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Algebra Examples
Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)
f
(
x
)
=
10
x
2
−
1
Find where the expression
10
x
2
−
1
is undefined.
x
=
−
1
,
x
=
1
Since
10
x
2
−
1
→
∞
as
x
→
−
1
from the left and
10
x
2
−
1
→
−
∞
as
x
→
−
1
from the right, then
x
=
−
1
is a vertical asymptote.
x
=
−
1
Since
10
x
2
−
1
→
−
∞
as
x
→
1
from the left and
10
x
2
−
1
→
∞
as
x
→
1
from the right, then
x
=
1
is a vertical asymptote.
x
=
1
List all of the vertical asymptotes:
x
=
−
1
,
1
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
where
n
is the degree of the numerator and
m
is the degree of the denominator.
1. If
n
<
m
, then the x-axis,
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
.
3. If
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
and
m
.
n
=
0
m
=
2
Since
n
<
m
, the x-axis,
y
=
0
, is the horizontal asymptote.
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
1
,
1
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
image of graph
The vertical asymptotes of the given function are x = 1 and x = -1,
We have given the rational function is 10/(x²-1).
We need to find the vertical asymptotes of this function.
Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.
To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.
x²-1=0
x²=1
x=±√1
x=±1
Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.
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Desarrolla el siguiente cuadrado de binomio (2x³ - 6x)²
Answer:
[tex]4x^{6} - 24x^{4} + 36x^{2}[/tex]
Step-by-step explanation:
At a high school football game, admission is $5 for students and $10 for non-students. There were 500 people at the first game, and the school made $4,000 from admissions. In this activity, you will find the number of students and non-students at the game.
Please write the two equations algebraically and then solve :)
Answer:x = 200 students
y = 300 non-students
Step-by-step explanation:
5x + 10y = 4000
x + y = 500
Set y = 500-x
5x + 10(500-x) = 4000
5x + 5000-10x
-5x + 5000 = 4000
-5x = -1000
x = 200 students
y = 300 non-students
Let's double checks
5(200) + 10(300)
1000 + 3000 = 4000
"Just look at the graph," the player's agent said. "Phil's hits have doubled since last year. We are looking for a large raise and a long contract." Look at the graph. A bar graph titled Phil's hits has this year and last year on the x-axis, and number on the y-axis, from 100 to 200 in increments of 20. This year is 180, and last year is 120. How can you redraw this graph so it appears that Phil's hits have quadrupled since last year. a. Use the same scale and make the top bar twice as thick as the bottom bar. b. Alter the scale so the top bar appears four times as long as the bottom bar. c. Both a and b. d. Neither a or b.
Answer:
Awnser is C
Step-by-step explanation:
We just have to make the top bar seem bigger then it actually is
At Emily's summer camp, there are
6 counselors for every 40 girls. How many
counselors should the camp have for 100
girls?
Answer:
15
Step-by-step explanation:
3 counselors for every 20 girls
Answer:
15 counselors
Step-by-step explanation:
The ratio of counselors to girls is 6:40. Set this as a proportion:
[tex]\frac{6}{40}[/tex]=[tex]\frac{x}{100}[/tex]
Cross multiply to solve: 6×100=40x
600=40x
x=15
To satisfy the ratio, there needs to be 15 counselors for 100 girls.
I need help with this equation
Answer:
Here:)
Step-by-step explanation:
x= -8
Answer: x = -8
Step-by-step explanation:
8x = 4x - 32
subtract 4x from both sides
4x = -32
divide by 4 on both sides
x = -8
:)
Find the measure of the indicated arc.
pls help quickly thank you
Answer: $637
Step-by-step explanation:
1.) Select the correct equation for the following situation. Mariana had 134
crystals in her collection. This was 38 less than Rajesh's collection. How
many crystals are in Rajesh's collection?
38r = 134
r+ 38 = 134
r - 38 = 134
38 - r = 134
Answer:
r minus 38 equals to 134 this might be m not certain
The correct equation is, [tex]r-38=134[/tex] and Rajesh have 172 crystals .
Let us consider that, Rajesh had r crystals.
Mariana had 134 crystals in her collection.
Since, Rajesh has 38 more crystal than Marina . So , if we subtract 38 from crystals Rajesh have then both have equal number of crystals.
So, [tex]r-38=134[/tex]
Now, find crystals present in Rajesh collection.
[tex]r-38=134\\\\r=134+38=172[/tex]
Thus, Rajesh have 172 crystals .
Learn more about linear equation:
https://brainly.com/question/11733569
A formal proof uses all of the following components except what?
A.) theorems
B.) a set of examples
C.) geometry rules
D.) algebra rules
Answer:
The answer is B.
48 = -6a, a =
pls help hfjdjf
Answer:
a=-8
Step-by-step explanation:
what is the range of the function f(x)=-8x+13 when the domain is (-2,0,3)?
Answer:
The complete set of domain (x) and range values (y) is given by:
x y
-2 39
0 13
3 11
Step-by-step explanation:
Considering the function
[tex]f(x)=-8x+13[/tex]
As we know that the range of a function consists of the entire set of all possible resulting values of the dependent variable commanly called y or f(x), once we have substituted the domain.
Now
As the x values are -2, 0, and 3. So, the domain interval is (-2,0,3).Putting x = -2 in f(x) to determine the range for the value x = -2
[tex]f(x)=-8x+13[/tex]
[tex]f(-2)=-8(-2)+13=16+13=39[/tex]
Putting x = 0 in f(x) determine the range for the value x = 0
[tex]f(x)=-8x+13[/tex]
[tex]f(0)=-8(0)+13=0+13=13[/tex]
Putting x = 0 in f(x) determine the range for the value x = 3
[tex]f(x)=-8x+13[/tex]
[tex]f(3)=-8(3)+13=-24+13=11[/tex]
Therefore, the complete set of domain (x) and range values (y) is given by:
x y
-2 39
0 13
3 11
ivan scores 56 out of 80 marks in a maths test
what is his score as a percentage
Answer:
70%
Step-by-step explanation:
(56/80) * 100
0.7 * 100
70%
Heather has a bag with 3 marbles, 7 tennis balls, 3 apples, and 3 books. What is the ratio of books to tennis balls?
A.
(3/7) or 3:7
B.
(7/8) or 7:8
C.
(4/7) or 4:7
Answer:
B
Step-by-step explanation:
I hope it's correct and I'm thinking it is,. Sorry if it's not
Answer:
I think A
Step-by-step explanation:
3/7. Or 3:7
Cause there are 3 books and 7 tennis balls
i need the answer for this question
Answer:
x=5
y=7
(5,7)
Step-by-step explanation:
solved by substitution.
Can someone help pls
A litter of puppies had 2 white puppies and 5 brown puppies. What percent of white puppies are in the litter? Round to the nearest whole number
Answer:
29%
Step-by-step explanation:
0.28571428571 as an approximate percent is 29%. There are 2 white puppies and 7 total puppies(2 white + 5 brown)
Hope this helps!
Answer:
29%
Step-by-step explanation:
0.28571428571 is the original number which makes 29%
Hope this helps! Have a great day :)
what does x = ? need help with the pythagorean theorem
Answer:
The answer is 9
Step-by-step explanation:
set up the equation as 12^2 + b^2 = 15^2
solve the exponents and you get 144 + b^2 = 225
Then subtract 144 from both sides and get 81
After that just do the square root of 81 and you get 9
pls mark brainliest
Teresa feeds her dog 1/3 can of dog food each day. How many days can Teresa feed her dog with 5 cans of food?
Ok I need to know if I did this right so: 8^0 = 1 right (exponents) please help
Answer:
Yes that's correct. I just took a test on this not to long ago and got a 100%. I had this type of problem.
Step-by-step explanation:
Hope this helps!
Answer:
Yes you are correct. It would be one.
Step-by-step explanation:
gordon types 1800 words in 25 minutes. word per minute
Answer:
72
Step-by-step explanation:
words per minutes= 1800÷25=72
Your payment is $350 per month for 48 months and you made a 3,000 down payment?
Answer:
Your total cost would be $19800
Step-by-step explanation:
350*48
=16800
+3000
=19800
please help! i only got 9 minutes left!!
Answer:
D) -5/2
Step-by-step explanation:
(0, 5) (8, -15)
-15 - 5 = -20
8 - 0 = 8
-20/8 = -5/2
Find the equation of the line shown.
Answer:
I think that it is y= -2x +9
Step-by-step explanation:
I am sure about the slope but the y-intercept (9) might be wrong.
Mrs. Daniels recorded the weights of nine boxes of strawberries in her booth at a farmer's market. The weights of the boxes
shown.
2
What is the average weight, in pounds, of the boxes of strawberries?
OB.
OA 13 pounds
1 pounds
OC. 2 pounds
OD. 2, pounds
Reset
Next
Answer:
The answer is C. 2 pounds
Step-by-step explanation:
Add all the numbers up and then divide by the numbers of sets. The average is the same as the mean.
This is for the ones on Plato
What would be the second step in solving the equation y−16=3y?
Divide both sides by 4
Divide both sides by 2
Divide both steps by -2
Divide both steps by -4
Answer:
Divide both sides by 4
Step-by-step explanation:
Please give brainliest
Answer:
divide both sides by 2
Step-by-step explanation:
becoz first step is move the numbers
pliz give a brainliest
Name the coefficients in a +2a+3a-4a
Answer:
2,3,4
Step-by-step explanation: there next to veribuls
Phoebe, Andy and Polly share £270
Phoebe gets three times as much as Andy who gets twice as much as Polly.
How much do they each get?
Answer:
Andy gets 60
Polly gets 30
Phoebe gets 180
Can someone help me out with this please!
What is the domain and range of the function: y= 10(4) + 100
Domain: ____
Range: ____
solve each system using elimination
8x+lly = 20 5x - 11y = -59
Answer:
8x+lly=205x-11y=-59u200b
Step-by-step explanation:
i calculated it
A store sells 3 cans of beans for $9. What is the price of 7 cans of beans?
Answer:
21
Step-by-step explanation:
because you divide 9 byy 3 and you get 3 so then you do 7 x 3 7x3 is 21