Hello!
Vertical asymptotes are determined by setting the denominator of a rational function to zero and then by solving for x.
Horizontal asymptotes are determined by:
1. If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.
2. If the degree of the numerator = degree of denominator, then y = leading coefficient of numerator / leading coefficient of denominator is the horizontal asymptote.
3. If degree of numerator > degree of denominator, then there is an oblique asymptote, but no horizontal asymptote.
To find the vertical asymptote:
2x² - 10 = 0
2(x² - 5) = 0
(x - √5)(x + √5) = 0
x = √5 and x = -√5
Graphing the equation, we realize that x = -√5 is not a vertical asymptote, so therefore, the only vertical asymptote is x = √5.
To find the horizontal asymptote:
If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.
Therefore, the horizontal asymptote of this function is y = 0.
Short answer: Vertical asymptote: x = √5 and horizontal asymptote: y = 0
Alright, I'll explain them as well.
1. The answer is 7, The open end of the sign is always to the larger number.
2. The answer is 4, and again, the open end of the sign is always to the bigger number.
3. The answers is two, and as before, 2 is the only number that will not make it negative or 0 and make the larger number be to the open end of the sign.
4. I'm not entirely sure on this one, so I won't answer it because I don't want to be the reason you get it incorrect.
5. For this one, divide 180 by 2.25, this will give you 80. The inequality should be 2.25k ≥ 180, k <span>≥ 80.
I hope this helps, have a nice day :)</span>
5x + 2y = 15
y = -3x - 2......so sub in -3x - 2 in for y in the other equation
5x + 2(-3x - 2) = 15
5x - 6x - 4 = 15
5x - 6x = 15 + 4
-x = 19
x = -19
y = -3x - 2
y = -3(-19) - 2
y = 57 - 2
y = 55
so ur solution is (-19,55)
Solve <span>3x+2y-6=0 for y
2y-6=-3x
2y=-3x+6
y=-1.5x+3
So the slope of the reference line is -1.5. For two lines to be parallel they must have the same slope so our line will also have a slope of -1.5 so we have:
y=-1.5x+b, now we can solve for b given the point (0,0)
0=-1.5(0)+b
0=0+b
b=0 so our line is:
y=-1.5x</span>
Answer:
magnitude = √10
theta=
= -18.435° or 341.565°
Step-by-step explanation:
hmu if u want an explanation. numbers were gotten using desmos
