State the property or properties of logarithms used to rewrite the expression.
1 answer:
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Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
Here we can first find the area of yard and then subtract the area of vegetable garden to get the required area.
The formula to find area is given by:
Now we find area of yard:
length is 25 ft and width is 15 ft.
Area of yard = 375 ft²
Area of vegetable garden:
length = 8ft and width =8ft
So the vegetable garden is a square.
Area = 8*8
Area of vegetable garden =64 ft²
Area of backyard to be laid with grass = Area of yard-Area of vegetable garden
Area required = 375 -64 = 311 ft²
Answer : The area of backyard in which grass is to be laid is 311 square feet.