Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.
Answers
Answer:
See below
Step-by-step explanation:
I assume you mean [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex]:
Holes: Since [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex] reduces to [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex], then there is a hole at [tex]x=0[/tex] as [tex]x[/tex] exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).
Vertical Asymptotes: If we further reduce [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex] to [tex]f(x)=\frac{x-2}{(x+10)(x-1)}[/tex], then we see that there are vertical asymptotes at [tex]x=-10[/tex] and [tex]x=1[/tex]
Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator ([tex]2<3[/tex]), then there is a horizontal asymptote at [tex]y=0[/tex]
Related Questions
Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.
Question 6 options:
A)
x = –3, x = –5∕2
B)
x = –3, x = 5∕2
C)
x = 5∕2, x = 3
D)
x = – 5∕2, x = 3
which one is right. keep it simple
Answers
Answer:
B) x = 3 or x = -5/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 - x = 15
Subtract 15 from both sides:
2 x^2 - x - 15 = 0
x = (1 ± sqrt((-1)^2 - 4×2 (-15)))/(2×2) = (1 ± sqrt(1 + 120))/4 = (1 ± sqrt(121))/4:
x = (1 + sqrt(121))/4 or x = (1 - sqrt(121))/4
sqrt(121) = sqrt(11^2) = 11:
x = (1 + 11)/4 or x = (1 - 11)/4
(1 + 11)/4 = 12/4 = 3:
x = 3 or x = (1 - 11)/4
(1 - 11)/4 = -10/4 = -5/2:
Answer: x = 3 or x = -5/2
help pls!! I will mark brainliest!! :(
Answers
Answer:
Three choice
Step-by-step explanation:
I think.
if a= { } b= {1,2} then n(a×b) is
Answers
Answer:
A={a,b,c}
B={1,2}
A×B={(a,1),(a,2),(b,1),(b,2),(c,1),(c,2)
What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0)?
Enter your answers in the boxes.
y−
=
(x−2)
Answers
Answer:
y = -5x + 15
Step-by-step explanation:
We'll look for a linear function of the form y = mx + b, where m is the slope and b is the y-intercept.
We can determine a slope from the two given points by calculating a Rise/Run. Starting at (2,5) and going to (3,0):
Rise = (0 - 5) = -5
Run = (3-2) = 1
Rise/Run = Slope, m) = -(5/1) or -5
Now we have y = -5x + b
To find b, enter either of the two points and solve for b. I'll use (3,0), because I know my zero multiplication and addition tables by heart.
y = -5x + b
0 = -5(3) + b
b = 15
The equation becomes y = -5x + 15
See attachment.
k/5.6+ 41.5 = 10.8
The solution is k=
Answers
Answer: The solution is k = -171.92.
Answer:
k = - 171.92
Step-by-step explanation:
[tex]\frac{k}{5.6}[/tex] + 41.5 = 10.8 ( subtract 41.5 from both sides )
[tex]\frac{k}{5.6}[/tex] = - 30.7 ( multiply both sides by 5.6 to clear the fraction )
k = - 171.92
A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward
to form an open box. If the volume of the box is 594 in,what were the original dimensions of the piece of metal?
What is the original width in inches?
Answers
(x-2)(x+5-2)(1) = 644
Now just solve for x.
The width of the piece of metal will be 24 inches while the length will be 29 inches.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
594 = w² + 2w + 3w - 6
w² + w - 600 = 0
By solving this
w = 24 so width will be 24 and length will be 24 + 5 = 29.
Hence "The width of the piece of metal will be 24 inches while the length will be 29 inches".
For more about rectangles,
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f(x) = -3x – 12
g(x) = 3x2 – 2x – 14
Answers
Answer:x
=
2
3
,
−
1
Step-by-step explanation:
What is the value of the expression
Answers
Answer:
Option C) 5/8 is correct.
For explanation, Refer to the attachment.
[tex]\Large\textsf{Hope \: It \: Helped}[/tex]
Answer:
C
Step-by-step explanation:
Substitute the values for v and w into the expression.
[tex]\frac{1}{2}[/tex] + ([tex]\frac{3}{4}[/tex] - [tex]\frac{5}{8}[/tex] )
= [tex]\frac{1}{2}[/tex] + ([tex]\frac{6}{8}[/tex] - [tex]\frac{5}{8}[/tex] )
= [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{8}[/tex]
= [tex]\frac{4}{8}[/tex] + [tex]\frac{1}{8}[/tex]
= [tex]\frac{5}{8}[/tex] → C
If 7 is subtracted from half of a number, the result is 14. Find the number.
a.41
b.42
c.43
d.44
Answers
Answer:
The number is 42.
Hope you could get an idea from here.
Doubt clarification - use comment section.
GIVING BRAINLIEST. please help!
Answers
PLEASE HELP AS SOON AS POSSIBLE I NEED TO SUBMIT THIS IN 10 MINUTES!!!!
IT GIVES 20 points!!!
Answers
Answer:
1. A. falling asleep
2. D. taking more time to wind down before bedtime
3. B. There is more than one reason that people have trouble sleeping.
4. C. The problem of falling asleep has been around for a long time and affects many people
5. A. why kids have trouble falling asleep and what they can do about it
6. A. something done over and over
Step-by-step explanation:
solve the equation (x-4) (x+9) = 0
Answers
Answer:
x = 4,-9
Step-by-step explanation:
This is a quadratic equation in x-intercept pattern. Since this is completely factored, we can simply solve the equation like a linear.
First, separate two equations. Let r be the roots of equation, therefore:
[tex]\displaystyle \large{r=\begin{cases}x-4=0\\ x+9=0 \end{cases}}[/tex]
I use the r-variable to denote the roots of equations (not necessary), simply separate both then solve it like a linear.
[tex]\displaystyle \large{r=\begin{cases}x-4+4=0+4\\ x+9-9=0-9 \end{cases}}\\\displaystyle \large{r=\begin{cases}x=4\\ x=-9 \end{cases}}[/tex]
Therefore, the roots of equation are x = 4 or x = -9. In short, we can write as x = 4,-9.
The reason why we use OR instead of AND because one of x-values satisfy the quadratic equation hence ‘or’ is more suitable than ‘and’. However, you must write all valid solutions instead of writing only one x-value from two.
___________________
Let me know in the comment if you have any questions.
a floor 9 feet by 12 feet, is to be tiled with 4-inch-by-6-inch tiles. how many tiles are needed to cover the floor?
Answers
9x12=108feet
6x4=24in
Convert 108 feet into inches which will become 1296 inches.
1296/24 will give u 54 tiles
Answer:
Step-by-step explanation:
12 inches per foot
The floor is 9(12) = 108 inches by
12(12) = 144 inches
The floor area is 108(144) = 15552 sq. In.
Each tile is 4(6) = 24 sq. in.
Need 15552/24 = 648 tiles
Group Work 2.6 Newton's Law of Cooling states that an object cools at a rate proportional to the difference between the temperature of the object and the room temperature. The temperature of the object at a time t is given by a function f(t)= alpha x^ prime prime +a where a = mc * pi temperature c = initial difference in temperature between the object and the room r = constant determined by data in the problem Suppose you make yourself a cup of tea. Initially the water has a temperature of 95 degrees * C ; 5 minutes later the tea has cooled to 65 degrees * C Problem: When will the tea reach a drinkable temperature of 40°C? Hint: Assume that the room temperature a = 22 degrees * C . First solve for r and then find tapplying the natural logarithm.
Answers
Answer:
ΔT = ΔT0 e^-K T
As I understand Newton's Law of Cooling
ΔT at any time is the difference between the temperature and the surroundings
Originally ΔT0 = 95 - 22 difference between 95 and room temperature
65 - 22 = 33 = 73 e^-KT where t is time to cool to 65 deg
ln (33/73) = -KT K = .794 / 5 = .159 where 5 is time to cool to 65 deg
40 - 22 = 73 e^-.159 T where t is time to cool to 40 deg
18 = 73 e^-.159 T
ln (18 / 73) = -.159 T
T = 8.8 min
It would take 8.8 min for the object to cool to 40 deg C
Suppose the object cooled from 95 to 90 deg, then
ln 68 / 73 = -.159 T and T = .45 min
Answer:
13.2 minutes
Step-by-step explanation:
We cannot tell what your equation is supposed to be. Usually, the equation will have the form ...
f(t) = c·e^(kt) +r
where c is the initial temperature difference (95 -22 = 73) and r is the room temperature (22). The value of k can be found from the given intermediate temperature and time.
f(5) = 65 = 73·e^(k·5) +22
43/73 = e^(5k)
Taking the natural log gives ...
5k = ln(43/73)
k = ln(43/73)/5 ≈ -0.105852
__
We want to find t for f(t) = 40. Then ...
f(t) = 40 = 73·e^(-0.105852t) +22
18/73 = e^(-0.105852t)
t = ln(18/73)/-0.105852 ≈ 13.227
The tea will be drinkable after 13.2 minutes.
__
In the attached, we have used exponential regression to find the equation of the temperature curve.
(1 pc
3. A recipe calls for 4 cups of sugar to make 4 dozen cookies. Use the proportion to calculate
how much sugar is needed to make 8 dozen cookies.
4 cups
x cups
4 dozen 8 dozen
O2 cups
08 cups
08.5 cups
0 12 cups
I really need help! I give Brainly-est
Answers
Answer:
8cups
Step-by-step explanation:
if it takes 4-cups for 4-dozen. That's 1-cup each dozen so 8-dozen is 8-cups
How do I find the percentage of two column data table?
Answers
Answer:
a) 47.7%
b) 87.2%
Step-by-step explanation:
Find the ratio of interest, and convert it to a percentage.
a)(messy right-handed writers)/(right-handed writers)
= 31/65 = 31/65 × 100% ≈ 47.7%
__
b)(neat right-handed writers)/(neat writers)
= 34/39 = 34/39 × 100% ≈ 87.2%
Farhad George and Tom each did a test here are the marks for the test George drew this bar chart to show the mask they got the butcher is not fully correct write-down two things that are wrong with George bar chart
Answers
Answer:
where is the bar chart can u post an image to help
Express the following as:
ax+by+c=0
-2x+3y=6
Answers
[tex] \color{magenta} \huge{answer}{} [/tex]
it can be expressed as -2x + 3y = 6on comparing with ax+by+c=0
We can find out that
[tex] \green{ \huge{a= -2}{} }[/tex]
[tex] \pink{ \huge{b = 3}{} }[/tex]
[tex] \color{magenta} \huge{c = 6}{} [/tex]
hope it helpsThe expression -22x + 3y = 6 in the form ax + by + c = 0 is -2x + 3y - 6 = 0
Linear EquationsThe given equation is:
-2x + 3y = 6
Comparing the equation above with ax + by + c = 0
Rewrite -2x + 3y = 6 in the form ax + by + c = 0
-2x + 3y - 6 = 0
If -2x + 3y - 6 = 0 is compared with ax + by + c = 0
a = -2, b = 3, c = -6
Therefore, the expression-22x + 3y = 6 in the form ax + by + c = 0 is -2x + 3y - 6 = 0
Learn more on linear equations here: https://brainly.com/question/14323743
how much coffee is in the cup, it the cup if 7 feet by 7 feet, and 1 cubic foot = 7.48052
How much coffee in the cup, please show how you did it with pi, volume radius etc.
Answers
Answer:
the volume of a cylinder is pi r^2 h = 3.14.(3.5)^2. 5.5=211.55 cubic foot
211.55 x 7.48052 =1583.36 gallons.
Step-by-step explanation:
A lifeguard received 15 hours of first aid training and 10 hours of CPR training. What is the ratio of hours of CPR training to hours of first aid training?
Answers
Answer:
The ratio of hours of CPR training to hours of first aid training is 10:15
Step-by-step explanation:
Find the values of the variable and the lengths of the sides.
Answers
Answer:
See answers below
Step-by-step explanation:
2x - 7 = x + 1 sides are equal
x - 7 = 1
x = 8
Find the length of each side
AD = 2x -7 BC = x + 1 AB = 2x - 2 DC = x - 1
AD = 2(8) - 7 BC = 8 + 1 AB = 2(8) - 2 DC = 8 - 1
AD = 16 - 7 BC = 9 AB = 16 - 2 DC = 7
AD = 9 AB = 14
3. Luigi lives 10 miles from work and rides his fancy Segway there each day. He rides past one
block every 45 seconds. Each block is 360 feet long. What is the rate, in feet per second at
which Luigi rides his Segway?
А
36 feet per second
B
80 feet per second
с
4.5 feet per second
D
8 feet per second
Answers
Method:
360/45=8
Tadaaaaa
Which expression shows a way to factor 20+24?
Answers
Answer:
20+24= 2(10+12) = 4(5+6)
Those are two ways to factor 20+24.
Please HELP!!!
What are the first 4 terms of the arithmetic sequence in the graph?
Enter your answers in the boxes.
_,_,_, and _
Answers
Answer:
- 3, 1, 5, 9
Step-by-step explanation:
The first 4 terms are the values of y corresponding to x = 1, 2, 3, 4 , that is
(1, - 3 ) , (2, 1 ) , (3, 5 ) , (4, 9 )
first 4 terms are - 3, 1, 5, 9
ASAP HELP Can a triangle have sides with the given lengths? Explain, showing all the work
8 ft, 9 ft, 18 ft
PLEASE EXPLAIN
Answers
Answer:
Yes
Step-by-step explanation:
the triangle is a scalene triangle (has no equal parts
Anu and Aji solve an equation. In solving Anu commits a mistake in constant term and finds the roots 8 and 2. Aji commits a mistake in the coefficient of x. The correct roots are (a) 9,1 (b)-9,1 (c) 9, -1 (d) -9.-1
Answers
The correct roots of the equation are (a) 9 and 1
From the complete question, their mistakes are:
Anu
Roots: 8 and 2Wrong constant termAji
Roots: -9 and -1Wrong coefficientA quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
Where:
[tex]\alpha\beta = \frac ca[/tex] --- product of roots
[tex]\alpha + \beta = -\frac ba[/tex] --- sum of roots
Anu made a mistake in the constant term, so we consider the sum of roots
[tex]Sum = 8 + 2[/tex]
[tex]Sum = 10[/tex]
Aji made a mistake in the coefficient, so we consider the product of roots
[tex]Product = -9 \times -1[/tex]
[tex]Product = 9[/tex]
The possible equations from the above sum and products are:
[tex]x^2 + 10x + 9 =0[/tex].[tex]x^2 - 10x + 9 =0[/tex].[tex]x^2 + 10x - 9 =0[/tex].[tex]x^2 - 10x - 9 =0[/tex]Of all the above equations, the most likely equation is [tex]x^2 - 10x + 9 =0[/tex], and it has a root of 9 and 1
Hence, the correct roots are (a) 9 and 1
Read more about roots of equations at:
https://brainly.com/question/3923172
A triangle can have the side lengths of: 1, 10, and 10.
O True
O False
Answers
Answer:
True
Step-by-step explanation:
If you do this on paper, you can make a triangle but it will be close to a line, since the two side lengths are the same and that the last side length is 1.
1.(01.01)
Evaluate -6 - (-1). (1 point)
5
-5
6
Answers
Answer:
I don't understand the question. Write it again & briefly.
Answer this question.
You get a thank you and 5 stars if it's the correct answer.
Answers
Answer:
w = 5, x = 7, y = 6, z = 12
Step-by-step explanation:
Evaluate each row by solving the corresponding equation, that is
row 1
4w = 20 ( divide both sides by 4 )
w = 5
row 2
2w + 2x = 24 ( substitute w = 5 )
2(5) + 2x = 24
10 + 2x = 24 ( subtract 10 from both sides )
2x = 14 ( divide both sides by 2 )
x = 7
row 3
w + 2x + y = 25 , that is
5 + 2(7) + y = 25
5 + 14 + y = 25
19 + y = 25 ( subtract 19 from both sides )
y = 6
row 4
w + x + y + z = 30 , that is
5 + 7 + 6 + z = 30
18 + z = 30 ( subtract 18 from both sides )
z = 12
What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form? Lin walked south, creating a right triangle. Lin walked southwest, creating an obtuse triangle. Lin walked southeast, creating an acute triangle. Lin walked directly east, creating a right triangle.
Answers
The correct statement is ''Lin can walk southwest by creating an obtuse triangle to reach his house from the gym'' and it can be determined by using the properties of triangle.
We have to determine
What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?
According to the question,
Types of Triangle;1. Lin walked south, creating a right triangle-
When someone walked in only one direction then a straight line is made by him over his path.
Here Lin can not make a right triangle just by walking in one direction.
Thus statement 1 is incorrect.
2. Lin walked southwest, creating an obtuse triangle.
When someone wants to reach a diagonal direction he can use either the right angle triangle path or the obtuse triangle.
Lin can walk southwest by creating an obtuse triangle to reach his house from the gym.
Thus statement 2 is correct.
3. Lin walked southeast, creating an acute triangle.
Actuate triangle is a triangle in which all three angles are less than the right angles (90 degrees).
With walking in actuate triangle one can make Lin can not go in his diagonal direction.
Thus statement 3 is incorrect.
4. Lin walked directly east, creating a right triangle.
When someone walked in only one direction then a straight line is made by him over his path.
Here Lin can not make a right triangle just by walking in one direction.
Thus statement 4 is incorrect.
Hence, Lin can walk southwest by creating an obtuse triangle to reach his house from the gym. Thus statement 2 is correct.
For more details about the Equation refer to the link given below.
https://brainly.com/question/9719077
Answer:
its B Lin walked southwest, creating an obtuse triangle