The equation of the piecewise function is 
<h3>The piecewise function</h3>
On the graph, we have:
- y = 3 for all x values not more than -1
- y = -1 for all values greater than 2
Hence, the piecewise function is:
<h3>The domain of the function</h3>
This is the set of input values
In (a), we have:
x ≤ -1 and x > 2
Hence, the domain is (∞, 3] u (2, ∞)
<h3>The range of the function</h3>
This is the set of output values
In (a), we have:
f(x) = 3 and f(x) -1
Hence, the range is [3] u (-1)
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Answer:
x^2 + y^2 + 16x + 6y + 9 = 0
Step-by-step explanation:
Using the formula for equation of a circle
(x - a)^2 + (y + b)^2 = r^2
(a, b) - the center
r - radius of the circle
Inserting the values given in the question
(-8,3) and r = 8
a - -8
b - 3
r - 8
[ x -(-8)]^2 + (y+3)^2 = 8^2
(x + 8)^2 + (y + 3)^2 = 8^2
Solving the brackets
( x + 8)(x + 8) + (y +3)(y+3) = 64
x^2 + 16x + 64 + y^2 + 6y + 9 = 64
Rearranging algebrally,.
x^2 + y^2 + 16x + 6y + 9+64 - 64 = 0
Bringing in 64, thereby changing the + sign to -
Therefore, the equation of the circle =
x^2 + y^2 + 16x + 6y + 9 = 0
Answer:
22 grams
Step-by-step explanation:
loses 50% of it's mass per 22 years
so after 22 years the mass would be 44 grams
22 years later would leave 50% of 44 grams = 22 grams
Answer:
20 males, 7 females
Step-by-step explanation:
x=males
x-13=females
x+x-13=27
2x-13=27
2x=40
x=20
20-13=7
