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Answer:
The difference of the degrees of the polynomials p (x) and q (x) is 1.
Step-by-step explanation:
A polynomial function is made up of two or more algebraic terms, such as p (x), p (x, y) or p (x, y, z) and so on.
The polynomial’s degree is the highest exponent or power of the variable in the polynomial function.
The polynomials provided are:
The degree of polynomial p (x) is:
The degree of polynomial q (x) is:
The difference of the degrees of the polynomials p (x) and q (x) is:
Thus, the difference of the degrees of the polynomials p (x) and q (x) is 1.
Answer:
20 units²
Step-by-step explanation:
The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at
1.5 ± 5/2 = {-1, 4}
Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...
0 = a(4 -1.5)² +12.5
0 = 6.25a +12.5 . . . . . simplify
0 = a +2 . . . . . . . . . . . divide by 6.25
-2 = a
Then the standard-form equation of the parabola is ...
y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5
y = -2x² +6x +8
This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...
A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²
