To find the common ratio, u take ur 2nd term, and divide it by ur 1st term
(-1/6) / (5/12) =
-1/6 * 12/5 =
- 2/5 <== ur common ratio
Answer:
x = - 2, x = 6
Step-by-step explanation:
Given f(x) = 18 we require to solve
3 | x - 2 | + 6 = 18 ( subtract 6 from both sides )
3 | x - 2 | = 12 ( divide both sides by 3 )
| x - 2 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
x - 2 = 4 ( add 2 to both sides )
x = 6
OR
- (x - 2) = 4
- x + 2 = 4 ( subtract 2 from both sides )
- x = 2 ( multiply both sides by - 1 )
x = - 2
As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
x = - 2 → 3|- 2 - 2| + 6 = 3|-4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
Hence solutions are x = - 2, x = 6
Answer:
Step-by-step explanation:
Since g(x)=0, you input 0 into every x
Which then becomes:
Take out the 0 and there's your answer
Answer: Choice B) x < 10
=======================================================
Explanation:
There's 300 square feet total (land+water). Of that, 100 sq ft is taken up by the pond, so we have 300-100 = 200 sq ft of dry land.
1 duck needs more than 20 sq ft of dry land
2 ducks need more than 40 sq ft of dry land (note how 2*20 = 40)
3 ducks need more than 60 sq ft of dry land (note how 3*20 = 60)
and so on...
In general,
x ducks need more than 20*x square feet of dry land
The max amount of dry land we have is 200 sq ft
The total amount of space the ducks take up must be less than 200 sq ft
In terms of symbols, we have
T = total space ducks take up on dry land
T = 20*x
T < 200
So we can arrive at this inequality
20*x < 200
after replacing the "T" with "20*x"
Afterward, divide both sides by 20
20*x < 200
20*x/20 < 200/20
x < 10
So we must have less than 10 ducks
If we had 10 ducks exactly, then they would take up more than 20*10 = 200 sq ft, but we only have 200 sq ft
The largest number of ducks we can have is 9 ducks.
So that's why we have a "less than" symbol instead of a "less than or equal to" symbol.
