Answer:
y = 1 + 1/((x -1)(x -4))
Step-by-step explanation:
To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.
To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.
Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.
... y = 1 + 1/((x -1)(x -4))
If you like, this can be "simplified" to ...
... y = (x² -5x +5)/(x² -5x +4)
_____
In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).
Answer:
Step-by-step explanation:
3
Answer:
One solution. (x,y) = (-5,25)
Step-by-step explanation:
y = -5x
x + y = 20
x + (-5x) = 20
-4x = 20
x = -5
y = -5 (-5)
y = 25
Answer:
Step-by-step explanation:
<u>According to the triangle inequality theorem, any side length is less than the sum of the other two:</u>
- x < 2x + 1 + x + 4 ⇒ x < 3x + 5 ⇒ 2x > - 5 ⇒ x > - 2.5
- 2x + 1 < x + x + 4 ⇒ 2x + 1 < 2x + 4 ⇒ 1 < 4, any value of x
- x + 4 < x + 2x + 1 ⇒ x + 4 < 3x + 1 ⇒ 2x > 3 ⇒ x > 3/2
<u>Common solution of the three inequalities above is:</u>
Correct choice is C
Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
<h3>Form of quadratic equation</h3>
The form of quadratic equations is given as
ax2 + bx + c = 0
So, for the quadratic equation, we have
x² - x = 12
Let's make it into quadratic form
x² - x - 12 = 0
Bill solved it as
x(x - 1) = 12
This is wrong, because quadratic equations must be written in the form before solving for the variables
Jenna solved it as
x 2 - x - 12 = 0
Jenna is correct because she converted the equation to a quadratic form before solving for the variables.
Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
Learn more about quadratic equations here:
brainly.com/question/7784687
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