What is the 4th term when 8+2x^2-4^4+7x^3 is arranged is descending order? 8, 2x^2, -4x^4, or 7x^3
1 answer:
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Answer:
- a) 3
- b) 6
- c) 9
- d) the outputs are 3 times as far apart as the inputs
Step-by-step explanation:
(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.
That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.
(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)
(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.
(d) The ratio of output differences to input differences can be seen to be ...
... 3/1 = 6/2 = 9/3 = 3
Output differences are 3 times input differences.
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<em>Comment on the problem</em>
These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.
Geometric shapes are mathematical shapes that include squares and triangles
<h3>How to prove the shape is a square</h3>The side lengths of a square are congruent, and the adjacent sides are perpendicular.
So, we start by calculating the side lengths using the following distance formula
Using the above formula, we have:
The above shows that the side lengths of the square are congruent.
Next, calculate the slope of the sides using:
So, we have:
Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.
The above highlight, and the equal side lengths show that the figure (1) is a square
<h3>How to prove the shape is a right isosceles triangle</h3>The legs of a right isosceles triangle are congruent, and the legs are perpendicular.
So, we start by calculating the lengths of the legs using the following distance formula
Using the above formula, we have:
The above shows that the legs of the right isosceles triangle are congruent.
Next, calculate the slope of the legs using:
So, we have:
Notice that the slopes are opposite reciprocal.
The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle
Read more about geometric shapes at: