Answer:
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Step-by-step explanation:
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The volume of this right prism that has a triangular base is equal to 108 cubic meters.
<h3>The volume of a right prism.</h3>
Mathematically, the volume of a right prism is given by this formula:
V = L x W x H
<u>Where:</u>
<u>Given the following data:</u>
Length of base = 6 meters.
Width of base = 4 meters. cm.
Height of prism = 4.5 meters.
Substituting the given parameters into the formula, we have;
V = 6 x 4 x 5
V = 108 cubic meters.
Read more on volume of prism here: brainly.com/question/3867601
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:
19338 kWh
Step-by-step explanation:
In Arizona, electricity cost eleven cents per kilowatt-hour.
The average home uses 66 million BTU per year i.e. 66000000 BTU per year.
Now, it is given in the question that 1 BTU is equivalent to 0.000293 kWh.
So, the average home uses (66000000 × 0.000293) = 19338 kWh per year.
Therefore, the number of kilowatt-hours used per year will be 19338. (Answer)
