Jane pulled weeds in the garden 7 times. She was paid $5 each time she pulled weeds a for more than 1 hour. If Jane received $39
2 answers:
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Answer:
Area of the garden:
Explanation:
Given the below parameters;
Length of the rectangle(l) = 23 ft
Width of the rectangle(w) = 14 ft
Value of pi = 3.14
Since the width of the rectangle is 14 ft, so the diameter(d) of the semicircle is also 14 ft.
The radius(r) of the semicircle will now be;
Let's now go ahead and determine the area of the semicircle using the below formula;
Let's also determine the area of the rectangle;
We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;
Therefore, the area of the garden is 398.93 ft^2
Answer:
Step-by-step explanation:
Let the quadratic equation of the function by the points in the given equation is,
f(x) = ax² + bx + c
If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),
For (0, 8),
f(0) = a(0)² + b(0) + c
8 = c
For a point (-3, -10),
f(-3) = a(-3)² + b(-3) + 8
-10 = 9a - 3b + 8
9a - 3b = -18
3a - b = -6 --------(1)
For (-4, -8),
f(-4) = a(-4)² + b(-4) + 8
-8 = 16a - 4b + 8
-16 = 16a - 4b
4a - b = -4 ------(2)
Subtract equation (1) from equation (2)
(4a - b) - (3a - b) = -4 + 6
a = 2
From equation (1),
6 - b = -6
b = 12
Function will be,
f(x) = 2x² + 12x + 8
= 2(x² + 6x) + 8
= 2(x² + 6x + 9 - 9) + 8
= 2(x² + 6x + 9) - 18 + 8
= 2(x + 3)² - 10
By comparing this function with the vertex form of the function,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the function 'f' will be (-3, -10)
And axis of symmetry will be,
x = -3
From the given graph, axis of the symmetry of the function 'g' is; x = -3
Therefore, both the functions will have the same axis of symmetry.
y-intercept of the function 'f' → y = 8 Or (0, 8)
y-intercept of the function 'g' → y = -2 Or (0, -2)
Therefore, y-intercept of 'f' is greater than 'g'
Average rate of change of function 'f' = in the interval [a, b]
=
=
= -6
Average rate of change of function 'g' =
=
=
= 3
Therefore, Average rate of change of function 'f' is less than 'g'.