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Graphing Asymptotes for Rational Functions
Two copies of the same Rational Functions are shown below.
On the graph on the left, draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
On the graph on the right, draw the Vertical Asymptote and write the equation for the Vertical Asymptote underneath.
Answers
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 [tex]f(x)=\frac{2x}{x-3}[/tex]
The answer will be 2. 2 is the quotient. You only want quotient not remainder.
y=2.
Related Questions
Tim asked his classmates if they preferred rock music or pop music. The ratio of students who liked pop music to rock music was 3 to 4. If Tim asked 14 classmates, how many like pop music?
Answers
Answer:
10.5 people like pop music.
Step-by-step explanation:
3/4 like pop music
3/4 = 0.75
75% of 14 = 0.75x14=10.5
what is the LCD of 3/5, 1/10, 1/2
Answers
Solve for the variable
9b+4−8b=7
b = ?
Answers
B+4=7
B=7-4
B=3
MATH Topic - Coordinate system and Linear graphs Q.1) Complete the following tables and plot the points on the graph paper to represent the equations given below 1 2 3 X y=x+1 y=-3x (x, y) (x, y)
Answers
Step-by-step explanation:
Given Question
Complete the following tables and plot the points on the graph paper yo represents the equations given below :-
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
and
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf & \sf & \sf \\ \\ \sf (x,y)& \sf & \sf & \sf \\ \end{array}} \\ \end{gathered} \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
[tex]\rm \longmapsto\:y = x + 1[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = 1 + 1[/tex]
[tex]\rm \longmapsto\:y = 2[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = 2 + 1[/tex]
[tex]\rm \longmapsto\:y = 3[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = 3 + 1[/tex]
[tex]\rm \longmapsto\:y = 4[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = x + 1 & \sf 2 & \sf 3 & \sf 4\\ \\ \sf (x,y)& \sf (1,2) & \sf (2,3) & \sf (3,4)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , 2), (2 , 3) & (3 , 4)
---------------------------------------------
Given equation is
[tex]\rm \longmapsto\:y = - 3x[/tex]
On substituting x = 1, we get
[tex]\rm \longmapsto\:y = - 3 \times 1[/tex]
[tex]\rm \longmapsto\:y = - 3[/tex]
On substituting x = 2, we get
[tex]\rm \longmapsto\:y = - 3 \times 2[/tex]
[tex]\rm \longmapsto\:y = - 6[/tex]
On substituting x = 3, we get
[tex]\rm \longmapsto\:y = - 3 \times 3[/tex]
[tex]\rm \longmapsto\:y = - 9[/tex]
Hence,
[tex]\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf x & \bf 1 & \bf 2& \bf 3\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf y = - 3x & \sf - 3 & \sf - 6 & \sf - 9\\ \\ \sf (x,y)& \sf (1, - 3) & \sf (2, - 6) & \sf (3, - 9)\\ \end{array}} \\ \end{gathered}[/tex]
Now, draw a graph using the points (1 , - 3), (2 , - 6) & (3 , - 9)
how to find root hair
Answers
The coordinates of the vertices of □PQR are (-2,5), Q(-1,), and R(7,3). Determine whether □ PQR is a right triangle. Show Your Work. ( Will Mark Brainliest and please Do Not Repost Someone Else's Answer On Here.
Answers
Answer:
Slope of PQ
m
r
=
y
Q
−
y
P
x
Q
−
x
P
=
1
−
5
−
1
−
(
−
2
)
=
−
4
Slope of QR
m
p
=
y
R
−
y
Q
x
R
−
x
Q
=
3
−
1
7
−
(
−
1
)
=
1
4
Slope of RP
m
q
=
y
R
−
y
P
x
R
−
x
P
=
3
−
5
7
−
5
=
−
1
Since slopes PQ & PR,
m
r
=
−
1
m
p
, it's a right triangle
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
Answer: 2,208$
Step-by-step explanation:
To solve this problem, simply determine how much each attendee costs by doing 960$/30attendees = 32$/attendee. Then, simply multiply this number by 69 to get: 2,208$
Hope it helps :) and let me know if you want me to elaborate further.
Why is it more difficult to get out of debt when only paying the minimum payment?
Your entire minimum payment goes toward principal and the interest continues to compound.
The majority of your minimum payment is going toward interest and finance charges and only a small amount toward the principal.
Your credit limit always resets, so you have a lot of spending power each month.
Answers
Answer:
The majority of your minimum payment is going toward interest and finance charges and only a small amount toward the principal.
Step-by-step explanation:
help me out with this problem ?
Answers
Answer:
(-4.5, 2.5)
Step-by-step explanation:
The solution for two graphed linear equations is the intersection (The point where two lines meet or cross).
4. Allen is showing his work in simplifying -8.3 + 9.2 - 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feedback to Allen explaining the mistake he made and how to correct his work. (5 points) Step Work Reasoning −8.3 + 9.2 − 4.4 + 3.7 Original problem 1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse 2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property 3 −8.3 + (4.4 + 9.2 + 3.7) Associative property 4 −8.3 + 17.3 Simplify 5 9 Simplify
Answers
Answer:
-8.3 + 9.2 - 4.4 + 3.7
= -8.3 + 9.2 + (-4.4) + 3.7 {Additive inverse}
= -8.3 + (-4.4) + 9.2 + 3.7 {Commutative Property}
= [ -8.3 + (-4.4] + [ 9.2 + 3.7] {Associative property}
= - 12.7 + 12.9
= 0.2
Step-by-step explanation:
Find the slope of the line that passes through (−1, 3) and (1, 13).
Answers
Answer:
Step-by-step explanation:
Slope = (change in y)/ (change in x)
= (13 - 3)/(1 - (-1))
= (13 - 3)/(1 + 1)
= 10/2
= 5
If x varies directly as y,and x=18x=18when y=3.6,what is x when y=12
Answers
Answer:
x = 60
Step-by-step explanation:
Write an equation using the ratio between x and y:
18/3.6 = x/12 Multiply both sides by 12:
216/3.6 = x
60 = x
Find the total future amount for $500 invested at 2.02% for 5 years
compounded monthly.
State your answer in terms of dollars rounded to the nearest cent
(hundredth).
Do not include a $ sign with your response.
Correct Answer is but explain how
553.09
Answers
P(1+(r/12)^12t
Where p is the principal amount (starting money), r is the rate (in decimal form), and t is time
2.02% is 0.0202 in decimal form
So to plug in our values:
500(1+0.00168333)^12(5)
Plug that in the calculator and then you get
553.09134377
Round to the nearest cent (unless indicated otherwise)
And then you get
553.09
Two bicyclist are 180 miles apart when they start racing towards each other. If their speeds are 14 mph and 16 mph respectively, how long will it be before they are twenty miles apart? I WILL MARK AS BRANLIEST IF YOU GOT THIS CORRECT!
Answers
Answer:
5 hours 20 minutes
Step-by-step explanation:
Distance traveled to be 20 miles apart
180 - 20 = 160 miles
Combined speed
14 + 16 = 30 mph
time = distance / speed
t = 160/30
t = 5 1/3 hours
t = 5 hours 20 minutes
Answer:
5 hours and 20 minutes
Step-by-step explanation:
it will take them 5 hours and 20 minutes.
The lines graphed below are parallel. The slope of the red line is - What is
.
the slope of the green line?
X
-5
5
m =
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4
3
O c. -
O c c
O D.
O
3
4
Answers
Answer:
C. -4/3
Step-by-step explanation:
Parallel lines have the same gradient (steepness) and this means that they will never intersect.
Hope this helps!
The slope of the red line will be {m} = - 4/3.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
{m} is the slope of the line.
{c} is the {y} - intercept.
Given is that the straight lines graphed below are parallel.
The slope of the red line could be calculated from the points through which the line passes. The points are : (- 3, 0) and (0, 4).
{m} = (- 4 - 0)/(0 + 3)
{m} = - 4/3
Since the lines are parallel, we can write the slope of the green line as same as that of the red line.
Therefore, the slope of the red line will be {m} = - 4/3.
To solve more questions on straight line, visit the link-
https://brainly.com/question/29223887
#SPJ7
: $800 invested at a 9% interest rate for 8 years.
Answers
Answer:
576$
Step-by-step explanation:
$800×9/100×8=576$
[tex]\sqrt{72x^{7} q^{8} }[/tex]
Answers
Evaluate the expression when t = 0.2.
300t2−0.5÷t
Enter your answer as a decimal in the box.
help asap
Answers
Answer:
9.5
Step-by-step explanation:
Just put the 0.2 in the correct.
Answer:
9.5
Step-by-step explanation: I'm in K12 good luck.❣
50×54+35-44
Simplification
no spam
steps must
Answers
Answer:
=2691
Step-by-step explanation:
=2700+35−44
=2735−44
=2691
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
just write like the (this is a example) 2x+6=5x
just put m instead of x but just make it make sence
increase 600 by 8⅓ percent
Answers
Answer:
650
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
2.) Carl had 16 candles that he spent $44.56 on. If his budget was $35 dollars how much did he
go over.
Answers
Answer:
he went $9.56 over
Step-by-step explanation:
Convert the 144 km/h into meters per second
Answers
Answer:
144 Kilometers per Hour = 40 Meters per Second
Step-by-step explanation:
multiply the value in kilometers per hour by the conversion factor '0.27777777777778'.
So, 144 kilometers per hour = 144 × 0.27777777777778 = 40 meters per second.
please mark 4 brainliests.
Answer: 40 m/s
Step-by-step explanation: you can multiplied by 5/18 to convert km/h to m/s ,and you can multiplied by 18/5 to convert m/s to km/h.
plot 1 1/2 and its opposite on the number line
Answers
Answer:
the opposite of 1 1/2(1.5) is -1 1/2(-1.5)
Step-by-step explanation:
Use the functions f(x) and g(x). to evaluate below.
Answers
Given the graph and the table of functions, f(x) and g(x), the following evaluated:
a. f(0) = 9
b. g(2) = -3
c. f(-1) = 5
Given the functions, f(x) and g(x), the following can be evaluated:
a. Find f(0):
Using the table given, what we need to determine is the of the output, f(0) that an input value, x = 0, will give.
From the table, we see that when x = 0, f(x) =9.Therefore,
f(0) = 9
b. Find g(2):
From the graph, find the corresponding value of g(x) that corresponds with x = 2.
From the graph, when x = 0, g(x) = -3Therefore,
g(2) = -3
c. Find f(-1):
From the table, find the corresponding value of f(x) that corresponds with x = -1.
From the table, when x = -1, f(x) = 5Therefore,
f(-1) = 5
Learn more here:
https://brainly.com/question/19639627
Suppose that $590 is deposited into an account that pays 3.5% compounded quarterly. How long will it
will take for the account to contain at least $800? Round to the nearest year.
Answers
Answer: 9 years
Step-by-step explanation:
Let 's use the compound interest formula :
[tex]\rm \displaystyle S=A\left( 1+\frac{N}{100} \right)^{\rm \big r}[/tex]
Where N- the percentage by which we raise the price ; r-years ; A-the original price
In our case
N=3,5% ; r=? ; A=590$
And we know :
[tex]\rm \displaystyle S= 800 \\\\ 590 \left( 1+ \frac{3,5}{100} \right)^{\big {r}}=800 \\\\\\(1,035)^{\big r} = \frac{80}{59}\approx1,355 \\\\\\ r= \log_{1,035}\ 1,355=8,\underline831 \approx9 \ years[/tex]
530÷34= ? Write answer as a whole number and remainder.
Answers
Answer:
15 with a remainder of 20
Step-by-step explanation:
hope it helps :)
Answer:
168 and the remainder is 7
Step-by-step explanation:
if is wrong i'm sorry
Looking at the two, 7[tex]a^{4} b^{2} c^{2} and14abc^{6}[/tex]
what is the GCF of these
Answers
Answer:
[tex]7abc^{2}[/tex]
Step-by-step explanation:
Record the following data in the circle graph 25% of the people like science the best ,half of the people like math the best, 25% of the people like reading the best.
Answers
Answer:
ok so it would be square root 2
Step-by-step explanation:
Given: 5n - 42 = 12n; Prove: n= -6
What are the Statements
What are the Reasons
Answers
Answer:
-72=-72
Step-by-step explanation:
5n-42=12n
n=-6
5*(-6)-42 = 12*(-6)
-30-42=-72
-72=-72
So, n= -6 is the right number for this equation
