Answer:
Part 1)
A
Part 2)
C
Step-by-step explanation:
1)
We are given:
And that:
And we want to now for which values of x is h(x) undefined.
So, by substitution:
Remember that for rational functions, the function will be undefined if and only if the denominator is 0.
This is because we cannot divide by 0.
So, to find the values for which the denominator is 0, set the denominator to 0 and solve for x. Therefore:
Add 9 to both sides:
Take the square root of both sides. Since we are taking an even-root, we will need plus/minus. Therefore:
So, h(x) is undefined for ±3.
Our answer is A.
2)
We are given:
And we want to find:
So:
Distribute:
Combine like terms:
Rewrite:
Factor out:
So, our answer is C.
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 = 4
b = 4
Step-by-step explanation:
This is a special right triangle with angle measures of 45° 45° 90° and side lengths x x x√2