The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is
When the grasshopper land on the ground,
that is,
Multiplying whole equation by 12 to get rid of denominators 3 and 4
And time cant be negative, so the correct option is
Correct option is C .
Answer:
It is m(x) = 20,000(0.97)^x.
Step-by-step explanation:
After 1990, each year has (100-3) = 97% ( or 0.97) of visitors that it had the previous year.
So m(x) = 20,000(0.97)^x (answer).
Answer:
- length: 14 feet , width: 43 feet, or
- length: 86 feet, width: 7 feet
Both solutions are valid.
Explanation:
1. First assumption is that the shape of the fence is <u>rectangular</u>.
2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet
3. The, the area of the fence will be:
- length × width = xy = 600
4. Now you have two equation with two variables which you can solveL
- Solve for y in the first equation: y = 100 - 2x
- Substitute the value of y into the second equation: x (100 - 2x) = 600
5. Solve the last equation by completing squares:
- Distributive property: 100x - 2x² = 600
- Divide both sides by - 1: 2x² - 100x = - 600
- Divide both sides by 2: x² - 50x = -300
- Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
- Factor the left side: (x - 25)² = 325
- Square root both sides: x - 25 = ± 18.028
- Clear x: x = 25 ± 18.028
- x = 43.028 ≈ 43 or x = 6.972 ≈ 7
Both values are valid,
If x = 43 , then y = 600/43 = 14
If x = 7, then y = 600/7 = 86
Thus, the lenght and width of the fence may be:
- 43 feet (width) and 14 feet (length), or
- 7 feet (width) and 86 feet (length).
Answer:
Natalia's work is wrong.
Step-by-step explanation:
Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:
1) 
Given.
2) 
Definition of addition.
3) 
Distributive property.
4) 
Definitions of multiplication and decimal number.
5) ![x = 72 +[2\cdot (10)^{-1}]\cdot 12](https://tex.z-dn.net/?f=x%20%3D%2072%20%2B%5B2%5Ccdot%20%2810%29%5E%7B-1%7D%5D%5Ccdot%2012)
Definition of division/Associative property.
6) ![x = 72 + [2\cdot 12]\cdot (10)^{-1}](https://tex.z-dn.net/?f=x%20%3D%2072%20%2B%20%5B2%5Ccdot%2012%5D%5Ccdot%20%2810%29%5E%7B-1%7D)
Associative property.
7) 
Definition of multiplication.
8) 
Definition of divsion.
9) 
Defintion of decimal number.
10) 
Definition of addition/Result
Natalia's work is wrong.
Answer:
The answer is to rotate O"N"P 180 Degrees by point N
Step-by-step explanation:
This will show the similarity between the two triangles angles.
