Using the following function, explain how the following features (asymptotes,
intercepts, holes) can be identified/constructed in the graph.
3(2-3)(x+2)(x-4)/8(6+9) (2-3)
Answers
The given asymptote, intercepts and holes of the given function depends
on the numerator and denominator of the function from which we have;
The vertical asymptote is the line x = -9The x-intercept occurs at the points, x = -2, and x = 4, the y-intercept is located at the point at which y = [tex]-\dfrac{1}{3}[/tex]The hole is at the point (3, 0)How can the properties of the function be found?The given function is presented as follows;
[tex]f(x) = \mathbf{ \dfrac{3 \cdot (x - 3) \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9) \cdot (x - 3)}}[/tex]
Given that there is a common factor of (x - 3) in the numerator and the denominator, we have;
[tex]f(x) = \mathbf{\dfrac{3 \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9)}}[/tex]
The asymptote is obtained by equating the denominator to zero as follows;
8·(x + 9) = 0
x = -9
The asymptote is the line x = -9The intercepts is given by the points the x or y-value are zero, which gives;
[tex]At \ an \ intercept, \ f(x) = \dfrac{3 \cdot (x - 3) \cdot (x + 2) \cdot (x - 4)}{8 \cdot (x + 9) \cdot (x - 3)}= 0[/tex]
3·(x - 3)·(x + 2)·(x - 4) = 0
Therefore;
x = -2, x = 4 at the x-intercepts[tex]At \ the \ \mathbf{y-intercept}, \ f(0) = \dfrac{3 \cdot (0- 3) \cdot (0 + 2) \cdot (0 - 4)}{8 \cdot (0 + 9) \cdot (0 - 3)}= -\dfrac{1}{3}[/tex]
The hole is given by the point where the function is zero.
Placing (x - 3) = 0 in the denominator
Therefore;
A hole is the point x = 3Learn more about asymptotes and intercepts here:
https://brainly.com/question/9170705
Related Questions
How to solve x/2-y/3=1, x-y/4=4 using method of elimination
Answers
Answer:x+y=14 .....(1)x−y=4 ......(2)On adding 1 and 2, we get,2x=18x=9Putting this value in equation 2, we get,9−y=4y=5Hence, x=9 and y=5.
Choose the student who correctly used substitution to determine if 19 was a solution to the equation. 6 m = 24. 6 19 = 24. 24 = 24. 19 is a solution. 6 m = 24. 6 19 = 24. 25 not-equals 24. 19 is not a solution. 6 m = 24. 6 24 = 24. 30 not-equals 24. 19 is not a solution. 6 m = 24. 6 19 = 24. 25 = 24. 19 is a solution.
Answers
Answer:
it is Juan’s work I just did the answer it works
Step-by-step explanation:
The value of a professional basketball player's autograph rose 30% in the last year. It is now worth $351.00. What was it worth a year ago?
Answers
Answer:
$270
Step-by-step explanation:
130%/100%=$351/X
(351*100)/130=$270
Corresponding Angles
I
16. Given that I lm, find the value of 'X'.
4x + 10
m
8x – 25
Answers
Answer:
x = 8.75
Step-by-step explanation:
The given angles are corresponding and congruent, thus
8x - 25 = 4x + 10 ( subtract 4x from both sides )
4x - 25 = 10 ( add 25 to both sides )
4x = 35 ( divide both sides by 4 )
x = 8.75
Please solve the equation shown below
Answers
Answer: slope = [tex]\frac{6}{4}[/tex]
Step-by-step explanation:
To find the slope, choose two points. (0,0) and (4,6)
slope = (y2 - y1) / (x2 - x1) = (6 - 0) / (4 - 0) = 6 / 4
I want to choose a license plate which is 3 characters long, where the first character is a letter, the last character is a digit, and the middle is either a letter or a digit. I also want there to be two characters on my license plate which are the same. How many ways are there for me to choose a license plate with these restrictions
Answers
Answer:
Step-by-step explanation:
* * *
let the middle digit is a letter.
as first and second letters are same so consider them as one letter.
It can be filled in 26 ways.
third place is filled in 10 ways (0,1,2,3,4,5,6,7,8,9)
total number of ways=26×10=260 ways
again consider second place is a digit.
so consider second and third place as one digit.
it can be filled in ways=10
first place can be filled in ways=26
Hence number of ways=26×10=260
so total number of ways=260+260=520
5. The diagram shows two paths that lead through a park. Would a jogger run a greater distance on Path A
or Path B? Explain.
Answers
Answer:
I wish I've known, but try using Symbo-Lab or Math-Way. They help a lot.
Step-by-step explanation:
which number comes after 3,265 and before 5,631?
Answers
Step-by-step explanation:
after 3265 , 3266 will come
before 5631 , 5632 will come
2x and 2y are like terms. True False
plzzz help mee
Answers
false bc one's an x and the other's a y.
Step-by-step explanation:
The answer is false. 2x and 2y are no like terms because they do not have the same variable
Determine the x- and y-intercepts of the graph of 3x+9y=18. Then plot the intercepts to graph the equation.
Answers
Answer:
[tex]x[/tex] intercept is at (6, 0).
[tex]y[/tex] intercept is at (0, 2).
Step-by-step explanation:
Given the equation of graph:
[tex]3x+9y=18[/tex]
To find:
[tex]x[/tex] and [tex]y[/tex] intercepts of the graph and then plotting the graph.
Solution:
[tex]x[/tex] intercept is the point on graph where the value of [tex]y[/tex] coordinate is zero.
[tex]y[/tex] intercept is the point on graph where the value of [tex]x[/tex] coordinate is zero.
Putting [tex]y=0[/tex] :
[tex]3x=18\\\Rightarrow x = 6[/tex]
So, [tex]x[/tex] intercept is at (6, 0).
Putting [tex]x=0[/tex] :
[tex]9y=18\\\Rightarrow y = 2[/tex]
So, [tex]y[/tex] intercept is at (0, 2).
Plotting the points of [tex]x[/tex] and [tex]y[/tex] intercepts on the graph and joining them to form the graph of given equation.
1. How does the distance formula help me know if two or three sides of a triangle are equal?
Answers
The distance formula is commonly seen as:
D= √(x1−x2)2+(y1−y2)2
We commonly write the Pythagorean Theorem as:
c= √a2+b2
Consider the following major points (in Euclidean geometry on a Cartesian coordinate axis):
The definition of a distance from
x
to ±c is |x−c|
.
There is the relationship where
√(x−c)2=|x−c|=x−c
AND −x+c
The distance from one point to another is the definition of a line segment.
Any diagonal line segment has an
x
component and a
y
component, due to the fact that a slope is
Δy/Δx
. The greater the
y
contribution, the steeper the slope. The greater the
x
contribution, the flatter the slope.
What do you see in these formulas? Have you ever tried drawing a triangle on a Cartesian coordinate system? If so, you should see that these are two formulas relating the diagonal distance on a right triangle that is composed of two component distances
x
and
y
.
Or, we could put it another way through substitutions based on the distance definitions above. Let:
x1−x2=±ay1−y2=±b
(depending on if x1>x2 or x1
If 5 a = 45, ba= 1, then b=
Answers
Answer:
1/9
Step-by-step explanation:
5a=45
divide it by 5 and a will =9
9b=1
divide 1 by 9
you get 1/9=b
therefore 9x1/9=1
3x - 5y = 15.
(a) Create a table of values for at least 4 points. Show your work on how you found the values for each
coordinate pair, and validated the points were on the line.
Work for Point 1
Work for Point 2
Work for Point 3
Work for Point 4
Answers
Answer:
[tex](0,-3)[/tex]
[tex](5,0)[/tex]
[tex](10,3)[/tex]
[tex](20,9)[/tex]
Step-by-step explanation:
Given
[tex]3x - 5y = 15[/tex]
Required
Form 4 pairs of (x,y) values
This question will be answered based on assumptions of x and y values;
Haven said that:
For point 1
Take x = 0
Substitute 0 for x in [tex]3x - 5y = 15[/tex]
[tex]3(0) -5y = 15[/tex]
[tex]-5y = 15[/tex]
Solve for y
[tex]y = 15/-5[/tex]
[tex]y = -3[/tex]
So; the first pair is:
[tex](0,-3)[/tex]
For point 2:
Take y = 0
Substitute 0 for y in [tex]3x - 5y = 15[/tex]
[tex]3x - 5(0) = 15[/tex]
[tex]3x = 15[/tex]
Solve for x
[tex]x = 15/3[/tex]
[tex]x = 5[/tex]
So, the pair is
[tex](5,0)[/tex]
For point 3:
Take x = 10
Substitute 10 for x in [tex]3x - 5y = 15[/tex]
[tex]3(10) - 5y = 15[/tex]
[tex]30 - 5y = 15[/tex]
Collect Like Terms
[tex]-5y = 15 - 30[/tex]
[tex]-5y = -15[/tex]
Solve for y
[tex]y = -15/-5[/tex]
[tex]y = 3[/tex]
So, the pair is:
[tex](10,3)[/tex]
For point 4:
Take y = 9
Substitute 9 for y in [tex]3x - 5y = 15[/tex]
[tex]3x - 5(9) = 15[/tex]
[tex]3x - 45 = 15[/tex]
Collect Like Terms
[tex]3x = 45 + 15[/tex]
[tex]3x = 60[/tex]
Solve for x
[tex]x = 60/3[/tex]
[tex]x = 20[/tex]
So, the pair is:
[tex](20,9)[/tex]
Answer:
the guy above me his answer is correct
Step-by-step explanation:
i got a A on my TGA
A company advertises that all of its bottles will now contain 20% more shampoo. jill writes the expression x+0.2x to represent how many ounces of shampoo will now be in a bottle that originally had x ounces. which expression also shows an increase by 20%
Answers
A 0.32-kg ball is moving horizontally at 30 m/s just before suddenly bouncing off a wall Just after the bounce, it is moving horizontally at 25 m/s but in the opposite direction. DOK 1 (4 marks) (a) What is the magnitude of the change in momentum of the ball during the bounce? (b) What percentage of the ball's original kinetic energy was lost in the collision?
Answers
We will see that the change in momentum is P' - P = -17.6 kg*m/s, and the percentage of kinetic energy lost is 30.56%.
How to get the change in momentum?The momentum is given by the product between the mass and the speed.
So the original momentum is:
P = 0.32kg*30m/s = 9.6 kg*m/s
After the bounce, the new velocity is -25m/s, then the new momentum is:
P' = 0.32kg*-25 m/s = -8 kg*m/s
The change in momentum is:
P' - P = -8 kg*m/s - 9.6 kg*m/s = -17.6 kg*m/s
How to get the change in kinetic energy?The kinetic energy is:
KE = (1/2)*M*v^2
The initial kinetic energy is:
KE = (1/2)*0.32kg*(30 m/s)^2 = 144 J
The final kinetic energy is:
KE = (1/2)*0.32kg*(-25 m/s)^2 = 100 J
The percentage lost is:
P = 100%*(144 J - 100J)/(144 J) = 30.56%
If you want to learn more about the momentum, you can read:
https://brainly.com/question/7538238
find the equation of the line
Answers
Answer:
[tex]\mathsf{y=-\dfrac13x+5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]\mathsf{y=mx+b}[/tex]
(where m is the slope and b is the y-intercept)
From inspection of the graph, the y-intercept is at (0, 5)
Therefore, b = 5
Choose another point on the line, e.g. (3, 4)
Now use the slope formula to find the slope:
[tex]\mathsf{slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where:
[tex]\mathsf{(x_1,y_1)=(0,5)}[/tex][tex]\mathsf{(x_2,y_2)=(3,4)}[/tex][tex]\implies \mathsf{slope=\dfrac{5-4}{0-3}=-\dfrac13}[/tex]
Therefore, the equation of the line is:
[tex]\mathsf{y=-\dfrac13x+5}[/tex]
Answer:
[tex]y=-\frac{1}{3} + 5[/tex]
Step-by-step explanation:
Pick two points (0,5) & (3,4) find the slope [tex]m= \frac{y_{2} - y_1 }{x_2 - x_1}[/tex] >> [tex]m = \frac{4-5}{3-0} = -\frac{1}{3}[/tex]Find y-intercept (where x is 0) >> y = 5what is the answer to this equation using the quadratic formula?
3x^2+2x+4x=0
Answers
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+4}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(4)}}{2(3)}\implies x=\cfrac{-2\pm \sqrt{4-48}}{6}[/tex]
[tex]x=\cfrac{-2\pm \sqrt{-44}}{6}\implies x=\cfrac{-2\pm \sqrt{(-1)(2^2)(11)}}{6}\implies x=\cfrac{-2\pm 2~i\sqrt{11}}{6} \\\\\\ x=\cfrac{2(-1\pm i\sqrt{11})}{6}\implies x=\cfrac{-1\pm i \sqrt{11}}{3}[/tex]
mind you that it has two complex roots, or imaginary values.
A local school has clubs. The number of students in each club is shown in the bar graph below. Use this bar graph to answer the questions.
(a) Which club has the most students?
Drama
Glee
Debate
French
Math
Chess
How many students does that club have?
(b) How many more students are in the Glee Club than in the Debate Club?
(c) How many clubs have fewer than 6 students?
Answers
five more than the quotient of a number and eight is 42
Answers
Answer:
5+n/8= 42
Step-by-step explanation:
Answer:
5+n/8= 42
Step-by-step explanation:
Evaluate 2^−1 + 2^−1.
Answers
Answer:
1
Step-by-step explanation:
2^−1 + 2^−1
2x2^-1
1
800x40 explanation pls
Answers
Answer:
800x40=32000
Step-by-step explanation:
Basically its 800 40 times.
Answer:
32,000
Step-by-step explanation:
First put 800 over 40
Second, multiply the 3rd zero by the first zero of 40
Multiply the 2nd zero by the same zero of 40
Multiply 8 by 4 and the result should be 800
Then you multiply 800 by 4.
0 x 4 is 0
0 x 4 is 0
8 x 4 is 32
(Make sure you add the zero from 40)
Put it together and you get 32,000
Pleaseeeee neeeddd helppp asappp
Answers
ANSWER:
Segment TS is a Chord
If AR = 14 , then QS = 14 ×2 = 28
∆ATS is an Isosceles Triangle
HOPE THIS HELP YOU , FOR ANY QUESTION PLEASE ASK ME
A d = 15
B c= 30
C b = 20
D a=9
Answers
Answer: A, C, D
Step-by-step explanation:
solve for x please help me
Answers
Answer:
wpowie
Step-by-step explanation:hhh
Pls help me I'm stuck
Answers
Answer
72°
Step-by-step explanation:
[tex]because\ AC=AB\ therefore\ < ACB= < ABC=6x\\ And\ because\ the\ sum\ of\ the\ angles\ of\ a\ triangle\\ is\ 180\ .\\ therefore\ < ACB+ < ABC+ < CAB=180\ degrees\\ 3x+6x+6x=180\ degrees\\ 15x=180\ degrees\\ x=12\ degrees\\ < ABC=6x=6\times12\ degrees=72\ degrees[/tex]
I hope this helps you
:)
Answer:
∠ABC = 72°
Step-by-step explanation:
When we look at the triangle carefully, we can see a bar on AC and AB. Those bars define that AC and AB are equivalent. This also means that the triangle is isosceles. Since this triangle is isosceles, the base angles of the triangle are equivalent.
⇒ AB = AC
We also know that the sum of its interior angles must be 180°.
⇒ ∠A + ∠B + ∠C = 180
Let's substitute their angle measures.
⇒ 3x + 6x + 6x = 180 [∠BAC = 3x; ∠ABC = ∠ACB = 6x]
Now, let's solve for x.
⇒ 3x + 6x + 6x = 180
⇒ 15x = 180
⇒ 15x/15 = 180/15
⇒ x = 12
Now, substitute the value of x into "6x" to find ∠ABC.
∠ABC = 6x
⇒ ∠ABC = 6(12)
⇒ ∠ABC = 72°
need help!!!!!!!!!!!!!
Answers
Answer:
3rd answer
Step-by-step explanation:
they all need to be parallel so that the angles are congruent
What is the answer for 20−2⋅7+1−(−3)+10
Answers
Answer:
20
Hope that helps!
Answer:
2
Step-by-step explanation:PEMDAS first multiply 2 and 7 you get 14 then add 1 that's 15 then add 10 that's 25 after that subtract 20 thats 5 then subtract 3 that's 2
4
(17) Billy has a babysitting job where he works the exactly 23
hours every day. After 16 days, how many hours will Billy
have worked?
Answers
Answer: 368 hours
Step-by-step explanation:
if hes working 23 hours every day, he will have worked 16x23 = 368 hours in 16 days
9. A motocross ramp is 12 feet tall and 24 feet long. What is the slope of the 1
ramp as a fraction in lowest terms? (Think rise over run.) *
12 ft
24 ft
O 12/24
O 24/12
O 1/2
0 2/1
Answers
Answer:
1/2
Step-by-step explanation:
12 is the rise 24 is the run
12/24 simplified is 1/2
The required slope of the given ramp is given by 1/2. Option C is correct.
Given that,
A motocross ramp is 12 feet tall and 24 feet long. What is the slope of the ramp as a fraction in the lowest terms is to be determined.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the ramp is evaluated as,
= vertical height / horizontal distance,
= 12 / 24
= 1 / 2
Thus, the required slope of the given ramp is given by 1/2. Option C is correct.
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ2
What is the correct answer for the first and second blank?
Answers
Answer:
Below.
Step-by-step explanation:
Using the given equation the rock will fall 16*(2)^2
= 16 * 4
= 64 feet in 2 seconds.
Therefore the rock will not hit the water in 2 seconds.