Find the horizontal asymptote of the graph of the rational function. y = x^2 + 6 ———— 4^2 - 7 Identify the horizontal asymptote for the graph of the function.
Answers
Given:
[tex]y\text{ = }\frac{x^2\text{ + 6}}{4x^2\text{ -7}}[/tex]The rule for horizontal asymptote is shown below:
For the given rational function, the degree of the numerator is equal to the degree of the denominator.
Hence, the horizontal asymptote is:
[tex]\begin{gathered} y\text{ = }\frac{1}{4} \\ \\ 1\text{ is the leading coefficient of the numerator} \\ and\text{ 4 is the leading coefficient of the denominator} \end{gathered}[/tex]Answer:
[tex]y\text{ = }\frac{1}{4}\text{ \lparen Option A\rparen}[/tex]
Related Questions
Here’s the question. Let me know when u have the answer. Also, this is just apart of a homework practice
Answers
Let f(x) be a function; thus, the reflection across the y-axis of f(x) is given by f(-x).
Therefore, in our case,
[tex]g(x)=f(-x)=-(-x)^3-8(-x)^2-9(-x)+11[/tex]Simplifying,
[tex]\Rightarrow g(x)=x^3-8x^2+9x+11[/tex]Thus, the answer is g(x)=x^3-8x^2+9x+11, the first option (top to bottom).
Write the equation of a line that passes through the points (-1, 3)and (2,6)
Answers
The equation of a line in 2 point form is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]So, inputting the points, we have
[tex]\begin{gathered} \frac{y-3}{x+1}=\frac{6-3}{2+1} \\ \frac{y-3}{x+1}=\frac{3}{3}=1 \\ \text{cross multiply} \\ y-3=x+1 \\ y=x+4 \end{gathered}[/tex]So, the equation of our line is y = x + 4
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answers
Answer: 85 cm
Step-by-step explanation:
What is the missing number in the solution to 968 divided 10
Answers
968 / 10
To divide by the move the coma one place to the left
968/10 = 96.8
The graph of f is given below. Use the graph to determine the following items.
• The z-values, if any, where f has a relative maximum.
• The value(s), if any, of the relative maximum(s) of f.
• The z-values, if any, where f has a relative minimum.
• The value(s), if any, of the relative minimum(s) of f.
Answers
Part 1
Relative maxima are where the function changes from increasing to decreasing.
No x-values satisfy this.Part 2
None, see above.
Part 3
Relative minima are where the function changes from decreasing to increasing.
No x-values satisfy this.Part 4
None, see above.
3aX7a= Because I need a lot of help and I also need the answer to 7aX13a
Answers
Answer:
3a x 7a= 21a^2
Step-by-step explanation:
7a x 13a=91a^2
next sequence of 3/2, 7/2, 13/4
Answers
Order the expressions by choosing <, >, or =.
Answers
On comparing the given expressions we get-
[tex]9^{-2} < (\frac{1}{9}) ^{-1}[/tex]
[tex](\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}[/tex]
[tex]9^{-1} > 9^{-2}[/tex]
Here, we are given 3 pairs of expression. Let us evaluate them one by one.
[tex]9^{-2}[/tex] _ [tex](\frac{1}{9}) ^{-1}[/tex]
The negative exponent means that the base is the reciprocal raised to a positive power. Thus, [tex]9^{-2}[/tex] can be written as- [tex](\frac{1}{9}) ^{2}[/tex] = 1/81
similarly, [tex](\frac{1}{9}) ^{-1}[/tex] can be written as- [tex](9}) ^{1}[/tex] = 9
Thus, the expression becomes-
1/81 _ 9
clearly we can see that 1/81 < 9
Now, we have [tex](\frac{1}{9}) ^{-1}[/tex] _ [tex](\frac{1}{9}) ^{-2}[/tex]
As shown above, the expression can be simplified as-
[tex](9) ^{1}[/tex] _ [tex](9) ^{2}[/tex]
9 _ 81
clearly we can see that 9 < 81
Next, we have- [tex]9^{-1}[/tex] _ [tex]9^{-2}[/tex]
we can write this as-
1/9 _ 1/81
Clearly, 1/9 > 1/81
Hence, we have solved the given inequalities.
Learn more about inequalities here-
https://brainly.com/question/25275758
#SPJ1
Albert is in a hot air balloon that has just taken off and is now floating 20 meters above its
launching point Isabelle is standing on the ground, 21 meters away from the launching point.
How far apart are Albert and Isabelle?
meters
Answers
Albert floating in hot air balloon and Isabelle standing at ground are 29 meters far apart from each other.
What is hot air balloon?
A hot air balloon is a lighter in weigh than air. It is an object made up of an envelope-like bag that holds heated air. A wicker basket, gondola, or capsule suspended below transports people and a heat source, typically an open flame produced by burning liquid propane. A capsule also carries passengers in some long-distance or high-altitude balloons.
Lets understand with the help of a right angle triangle, The point from where the hot air balloon taken off be point A, and the point where Isabelle is standing is point B, and the point where the balloon is point C.
The AB= distance between Isabelle and the point from where hot air balloon taken off = base of the imagined triangle,
AC = height at which hot air balloon is floating = perpendicular of the imagined triangle
BC = distance between Isabelle and hot air balloon = Hypotenuse of the imagined triangle
Applying Pythagoras theorem,
(BC)² = (AC)² + (AB)²
(BC)² = (20)² + (21)²
BC = 29
Hence Albert and Isabelle are 29 meters far apart.
To know more about hot air balloon, go to link
https://brainly.com/question/7541718
#SPJ13
100CPOINTS WILL GIVE BRAINLYEST
Answers
The value of the width is 13.5 cm which is the correct answer would be option (C).
What is the volume of a rectangular prism?The volume of the rectangular prism is the product of the base area and the height.
Given that the volume of a rectangular prism is 6,142.5 cm³. The height is 16.25 cm and the length is 28 cm
The volume of the rectangular prism
V = Length × Width × Height
6,142.5 = 28 × Width × 16.25
Apply the multiplication operation,
6,142.5 = 455 × Width
Width = 6,142.5 / 455
Apply the division operation, and we get
Width = 13.5 cm
Hence, the value of the width is 13.5 cm.
Learn more about the volume here:
brainly.com/question/23118276
#SPJ1
Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.(9, 12), y = 13x-4
Answers
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of the line and (x1,y1) is a point where the line passes through.
In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is
[tex]m_1=m_2[/tex]We know that the line we are looking for is parallel to the line
[tex]y=13x-4[/tex]we notice that this line in written in the slope-intercept form
[tex]y=mx+b[/tex]then its slope is 13.
Since the line is parallel to the one we are looking for, our slope is also 13.
Using the point (9,12) and the slope the equation of the line is
[tex]y-12=13(x-9)[/tex]now we have to write in the slope-intercept form
[tex]\begin{gathered} y-12=13x-117 \\ y=13x-117+12 \\ y=13x-115 \end{gathered}[/tex]Therefore the line is
[tex]y=13x-115[/tex]evaluate the expression 2x + 3 when x = 1.6
Answers
Given the following expression:
[tex]2x+3[/tex]You need to follow the steps shown below in order to solve the exercise:
1. Since you know the value of "x", you must substitute it into the given equation:
[tex]2x+3=2(1.6)+3[/tex]2. Now you must solve the multiplication:
[tex]=3.2+3[/tex]3. Finally, you need to solve the addition in order to find the value of the expression. Therefore, you get that the result is the following:
[tex]=6.2[/tex]The answer is:
[tex]=6.2[/tex]A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 100 copies of the book. Suppose that =C+10N700 gives C as a function of N during the first printing. Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
Answers
The correct description of the values in both the domain and range of the function are;
Domain is on the interval (0, 100) which are possible values of number of copies of the book produced.
Range is on the interval (700, 1700) which are the possible total cost of publishing the book
What is the domain and the range of the function?The formula for total cost is;
Total cost = fixed cost + variable cost or
We are given the function; C = 10N + 700
Where;
C is the total cost of publishing the book (in dollars).
N is the number of copies of the book produced.
a) Domain is possible values of N.
For the first printing, the company can produce up to 100 copies of the book.
Thus, the domain is on the interval (0, 100) but only integers.
The range is the possible cost.
Possible cost maximum = 10(100) + 700 = 1700
Thus, the range is on the interval (700, 1700) where any cost in that interval is not continuous, but follows a discrete sequence.
b) Reasonable values of the domain are [0, max] where the maximum value is the largest book sales ever in the market area, maybe 50 or 75
Reasonable values for the range are [700, max] where the maximum cost is 700 + 10 *50 or 75,
or 1200 or 1450.
Read more about Domain and Range at; https://brainly.com/question/2264373
#SPJ1
How do I graph this??
Answers
According to the given equation (y = (3/4)x -2) the value of y for x:
Y = {-5 , -2 , 1 , 4}
How is a coordinate plane defined simply?A coordinate plane is just a two-dimensional plane that is created when two number lines cross. These number lines include the x-axis, a horizontal number line, and indeed the y-axis, a vertical number line.
The coordinate plane where is it?In a coordinate plane, which is a two-dimensional number line, the vertical line is known as the y-axis and the horizontal line as the x-axis, as you might recall from pre-algebra. These parallel lines cross one another at their zero points. The origin is where we start from.
According to the given data:Equation:
y = (3/4)x -2
X = {-4 , 0 , 4 , 8}
for each value of x the value of the y :
For x = -4
y = (3/4)x -2
y = (3/4)(-4) -2
y = -5
For x = 0
y = (3/4)x -2
y = (3/4)(0) -2
y = 0 -2
y = -2
For x = 4
y = (3/4)x -2
y = (3/4)(4) -2
y = 1
For x = 8
y = (3/4)x -2
y = (3/4)(8) -2
y = 6 -2
y = 4
According to the given equation (y = (3/4)x -2) the value of y for x:
Y = {-5 , -2 , 1 , 4}
To know more about coordinate plane visit:
https://brainly.com/question/13611766
#SPJ13
Working together, Adam and Pranav can mop a warehouse in 4.63 hours. Had he done it alone it would have taken Pranav 11 hours. How long would it take Adam to do it alone?
Answers
1)
Note that the more people work together the less time they spend.
This is a question about Proportions, Inverse variation. So let's set the ratios and the proportion given these data.
So we can write out the following ratios:
[tex]\begin{gathered} \frac{1}{x}+\frac{1}{11}=\frac{1}{4.63} \\ \\ \frac{x+11}{11x}=\frac{1}{4.63} \\ \\ 4.63(x+11)=11x \\ 11x=4.63(x+11) \\ 11x-4.63x=11 \\ 6.37x=11 \\ \frac{6.37x}{6.37}=\frac{11}{6.37} \\ x=7.99\approx8 \end{gathered}[/tex]So, it would take 8 hours for Adam to do it alone.
Learn with an example
Submit
Watch a video
A line's slope is 6, and its y-intercept is -3. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
dihuyyh
Step-by-step explanation:
One 60-to-65 year old man is selected at random. What is the probability of the following events?
Answers
The probabilities that have been calculated here are:
0.240.890.3330.0395How to solve for the probabilitiesThe probability that he is a smoker = 0.08 + 0.16
= 0.24
The given probability that has been calculated is 0.24.
The probability that he does not have lung disease = 0.16 + 0.73
= 0.89
The probability that he has lung disease given that he is a smoker
= 0.08 / 0.08 + 0.16
= 0.08 / 0.24
= 0.333
The probability here is calculated to be 0.333
The probability that he has lung cancer given that he does not smoke
= 0.03 / 0.03 + 0.73
= 0.03 / 0.76
= 0.0395
The given probability here is 0.0395
Read more on probability here:
https://brainly.com/question/24756209
#SPJ1
10) If f(x) = 7 – 4x and the domain is {-2,0, 3/4}, find the range.
Answers
For this case we have the following function given:
[tex]f(x)=7-4x[/tex]We also know that the domain is given by:
[tex]D=\left\lbrace -2,0,\frac{3}{4}\right\rbrace [/tex]and in order to find the range we need to use the domain given:
[tex]f(-2)=7-4(-2)=7+8=15[/tex][tex]f(0)=7-(4\cdot0)=7[/tex][tex]f(\frac{3}{4})=7-4\cdot\frac{3}{4}=7-3=4[/tex]So then the range for this case would be given by:
[tex]R=\left\lbrace 15,7,4\right\rbrace [/tex]The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?
____ cm/min
Answers
dA = (1/2)h(db) + (1/2)b(dh).
4 = (1/2)(8.5)db + (1/2)(194/8.5)(2.5), db = (4 - (1/2)(194/8.5)(2.5))/((1/2)(8.5)) =-5.77 cm/min.
875 viewsView upvotes
3
Forbes
Sponsored
What states offer the best public school systems?
WalletHub set out to determine which states have the top-ranked school systems from K-12. Read more.
Read More
276
Related questions (More answers below)
A small toy rocket is launched from a 48-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−3t'2+0t+48. How long will it take the rocket to hit the ground?
Answers
Given: A small toy rocket is launched from a 48-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula
[tex]h=-3t^2+0t+48[/tex]Required: To find out how long will it take the rocket to hit the ground.
Explanation: When the rocket hits the ground its height h=0. Hence
[tex]\begin{gathered} -3t^2+0t+48=0 \\ t^2=\frac{48}{3} \\ t^2=16 \end{gathered}[/tex]which gives
[tex]t=\pm4[/tex]Since time can't be negative. Hence t=4 seconds.
Final Answer: t=4 seconds.
.
The floor of an elevator shaft is a square with an area of 42.25 square feet. Find the length of
a side of the floor.
Chapter 2 Expor
Answers
Answer:
6.5ft
Step-by-step explanation:
[tex]A=s^{2} \\42.25=s^{2} \\\sqrt[2]{42.25}=\sqrt[2]{s} \\6.5=s[/tex]
Answer:
6.5ft
Step-by-step explanation:
what is the discrimant of x^2 +x-2=0
Answers
Answer:
Discriminant = 9.
Step-by-step explanation:
Discriminant
[tex]\boxed{b^2-4ac}\quad\textsf{when}\;ax^2+bx+c=0[/tex]
[tex]\textsf{when $b^2-4ac > 0 \implies$ two real roots}.[/tex]
[tex]\textsf{when $b^2-4ac=0 \implies$ one real root}.[/tex]
[tex]\textsf{when $b^2-4ac < 0 \implies$ no real roots}.[/tex]
Given function:
[tex]x^2+x-2=0[/tex]
Therefore:
a = 1b = 1c = -2Substitute the values of a, b and c into the discriminant formula:
[tex]\begin{aligned} \implies b^2=4ac&=(1)^2-4(1)(-2)\\&=1-4(-2)\\&=1+8\\&=9\end{aligned}[/tex]
Therefore, the discriminant of the given function is 9.
As the discriminant is greater than zero, this implies that there are two real roots.
Graph the inequality
x<5
Answers
Draw the graph of x-axis which is lesser than 5 .
What is Graph inequality ?
In mathematics, a relationship between two expressions or values that are not equal to each other is called inequality.In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.Graphing inequalities is the process of showing what part of the number line contains values that will "satisfy" the given inequality. A graph of this inequality will show what numbers may be used to replace x in our inequality to make a true statement.Linear inequalities can be graphed on a coordinate plane.The solutions for a linear inequality are in a region of the coordinate plane. A boundary line, which is the related linear equation, serves as the boundary for the region.Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities. Inequalities and equations are both math statements that compare two values.Equations use the symbol =; inequalities will be represented by the symbols <, ≤, >, and ≥.One way to visualize two-variable inequalities is to plot them on a coordinate plane.To learn more about Graph the inequality refer :
https://brainly.com/question/24372553
#SPJ13
0.25(8+x)=14 I understand just not fully
Answers
25(8+ x)=14
25*8+ 25x =14
200+ 25x= 14
25x=14-200
25x = -186
x = -186/25
x= -7.44
help please on this
Answers
Answer:
its was 100.6
Step-by-step explanation:
i hope this helps
BD bisects ZABC. Solve for x and find m ZABC.mZABD = 9x - 8. mZCBD=6x + 1XmZABC=°Enter your answer in the answer box and then click Check Answer.All parts showing
Answers
We will use the angle properties to determine the constituent angles.
We are given that a line segment ( BD ) is an angle bisector of < ABC. We will go ahead and represent this piece of information graphically as follows:
We will define the following angle as follows:
[tex]m\angle ABC\text{ = }\vartheta[/tex]The angle bisector ( BD ) divides the angle into two equal halves as follows:
[tex]m\angle ABD\text{ = m}\angle CBD\text{ = }\frac{\angle ABC}{2}=\frac{\vartheta}{2}[/tex]We are given expressions for both angles as follows:
[tex]\begin{gathered} m\angle ABD\text{ = 9x - 8 } \\ m\angle CBD\text{ = 6x + 1} \end{gathered}[/tex]We know from the property of angle bisector that the two constituent angles are equal i.e:
[tex]\begin{gathered} m\angle ABD\text{ = m}\angle CBD \\ 9x\text{ - 8 = 6x + 1} \\ 3x\text{ = 9} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 3}} \end{gathered}[/tex]Now we can use the value of ( x ) calculated above and determine either of the constituent angles as follows:
[tex]\begin{gathered} m\angle ABD\text{ = 9}\cdot(3)\text{ - 8 = 19 degrees} \\ m\angle CBD\text{ = 6}\cdot(3)\text{ + 1 = 19 degrees} \end{gathered}[/tex]Then we can use the angle bisector property relation again to determine the angle ABC as follows:
[tex]\begin{gathered} m\angle ABD\text{ = m}\angle CBD\text{ = }\frac{\angle ABC}{2} \\ 19\text{ degrees = }\frac{\angle ABC}{2} \\ \textcolor{#FF7968}{\angle ABC}\text{\textcolor{#FF7968}{ = 38 degrees}} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 3}} \\ \textcolor{#FF7968}{\angle ABC}\text{\textcolor{#FF7968}{ = 38 degrees}} \end{gathered}[/tex]PLEASE HELP ME !!!!
a) What is the real length of the ship in
centimetres?
b) What is the real length of the ship in
metres?
Answers
The real length of the ship in centimeters is 800000 cm and the real length of the ship in meters is 8000 m
What is ratio and proportion?Ratio is a comparison tool for like-kind amounts. A:B or a/B is the ratio formula for two numbers, a and b. A ratio is considered to be in proportion when two or more ratios are equal. Fractions form the foundation of the ratio and proportion concepts. The primary pillars on which many other mathematical notions are built are ratio and proportion. When comparing heights, weights, distances, or times, or when adding ingredients to a recipe, for example, ratio and proportion can be used to solve a variety of everyday problems. Ratios are created by dividing two amounts, and proportions are created when two ratios are equivalent. Different ways, such as x: y or x/y, can be used to express a ratio.
The real length in cm
= 8 000 meters in cm
= 800000 cm
The real length
= 8000 m
To know more about ratio proportion ,visit:
brainly.com/question/14023900
#SPJ13
If £25 = 800 rubles, how many £ are in 992 rubles?
Answers
Answer:
31
Step-by-step explanation:
800/25=32
992/32=31
Answer:
£31
Step-by-step explanation:
let me know if you want a through explanation
Julia had a bag filled with gumballs. There were 2 lemon-lime, 3 watermelon, and 5 grape gumballs. What is the correct sample space for the gumballs in her bag?
a. Sample space = 2, 3, 5
b. Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
c. Sample space = lemon-lime, watermelon, grape
d.Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
Answers
If Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
The number of lemon limes in the bag = 2 lemon-lime
Number of watermelon in the bag = 3 watermelon
Number of grape gumballs in the bag = 5 grape gumball
Sample space is the set of all the possible outcomes the experiment
Here there are 2 lemon-lime, 3 watermelon and 5 grape gumball
Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
Learn more about sample space here
brainly.com/question/24273864
#SPJ1
Answer:Option B is the correct answer
From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary
Answers
We will first sketch the problem
Let x be the vertical distance above the ground
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan 31=\frac{x}{316}[/tex]cross-multiply
[tex]x=316\tan 31^o[/tex][tex]x\approx189.9[/tex]