Answer:
The domain is -7, 0, and 5
The range is -1, 0, and 8
Step-by-step explanation:
The domain of a set of points is the x-value. In this case the x-values are -7, 0, and 5 respectively. The range of a set of points is the y-value so in this case the range is -1, 0, and 8.
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Answer:
280 cubic inches
Step-by-step explanation:
Cubic inches of foam required = volume of the box - volume of the basketball
The box has a shape of a cube, so that;
volume of the box = 
where l is the length of the sides of the box.
volume of the box = 
= 729 cubic inches
volume of the box = 729 cubic inches
The basketball has the shape of a sphere, so that;
volume of the basketball = 
= x 3.14 x 
= 448.693
volume of the basketball = 448.693 cubic inches
Thus,
cubic inches of foam required = 729 - 448.693
= 280.307
The cubic inches of foam to be used is 280 cubic inches.
Answer:
Creo que la respuesta sería B: 2 horas y 15 minutos.
Step-by-step explanation:
Answer:
20x² + 25 x + 8
Step-by-step explanation:
f(x) = 4x² + 5x + 3
g(x) = 5x -7
Then:
g(f(x)) = 5(4x² + 5x + 3) -7
g(f(x)) = 20x² + 25x + 15 - 7
g(f(x)) = 20x² + 25x + 8
