Answer:
5
Step-by-step explanation:
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.
Answer:
a). We want to know how much each point was worth.
b). 
c). Each problem worth 3 points.
Step-by-step explanation:
a). We want to know how much each problem was worth. Because we have the total points of the test, and how much was the bonus. But we still don't know the worth of each problem.
b). We know that the total points of the test were 41, and the bonus 5 points. There were 12 problems on the test and we are going to use "x" for the unknown part (how many points each problem was worth).
The equation is :
Why 12x? Because if you multiply the twelve problems of the test with the worth of each one and then add the 5 points of the bonus you will obtain the total points of the test (41).
c). Now we have to solve the equation, this means that we have to clear "x":
Subtract 5 from both sides.
Finally divide in 12 both sides of the equation:
Then each problem worth 3 points.
