of a triangle is Area=(1/2)(base)(height)
since the problem is looking for the height, we can rewrite it as
Height=(Area)/((1/2)(Base))
then the number must be substituted in
Height=(187.5)/((1/2)(25))
and the answer is 15 inches.