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.
Answer:
P(a junior or a senior)=1
Step-by-step explanation:
The formula of the probability is given by:
P (AB) = P(A)
Where P(A) is the probability of occurring an event A, n(A) is the number of favorable outcomes and N is the total number of outcomes.
In this case, N is the total number of the students of statistics class.
N=18+10=28
The probability of the union of two mutually exclusive events is given by:
Therefore:
P(a junior or a senior) =P(a junior)+P(a senior)
Because a student is a junior or a senior, not both.
n(a junior)=18
n(a senior)=10
P(a junior)=18/28
P(a senior) = 10/28
P(a junior or a senior) = 18/28 + 10/28
Solving the sum of the fractions:
P(a junior or a senior) = 28/28 = 1
45 is if you x it so it’s 45
Answer: 2 30303/62500
Hope this helps! :)
Step-by-step explanation:
Answer: 45000
Step-by-step explanation:
From the question, we are informed that Patty buys a new car and gets it appraised every few years and that after owning the car for 3 years, its value is $15,000 and further told that after owning the car for 5 years, its value is $9,000.
Let the number of years be x
Let the value of the car be y.
From the first part of the question, we are told that after owning the car for 3 years, its value is $15,000.
Since an inverse variation will be:
x = k/y
3 = k/15000
k = 15000 × 3
k = 45000
Let's confirm the value of k for the second part of the question. After owning the car for 5 years, its value is $9,000. Here, x=5 and y = 9000
x = k/y
x = 45000/9000
x = 5
It's correct.
Therefore, the constant of proportionality is 45000
