AS we can see that there no degree in the given rational function, so, the value for horizontal asymptote will be 0.
What is the use of asymptotes?The asymptote of a curve is the location at which the curve converges. In other words, the curve and its asymptote are perpetually close, yet they never touch. Big O notation makes use of asymptotes, which are also simple approximations to complex equations and are useful for graphing rational equations among other things.
The asymptote(s) of a curve may often be found by looking at the limit of a value when the function is not defined. These points include and the point where the numerator of a rational function equals zero, as well as others.
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REMEMBER: f(2
1) If f(x) = 2x - 3,
a) f(-2) =
2. The product of √5 and which of the following numbers will result in an irrational number? A. √5 B. -√5 C. √2 D. 3√5
Answer:
C
Step-by-step explanation:
The radicands have at least one prime-factor that is not in common.
Find the midpoint of the segment with the following endpoints (4,6) (1,3)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]
PLSSSPLSS PLS HELP ME WILL GET BRIANLIEST
which option/graph
PLEASE PLEASE HELP
Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 3000feet and height of 1200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 10 inches.
What scale is Alexander using?
The scale of the drawing is 1 inch represents 300 feet .
What is the scale of the drawing?A scale drawing is a smaller image of a larger diagram or object in terms of dimensions. The scale drawing is usually reduced at a constant dimension.
In order to determine the scale of the drawing, divide the base of the actual Federal triangle by the base of the drawing.
Scale of the drawing = original dimensions / dimensions of the scale drawing
3000 / 10 = 300
1 inch represents 300 feet
1 inch : 300 feet
The scale of a drawing is usually written in this format - one a colon (:), the result of the division of the original dimension and the dimension of the scale.
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Given the algebraic expression ----- create an equivalent expression.
The equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.
This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the equivalent expression?The expression is given as
(64x^2/3)^-1/3
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^(2/3*-1/3)
Evaluate the product of the exponents
So, we have
(64x^2/3)^-1/3 = 64^-1/3 * x^-1/9
Evaluate the exponent
So, we have
(64x^2/3)^-1/3 = 1/4 * x^-1/9
Evaluate the product
So, we have
(64x^2/3)^-1/3 = 1/4x^-1/9
Rewrite as
(64x^2/3)^-1/3 = 1/(4x^1/9)
Hence, the equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)
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Please helppppp nowwwwww
Answer:
It has 2 angles right and acute
-5; -1/2; -0.05; -45% least to greatest
Answer:
-5, 1/2, -0.45, -0.05 would be the solution
Solve for w.
0.43 +2.7w = 3.7w - 0.47
Answer:
w = 0.9
Step-by-step explanation:
What I did is I subtracted 2.7 from 3.7 bc it was the least number and that gave me 1 so that left me with 0.43 = w - 0.47. Then I added 0.47 to 0.43 and that gives me 0.9 which would be the answer
If you don't understand how I got it I can try to explain a little better, but hopefully, you understand:)
what is the slope of the line that passes through the points (6, -5) and (6, -4)?
Answer (y2 -y1) / (x2 - x1)
hope this helps
Answer:
(y2 -y1) / (x2 - x1)
Step-by-step explanation:
Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.
The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
According to the given question:
Each block of horizontal is 1/8 hr = 7.5 min
Each block of vertical is 10 km/hr
Time Velocity (km/hr)
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
The acceleration in first 15 minutes = (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
The distance between the two cities =
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of train during the journey = 125/2 = 62.5 km/hr
Therefore,
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
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Find the inverse of each function. Is the inverse a function?
f(x)=2x² /5 +1
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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Enterprise will allow you to rent a car for $10 per day plus a $20 fee. Hertz will allow you to rent a car for $40 a
day. After how many days, x, will Enterprise cost more than Hertz?
Yes..............................
What would happen to a monthly payment if the interest rate increased?
OA. The payment would go up.
B. The payment would go down.
OC. The payment would remain the same.
OD. None of the above
x/a=y/b solve for x please help my homework is due today
h3lp
Which graph is the graph of the function [tex]g(x)=\frac{x^{2}-x }{x^{2} -1}[/tex]
see screenshot for answer choices
Answer:
A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.
Step-by-step explanation:
How much water would you have if you combine all wars together of 1/2 ,1/3 and 1/6 but you have to rewrite with common denominators and then solve
The addition of the fractions means that the value when combined is 1.
How to calculate the fraction?It should be noted that based on the information given, we simply have to add the fractions that are given and this will be:
= 1/2 + 1/3 + 1/6
= 3/6 + 2/6 + 1/6
= 6/6
= 1
Therefore, the addition of the fractions means that the value when combined is 1.
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Someone answer this plsss
The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
From the question, we are to determine the equation of the line that is perpendicular to the given equation.
A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
That is,
If m₁ is the slope of one of the lines
and m₂ is the slope of the other line
Then,
m₁ = -1/m₂
First, we will determine the slope of the given line
The equation of the given line is
y = 3x - 9
Compare the equation to the general form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
By comparison,
m = 3
∴ The slope of the given line is 3
Thus,
The slope of the line that is perpendicular to this line is -1/3
Now,
To determine the equation this line,
We have that the line passes through the point (3, 1)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
m = -1/3
x₁ = 3
y₁ = 1
Putting the parameters into the equation,
y - 1 = -1/3(x - 3)
Expressing the equation in standard form
3(y -1) = -1(x - 3)
3y - 3 = -x + 3
3y + x = 3 + 3
x + 3y = 6
Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6
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turn 4 3/5 into a decimal
Answer:
4.6
Step-by-step explanation:
1. Multiply the whole number by the denominator
4 x 5 = 20
2. Add the result of step 1 to the numerator
20 + 3 = 23
3. Divide the result of step 2 by the denominator
23 ÷ 5 = 4.6
Quotients Great and Small
Diving fractions
Thanks so much please show work!
1. 5/6 ÷ 5/8 or. 5/6 x 8/5=
2. 5/9 ÷ 1/2 or. 5/9 x 2/1 =
3. 9/10 ÷ 3/5 or. 9/10 x 5/3=
Step-by-step explanation:
GOOD RIGHT?
i need all 3 im confused on them
Answer:
1. 5/12 in exact form and 0.416 in decimal form
2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.
On each "6" there's a - on top!
ashley drove 605 miles in 11 hours at the same rate how long would it take her to drive 495 miles
Answer:
9 hours
Step-by-step explanation:
605 miles/11 hours = 55miles/hour
495 miles (time) = 495 / 55 =9
So, 9 hours
A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
The side length of the square in centimeters is 13 centimeters
What are areas?The area of a shape is the amount of space on the shape
How to determine the side length?The equation of the area of the square is given as
p² = 169
The area of a square is the product of its length
This means that we simply take the square root of both sides of the equation to determine the side length
Next, we take the square root of both sides of the equation
So, we have
√p² = √169
Evaluate the square roots
So, we have
p = 13
Hence, the side length of the square in centimeters is 13 centimeters
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A school dedicated 50% of the courtyard area for students to start a garden. The students want to know how much of the 632 yard the will be able to use?
The students will have 316 yards of the courtyard
The number of yards left for the students can be calculated as follows;
A school dedicated 50% of the courtyard area for students to start a garden
= 50/100
= 0.5
The number of yards is 632, the number of yards left for the students can be calculated as follows
= 0.5 × 632
= 316
Hence 316 yards are left for the students
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The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
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Question Completion:How many T-shirts were purchased by the Team?
Simplify. (3⁻²) (3⁵) .
About how much farther did she bike on Wednesday than Thursday?
the answer is 71 miles far
At the local movie theatre, there are 115 boys, 92 girls, and 28 adults.
a. Write the ratio of the number of boys to the number of girls.
115:92
b. Write the same ratio using another form (: vs. to ).
115 to 92
c. Write the ratio of the number of boys to the number of adults.
115:28
d. Write the same ratio using another form.
115 to 28
A. The ratio of the number of boys to the number of girls is; 115:92
B. The same ratio using another form is; 115 to 92
C. The ratio of the number of boys to the number of adults is; 115:28
D. The same ratio using another form is; 115 to 28
What is the Ratio?We are told that there are 115 boys, 92 girls, and 28 adults. Thus;
Number of boys = 115
Number of girls = 92
Number of Adults = 28
Now, we want to find some ratios and they are;
A) The ratio of boys to the number of girls = 115 : 92
B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;
115 to 92
C) The ratio of the number of boys to the number of adults is;
115:28
D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28
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For the function f(x)=∛2x , find f⁻¹(x) . Then determine the value of x when f(x)=16 .
The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex] when f(x) = 16 is [tex]x=2^\frac{11}{3}[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the functionWe have given a function [tex]f(x)=x\sqrt[3]{2}[/tex]. ....(1)
Let y = f(x)
[tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]y=\frac{x}{\sqrt[3]{2} }[/tex]
[tex]f^{-1}(x)=y[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]
It is given that f(x) = 16 on comparing it with equation (1) , we get
[tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]
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