Will mark brainliest and give 20 points! In what ways can vertical, horizontal, and oblique asymptotes be identified? Please use your own example to identify.
Answers
When you have a rational expression in which the denominator is zero, you have a vertical asymptote. So to find vertical asymptotes, just set the denominator of your rational expression equal to zero, and then, solve for [tex]x[/tex]:
[tex] \frac{x-1}{x-3} [/tex]
Set the denominator equal to zero:
[tex]x-3=0[/tex]
Solve for [tex]x[/tex]:
[tex]x=3[/tex] is the vertical asymptote of our rational expression.
Horizontal asymptote:
Here we have two scenarios.
1) Is the degree of the denominator is higher than the degree of the numerator, you will have a horizontal asymptote at [tex]y=0[/tex]:
[tex]y= \frac{x-1}{x^{2}+3} [/tex]
Since the degree of the denominator is higher of the degree of the numerator, our rational expression will have an asymptote at [tex]y=0[/tex]
2) If the degree of both denominator and numerator is the same, the rational expression will have an horizontal asymptote at the ratio of the leading coefficients:
[tex] \frac{3x^{2}+5}{2x^2-3x+1} [/tex]
Leading coefficients: 3 and 2
Ratio of leading coefficients:
[tex] \frac{3}{2} [/tex]. Our rational expression will have an horizontal asymptote at [tex]y= \frac{3}{2} [/tex]
Oblique asymptote:
If the degree of the numerator is higher than the degree of the numerator, you will have an oblique asymptote. To find it, we are going to perform long division; the quotient (without the remainder) will be the equation of the oblique asymptote line:
[tex] \frac{x^2+5x+2}{x+1} [/tex]
The quotient of the long division is [tex]x-1[/tex] with a remainder of 2; therefore, the equation of the oblique asymptote line will be:
[tex]y=x+4[/tex]
Related Questions
A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What are the coordinates of A’?
A. (1,-4)
B. (-5,2)
C. (1,10)
D. (11,2)
Answers
Solution:
The Point in the coordinate plane is A(-5,-4).
Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is
[tex]=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7[/tex]
When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).
Now, the Point B is translated by the rule , (x,y)—->(x+6,y),
So,the point B is translated to, (-5+6,10)=(1,10)
Option C: (1,10) is the glide reflection of point A(-5,-4).
The coordinates of A' after the glide reflection (translation and reflection over y = 3) from A(-5, -4) are (1, -4), so the answer is A.
In a glide reflection, first apply a translation and then a reflection. Let's follow the given transformations step by step:
Translation: (x, y) → (x + 6, y)
This means you move the point A(-5, -4) six units to the right and keep the same y-coordinate. Applying the translation:
A' = (-5 + 6, -4)
= (1, -4)
Reflection over the line y = 3:
In this reflection, points above the line will move below it and vice versa, while points on the line will remain unchanged.
Since the original point A(-5, -4) is below the line y = 3, its reflection A' will be above the line.
Therefore, the coordinates of A' are (1, -4) ,the correct option is A. (1, -4).
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Which expression gives the area of the triangle shown below?
Answers
On this picture the base is the length of the bottom part of the triangle (c). It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90 degree angle). X is the height of the triangle.
Therefore, 1/2cx is the answer.
The expression gives the area of the triangle shown below 1/2cx is the answer.
The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.
What is the formula of the triangle?
The formula of a triangle
A=1/2bh.
In this picture, the base is the length of the bottom part of the triangle (c).
It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).
X is the height of the triangle.
Therefore, 1/2cx is the answer.
So option D is correct.
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Find the equation of the axis of symmetry for the parabola y = x2 + 4x – 5 .
Answers
[tex]x = - \frac{b}{2a} [/tex]
[tex]x = - \frac{4}{2} [/tex]
[tex]x = - 2[/tex]
Help!! Would the answer be c??
The steps below show the incomplete solution to find the value of x for the equation 7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step? (4 points)
Select one:
a. 4x = 24
b. 4x = 16
c. 4x = 5
d. 4x = 80
Answers
Answer: is a
Step-by-step explanation:
In triangle abc, ac=10, bc=8, angle b =90 degrees and angle bda = 90. how long is line bd
Answers
we know that
applying the Pythagorean theorem in triangle ABC
AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6
in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4
in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1
in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2
equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)----------> BD=4.8 units
the answer is BD=4.8 units
make w the subject of the formula y-aw=2w-1
Answers
Solution step by step:
1) given formula: y-aw=2w-1
2) transpose aw and - 1
2w + aw = y + 1
3) common factor w:
w (a + 2) = y + 1
4) divide both sides by (a + 2):
w = [ y + 1] / [a + 2]
To make w the subject of the formula y-aw=2w-1, rearrange the equation as follows: add aw to both sides, factor out w on the right side, add 1 to both sides, and then divide by (a+2). The final equation is w=(y+1)/(a+2).
Explanation:The question is asking to rearrange the given formula y-aw=2w-1 to solve for the variable w. We can follow these steps:
Add aw to both sides of the equation to eliminate it on the left side. This gives us y=aw+2w-1. Factor out w from the right side. This gives us y=w(a+2)-1. Add 1 to both sides of the equation to eliminate it on the right side. This gives us y+1=w(a+2). Divide both sides of the equation by (a+2) to isolate w. This gives us w=(y+1)/(a+2).
Therefore, in the formula y-aw=2w-1, w=(y+1)/(a+2) when solved for w.
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Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
Answers
you can do this by dividing 10 and 1,000,000
The t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
To model the population of cells, we can use an exponential growth equation. Since the population doubles every day, the equation would be:
[tex]P(t)=P_{0} *2^{t}[/tex]
Where:
[tex]P(t)[/tex] is the population size at time t.
[tex]P_{0}[/tex] is the initial population size ([tex]10[/tex] cells in this case).
[tex]t[/tex] is the time in days.
So, for this scenario, the equation becomes:
[tex]P(t)=10*2^{t}[/tex]
Now, we want to find out how many days it will take for the population to reach [tex]1,000,000[/tex] cells. We can set up the equation:
[tex]1,000,000=10*2^{t}[/tex]
To solve for t, we need to isolate it. First, divide both sides by [tex]10[/tex] :
[tex]100,000=2 t[/tex]
Now, take the logarithm base 2 of both sides to solve for t:
[tex]log_{2} (100,000)=t[/tex]
Using a calculator, we find:
[tex]t=16.61[/tex]
Since t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
COMPLETE QUESTION:
Create an equation to model a population of cells which starts with [tex]10[/tex]cells and doubles in size every day. How many days will it take to reach [tex]1,000,000[/tex] cells?
please help asap! 14 points
Answers
The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 3x + 8. Which of the following shows the area of the rectangle in terms of x?
Answers
Width of the rectangle, W(x) = 4x² - 3x + 8
Area of a rectangle = Length * Width
Therefore, Area od the rectangle = 6x (4x² - 3x + 8)
= (4x² · 6x) - (3x · 6x) + (8 · 6x)
= 24x³ - 18x² + 48x
P = L X W
Now taking into account the given, we can say that:
[tex](L.W)(x) = (6x)(4 x^{2} - 3x + 8)[/tex]
Now let's simplify the expression by doing the operation and you will have this as your result:
[tex](L.W)(x) = 24x^{3} - 18x^{2} + 48x[/tex]
Create an equation to model an investment of 5000 dollars which increases 15% each year. Set up an equation to solve for how long it would take for the investment to double. ( you do not need to solve this problem)
Answers
Interest rate = 1.15
The amount increases exponentially.
Then we get the following equation
[tex]5000 \times 1.15 {}^{t} [/tex]
In this formula t represents time.
The equation of doubling time
[tex]5000 \times 1.15 {}^{t} = 10000[/tex]
[tex]1.15 {}^{t} = 2[/tex]
How do I solve this problem?
Answers
The square of the hypotenuse is equal to the sum of the squares of the other two sides. You may need to do some addition or subtraction and root-taking to find the value of interest.
4. 6^2 = 4^2 +x^2
.. x = √(36 -16) = 2√5
Match each problem (term) with its sum or difference (definition).
Term Definition
4.23 + 16.21 A) 26.09
42.3 + 1.621 B) 2.609
4.23 − 1.621 C) 20.44
42.3 − 16.21 D) 43.921
GET THIS RIGHT ILL GIVE U BRAINLIEST!!!!!!!
Answers
Each mathematical term has been calculated and the correct sum or difference matched with its definition: 4.23 + 16.21 matches with C) 20.44, 42.3 + 1.621 with D) 43.921, 4.23 - 1.621 with B) 2.609, and 42.3 - 16.21 with A) 26.09.
To match each mathematical term with its correct sum or difference, we simply perform the addition or subtraction:
4.23 − 1.621 = 2.609, so this term matches with definition B)
Each problem has been matched with its corresponding definition based on the results of the arithmetic operations.
Name the property of real numbers illustrated by the equation 16(3t + 4v) = 48t + 64v.
Answers
Therefore, the answer is: Distributive property.
As you can see, you have the equation 16(3t+4v), and when you apply the Distributive property, you obtain:
16(3t+4v)
(16)(3t)+(16)(4v)
48t+64v
HELP PLEASE!!! Which figure shows a reflection of pre-image DEFG over the x-axis ? ( there’s only an A B and C )
Answers
Please help simple math problem
Answers
When 2 lines intersect, they make vertical angles.
Vertical angles are congruent (equal).
Vertical angles are opposite one another.Supplementary angles add up to 180º = 40 degrees + 140 degrees = 180 degrees. Adjacent and Supplementary Angles = 120 + 60 = 180 degreesAdjacent angles are “side by side” and share a common ray. 130 degrees and 50 degrees.Complementary angles add up to 90º. = 60 degrees + 30 degrees = 90 degrees.
URGENT!!!! You must create a 6-character password using the letters A-Z and the numbers 0-9. Characters may be repeated. How many possible passwords are there?
Answers
hope this helps
Bianca has 3:5 The ratio of the number of books Bianca has to the number books Chrissy has 10:11 If amy has 36 books how many books does Bianca have
Answers
Combine and simplify these radicals. square root of 8 times square root of 20
Answers
sqrt(20) = sqrt(2 * 2 * 5) = 2 sqrt(5)
Now multiply
2*sqrt(2) * 2 sqrt(5)
= 2 * 2 * sqrt(2) * sqrt(5)
= 4 sqrt(10)
Answer:
√8 * √20 = 4√10
Step-by-step explanation:
√8 * √20= √(4*2) * √(4*5)
√8 * √20 = (√4)(√2)*(√4)(√5)
√8 * √20 = (2)(√2)*(2)(√5)
√8 *√20 = (2*2)(√2*√5)
√8 * √20 = (4)(√(2*5)
√8 * √20 = 4√10
Which number system BEST describes this set? {-10, 0, 28 7 , 102.9} A) integers B) natural numbers C) rational numbers D) irrational numbers
Answers
The 4 numbers in this list only all belong to the set of rational numbers. All of the other sets can be crossed off.
First, 102.9 is not an integer, so we can't select choice A.
Second, 0 is not a natural number, so we can't select choice B.
Third, none of the numbers are irrational, so we can't select choice D.
The only choice left is choice C - rational numbers.
A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B', has the coordinates (2, –3). What is the scale factor of the dilation?
110110
1515
5
10
Answers
Answer:
5
Step-by-step explanation:
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at
90
miles per hour. The eastbound train travels at
80
miles per hour. How long will it take for the two trains to be
272
miles apart?
Do not do any rounding.
Answers
272
train 2 = 80 miles per hour
90 + 80 = 170
272 / 170 = 1.6 hours = 1 hour 36 minutes
The sum of three consecutive odd integers is − 105 . find the numbers.
Answers
x+(x+2)+(x+2+2)=105
3x+2+2+2=105
3x+6=105
3x=99
x=33
so the answers would be 33, 35 and 37
Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answers
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
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BRAINLIESTTTTT ASAP!!!
Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)^2 = 3
(x − 3)^2 = 2
(x − 2)^2 = 1
(x − 1)^2 = 4
Answers
.. (x +(a/2)^2
You have a=-2, so the binomial square will be of the form (x -1)^2. You don't even need to work out the rest of it to know that ...
.. the 4th selection is appropriate.
The top of a rectangular table has an area of 100 square feet and width of 5 feet. What is the length in feet of the surface
Answers
The length of the surface of the rectangular table that has an area of 100 sq. ft is: 20 ft.
What is the Area of a Rectangle?Area of rectangle = (length)(width).
The table given has a rectangular surface.
Area of the rectangular table = 100 square feetWidth of the rectangular table = 5 feet(length)(5) = 100
Length = 100/5
Length of the rectangular table = 20 feet.
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Carl puts 1.10 in his penny bank every day in the month of July. His total savings was 55at the end of June. What’s the best estimate for Carl’s savings at the end of July
Answers
Answer:
About 85 is the answer
Compare the numbers in the following sequence and try to determine what the next number should be.
6, 9, 18, 21, 42, 45, ?
Now When i did the math I thought it might be 54 but I'm not sure can someone help me or tell me if I'm right!
Answers
6 + 3 = 9
9 * 2 = 18
18 + 3 = 21
21 * 2 = 42
42 + 3 = 45
45 * 2 = 90
90 + 3 = 93
93 * 2 = 186, etc.
Thus, the next number after 45 is 90.
If x is 6, then 7x = _____. 13 42 42x 76
Answers
Answer: 42
Step-by-step explanation:
x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x
=42
Which is a zero od the quadratic function f(x)=16x²+32x-9?
Answers
[tex]\left[\begin{array}{ccc}\Delta=b^2-4.ac\\ \\ x=\frac{-b\±\sqrt{\Delta}}{2.a}\end{array}\right][/tex]
a = 16
b = 32
c = -9
[tex] \Delta [/tex] = 32² - 4.16. (- 9)
[tex] \Delta [/tex] = 1024 - (- 576)
[tex] \Delta [/tex] = 1600
[tex] x'=\frac{-(32)+\sqrt{1600}}{2.16}=\frac{-(32)+40}{32}=\frac{8}{32}=0.25\\ \\ \\ x'' =\frac{-(32)-\sqrt{1600}}{2.16}=\frac{-(32)-40}{32}=\frac{-72}{32}=-2.25[/tex]
The coordinates of the vertices of / are G(–2, 3), H(–1, 2), and I(–3, 1). If / is reflected across the x-axis to create /, find the coordinates of the vertex located at point W.
Answers
Answer:
A. (–2, –3)
that is the answer