Are these quadratic functions?
1 answer:
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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
Answer:
C. 1.5 cm
Step-by-step explanation:
A pentagon is a polygon with 5 sides.
The formula for the area of a regular polygon is
where a is the apothem and p is the perimeter. The perimeter is found by multiplying the number of sides of the figure by the length of 1 of those sides:
5(2.2) = 11
Now we have everything we need to solve for the length of the apothem.
Begin by multiplying both sides by 2 to get rid of the fraction, so
16.6 = 11a Divide both sides by 11 to get
a = 1.5090909 or
C. 1.5 cm