Answer:
1a: f(x) = x³ -6x² +9x -4
1b: no breaks; the function is defined everywhere
2a: (-∞, 5]
2b: y = -3; y = -1
2c: x → -∞, y → -3; x → ∞, y → -1
Step-by-step explanation:
<h3>1A:</h3>
The factored form of f(x) is ...
f(x) = (x -4)(x -1)²
f(x) = (x -4)(x² -2x +1) = x³ -2x² +x -4x² +8x -4
f(x) = x³ -6x² +9x -4
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<h3>1B:</h3>
The function h(x) is defined for all values of x to be either f(x) or g(x). The function f(x) is a polynomial function, so has no breaks in its domain. The function g(x) is defined for all values of x, so has no breaks in its domain.
There are no breaks in the domain of h(x).
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<h3>2A:</h3>
See the attachment for a graph.
-∞ < y ≤ 5 . . . . range of f(x)
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<h3>2B:</h3>
The asymptote as x → -∞ is the asymptote of the exponential function. The exponential term has an asymptote of y=0, but shifting it down 3 units means the asymptote is 0 -3:
x → -∞, y → -3 . . . . asymptote is y = -3
The asymptote as x → ∞ is the asymptote of the rational expression. That is the ratio of the leading terms: -x²/x² = -1.
x → ∞, y → -1 . . . . asymptote is y = -1
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<h3>2C:</h3>
See part B.
Answer: d. 7 and 1/2 hours
Step-by-step explanation:
Given : The time taken by Ana and Beth do a job together = 3 hours
Time taken by Ana to do a job alone = 5 hours
Let t be the time taken by Beth to do a job .
Then, According to the question ,we have
i.e. Time taken by Beth to do a job =
Hence, the time taken by Beth to do a job alone = 7 and 1/2 hours
Answer:
11+5x=5x+20
We move all terms to the left:
11+5x-(5x+20)=0
We get rid of parentheses
5x-5x-20+11=0
We add all the numbers together, and all the variables
-9!=0
There is no solution for this equation
Step-by-step explanation:
I saw it from Google
Answer:
Step-by-step explanation:
Use FOIL.
Answer:
The time it takes for the cannonball to hit the ground is 6.49 seconds.
Step-by-step explanation:
You know that the height of the cannonball above the ground, h, in meters, in time, t, in seconds, is found by the function h(t) = -4.9t² + 30.5t + 8.4. You want to calculate the time it takes for the cannonball to hit the ground, that is, the time it takes for the bullet to reach zero height. So, being h(t) = 0 you have:
0 = -4.9t² + 30.5t + 8.4
To solve a quadratic function 0=a*x² + b*x +c, the expression is applied:
In this case, being a = -4.9, b =30.5 and c =8.4 you have:
Solving you get:
t1= -0.26 seconds and t2=6.49 seconds
Since time does not have a negative value, then <u><em>the time it takes for the cannonball to hit the ground is 6.49 seconds.</em></u>