Answer:
Horizontal Asymptote: y=2
Vertical Asymptote: x=3
Step-by-step explanation:
One way: Look at graph
Look at for a horizontal or vertical line that both lines don't touch.
Second Way:
When you look for vertical asymptotes, you set the denominator equal to zero and solve.
For example, the second question has a denominator of x-3.
x-3=0
x=3 (This is the vertical asymptote)
When you look for horizontal asymptote, you do long division.
For example, the first question 
The answer will be 2. 2 is the quotient. You only want quotient not remainder.
y=2.
Answer:you get two answers. y+6=-7/4(x+5) or y-1=-7/4(x+5)
Step-by-step explanation:
By the way the 7/4 is negative if you could not tell. You get this answer by finding the slope which is 1- -6/-5- -1 and get -7/4. Then you plug it into the formula y-y1=slope(x-x1). When you plug it in you should get that answer.
Answer: Either
or
depending on your teacher's preference. See the note at the bottom for more info.
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Let x be the speed limit. It is simply a placeholder. Think of it as a box with the number inside. We don't know what the number is, but we know that the largest it can be is 55. It cannot be larger than 55.
So x can be equal to 55 or it can be smaller
Put another way, x is less than or equal to 55 which is written as
(on the keyboard you would type " x <= 55 " without quotes).
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Note: since negative speeds make no sense, we also must imply that x can't be negative. Your teacher may want you to write this in to clearly state it. If so, then you would also have
which when combined with the first inequality, you get this compound inequality
(basically saying "x is some speed between 0 and 55 mph"). This very clearly states the boundaries on what x can be. Though your teacher may want you to stick to the first format as its simpler.
Step-by-step explanation:
x + y = 16 (*)
x^2 + y^2 = 146 (**)
(*) <=> x= 16-y
substitute x = 16 - y
(**) <=> (16-y)^2 + y^2 = 146
<=> y^2 - 2.16.y + 16^2 + y^2 = 146
<=> 2y^2 - 32y + 110 = 0
<=> y^2 - 16y + 55 = 0
<=> (y-11)(y-5) = 0
<=> y=11 or y= 5
For y = 11, we have x= 16-11=5
For y=5, we have x= 16-5=11
Answer: (x,y) = (11,5) ; (5,11)
