Explanation:
We will try to simplify the given expression into terms of ab and then substitute with ab = x as follows:
2a³b + a²b + ab
a² (2ab + ab) + ab
a² (3ab) + ab
a² (3x) + x
Since ab = x, therefore, a = x/b
Substitute with this in the above expression to get:
(x/b)²(3x) + x
+ x
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Answer:
146
Step-by-step explanation:
substitute x = 2, y = 3 into the expression
4(2)³ + 2(2)(3) - 2(3) + 3(2)²(3)²
= 4(8) + 12 - 6 + 3(4)(9)
= 32 + 12 - 6 + 108
= 38 + 108
= 146
a) The step function seen in the figure has 6 pieces, one for each step
b) There are 6 intervals, one for each piece. Their values are:
(0, 1]
(1, 2]
(2, 3]
(3, 4]
(4, 5]
(5, 6]
c) The open circles indicate that the endpoint is not included in the interval. The closed circles indicate the endpoint is included in the interval.
For example, in the second interval, 1 is not included (open circle) and 2 is included (closed circle).
d) This is a function because for eac value of x there iss one and only one of y. If the open circles were closed circles, then thi wouldnot be a function.
e) All the pieces are linear because their graph is a line (flat horizontal line)
f) The range of the function is the set of output values:
Range = {46, 48, 50, 32, 54, 56}
Answer:
-3/2
Step-by-step explanation:
We can find the slope between two points using
m = (y2-y1)/(x2-x1)
= (-7 - -1)/(5 - 1)
(-7+1(/(5-1)
-6/4
-3/2
Answer:
Step-by-step explanation:
The volume of a rectangular prism is given by .
Thus, we have the equation:
Solving, we get:
.