Answer:
Ducks = 8
Horses = 17
Step-by-step explanation:
From the question;
- Total number of animals = 25
- Total number of legs = 84 legs
We are required to determine the number of ducks and horses;
We need to know that;
A duck has two legs while a horse has four legs;
Assuming there were x ducks and y horses
Then;
x + y = 25 ................................Eqn 1
And;
2x + 4y = 84 .............................Eqn 2
Solving the two equations simultaneously we can get the number of each animal.
x + y = 25
2x + 4y = 84
Multiplying the first equation by 2, we get
2x + 2y = 50
2x + 4y = 84
Subtracting the two equations;
2x + 2y = 50
2x + 4y = 84
........................................................
- 2y = -34
y = 17
Solving for x
x = 25 -17
= 8
Therefore; there were 8 ducks and 17 horses in the field
Answer:
5x/3y2
Step-by-step explanation:
The third answer
1 quarter, 6 dimes, 1 nickel, 7 pennies
Part A: f(t) = t² + 6t - 20
u = t² + 6t - 20
+ 20 + 20
u + 20 = t² + 6t
u + 20 + 9 = t² + 6t + 9
u + 29 = t² + 3t + 3t + 9
u + 29 = t(t) + t(3) + 3(t) + 3(3)
u + 29 = t(t + 3) + 3(t + 3)
u + 29 = (t + 3)(t + 3)
u + 29 = (t + 3)²
- 29 - 29
u = (t + 3)² - 29
Part B: The vertex is (-3, -29). The graph shows that it is a minimum because it shows that there is a positive sign before the x²-term, making the parabola open up and has a minimum vertex of (-3, -29).
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Part A: g(t) = 48.8t + 28 h(t) = -16t² + 90t + 50
| t | g(t) | | t | h(t) |
|-4|-167.2| | -4 | -566 |
|-3|-118.4| | -3 | -364 |
|-2| -69.6 | | -2 | -194 |
|-1| -20.8 | | -1 | -56 |
|0 | -28 | | 0 | 50 |
|1 | 76.8 | | 1 | 124 |
|2 | 125.6| | 2 | 166 |
|3 | 174.4| | 3 | 176 |
|4 | 223.2| | 4 | 154 |
The two seconds that the solution of g(t) and h(t) is located is between -1 and 4 seconds because it shows that they have two solutions, making it between -1 and 4 seconds.
Part B: The solution from Part A means that you have to find two solutions in order to know where the solutions of the two functions are located at.