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:
y = (3/5)x - 3
Step-by-step explanation:
If 3x = 4 + 5y, then
5y = 3x - 4
y = (3/5)x - 4/5
*** The given equation's <u>slope is (3/5)</u>. For the new line to be parallel to the old one, it must have <u>the same slope</u> or 'slant', 3/5.
*** The requested <u>y-intercept is </u><u>-3</u>.
For y = mx + b, 'm' is the slope and 'b' is the y-intercept.
The answer should be y = (3/5)x - 3 in 'y = mx + b' slope-intercept form.
The value of cumulative frequency is the sum of all previous frequencies. We should have 26 at the end of the table because all frequency add up to 26
To graph the cumulative frequency, we would need the plots.
Use the end of value range against the cumulative frequency valueRange 40-49, use the value 49 against the cumulative frequency 1
(49, 1)(59, 3)(69, 5)(79, 12)(89, 21)(99, 26)
Plot these on graph and connect them as a curve.
This is the concept of numbers, given that the radicals sqrt2 and sqrt3, what we can deduce from the two radicals is that they are both like terms. This is because, they don't make perfect squares now that there are no integers such that x*x=sqrt 2 or x*x=sqrt3.
They are also not equal to each other because, 2 ≠ 3
Total degree in triangle is 180.
so, 180= x + 3x + (x+60)
180 = 5x +60
5x = 180-60
5x = 120
x = 24
Largest angle is 84
Middle angle is 72
Smallest angle is 24