Step-by-step explanation:
(3x2 - 2x - 4) (2x2 + x - 3)
6x4 + 3x3 - 9x2 - 4x3 - 2x2 + 6x - 8x2 - 4x + 12
Solving like terms
6x4 - x3 - 19x2 + 2x + 12
Answer:
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Step-by-step explanation:
Given
In 1990; Income= $39000
In 2010; Income= $70768
Solving (a): An equation in form of f(x) = ax + b
First, we need to determine the slope, a
Taking y as income and x as year index.
When x = 0; y = 39000
When x = 20; y = 70768
Substitute these values in the above formula
Next, is to determine the formula using:
<em>Considering :When x = 0; y = 39000, we have</em>
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<em>Make y the subject of formula</em>
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<em>Express y as a function of x</em>
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Solving (b): Income in 2005
<em>In 2005, x = 15</em>
So:
becomes
Let b be the number of blue beads and g the number of green beads that Giovanni can use for a belt.
He's supposed to use a total of between 70 and 74 beads, so
70 ≤ b + g ≤ 74
The ratio of green beads to blue beads is g/b, and this ratio has to be between 1.4 and 1.6, so
1.4 ≤ g/b ≤ 1.6
For completeness, Giovanni must use at least one of either bead color, so it sort of goes without saying that this system must also include the conditions
b ≥ 0
g ≥ 0
(These conditions "go without saying" because they are implied by the others. g/b is a positive number, so either both b and g are positive, or they're both negative. But they must both be positive, because otherwise b + g would be negative. I would argue for including them, though.)
