The rule of given table is (a÷2)-(b÷3).
Step-by-step explanation:
From the given table it is clear that
8 becomes 3
24 becomes 9
40 becomes 15
Rule
(8÷2)-(3÷3) = (4-1) = 3
(24÷2)-(9÷3) = (12-3) = 9
(40÷2)-(15÷3) = (20-5) = 15
So, the equation will be
(a÷2)-(b÷3)
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x-(3*x^3+8*x^2+5*x-7)=0
Step by step solution :Step 1 :Equation at the end of step 1 : x-((((3•(x3))+23x2)+5x)-7) = 0 Step 2 :Equation at the end of step 2 : x - (((3x3 + 23x2) + 5x) - 7) = 0 Step 3 :Step 4 :Pulling out like terms :
4.1 Pull out like factors :
-3x3 - 8x2 - 4x + 7 =
-1 • (3x3 + 8x2 + 4x - 7)
Checking for a perfect cube :
4.2 3x3 + 8x2 + 4x - 7 is not a perfect cube
Trying to factor by pulling out :
4.3 Factoring: 3x3 + 8x2 + 4x - 7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 3x3 - 7
Group 2: 8x2 + 4x
Pull out from each group separately :
Group 1: (3x3 - 7) • (1)
Group 2: (2x + 1) • (4x)
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Answer:
=-1)+(-3)-(-5)
=-1-3+5
=-4+5
=1
Step-by-step explanation:
answer is to your question is 1.
You can see how this works by thinking through what's going on.
In the first year the population declines by 3%. So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200. 3% of 1200 is the same as .03 * 1200. So the population at the end of the first year is 1200 - .03 * 1200. That can be written as 1200 * (1 - .03), or 1200 * 0.97
What about the second year? The population starts at 1200 * 0.97. It declines by 3% again. But 3% of what??? The decline is based on the population at the beginning of the year, NOT based no the original population. So the decline in the second year is 0.03 * (1200 * 0.97). And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year. So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.
So there's a pattern. If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.
So the population after x years is 1200 * 0.97x
