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Answer:
<em>Maximum: (-1,9)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic function</u>
If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:
Where a is the leading coefficient.
We are given the following function:
To find the vertex, we need to complete squares. First, factor -2 on the first two terms:
The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:
Taking out the -1:
Factoring the trinomial and operating:
Comparing with the vertex form we have
Vertex (-1,9)
Leading coefficient: -2
Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.
Maximum: (-1,9)
Distance = speed * time
d = st
The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family
car.
The equation for the sports car is
d = 95t
The family car travels the same distance, d, but since it left 4.5 hours earlier than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph.
The equation for the family car is
d = 35(t + 4.5)
We solve the two equations as a system of equations.
d = 95t
d = 35(t + 4.5)
Since d = d, set the right sides of the equations above equal to each other.
95t = 35(t + 4.5)
95t = 35t + 157.5
60t = 157.5
t = 2.625
The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.
Check:
In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles
The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours.
In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles.
The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.
Answer:
F(2, 11/2)
Step-by-step explanation:
The expression:
(x-2)² = 10(y - 3)
can be rewritten in the vertex form as follows:
(x-2)² = 10y - 30
(x-2)² + 30 = 10y
1/10(x-2)² + 3 = y
General vertex form is:
y = a(x-h)² + k
then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and <em>a </em>= 1/10
The focus of a parabola is located ar F(h, k+p), where <em>p</em> = 1/(4a). Replacing into these equations:
p = 1/(4*1/10) = 5/2
F(2, 3+5/2) = F(2, 11/2)
We can subtract from the number of strings of length 4 of lower case letters the number of string of length 4 of lower case letters other than x. Thus the answer is 264 − 254 = 66,<span>351</span>
