Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
Answer:
12t -3 = 18t
Step-by-step explanation:
Let
d = your friends distance in miles
t = time in hrs
Your equation:
d - 3 = 18t (1)
Because you are 3 miles behind your friend
Your Friend's equation:
d = 12t (2)
To find the amount of time t it takes for you to catch up with your friend,
Substitute (2) into (1)
d - 3 = 18t
12t - 3 = 18t
Equation to find the amount of time t it takes for you to catch up to your friend is 12t - 3 = 18t
Solving the equation
12t - 3 = 18t
Collect like terms
12t - 18t = 3
-6t = 3
t = 3/-6
= -0.5
t = 1/2 hour
Time can not be negative, therefore it will take 1/2 an hour to catch up with your friend
Answer:
The standard deviation of the sampling distribution of x overbarx, denoted sigma Subscript x overbarσx, is called the standard error of the mean . The standard deviation of the sampling distribution of x overbarx, denoted sigma Subscript x overbarσx, is called the standard distribution of the sample.
Step-by-step explanation:
The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation. It is called the standard error of the mean (SEM) if the parameter or the statistic is the mean.
