Write a rational function with an x-intercept at (-9,0), a vertical asymptote at x=3, and a hole located at (1,-5). Then, identify the horizontal asymptote.
Answer:
The rational function is [tex]f(x) = \dfrac{x^2 + 8\cdot x - 9}{x^2 - 4 \cdot x + 3}[/tex]
The horizontal asymptote occur at y = 1
Step-by-step explanation:
Given that the function has an x-intercept at (-9, 0), we have;
(x + 9) is a factor of the function
Also, given that the function has a vertical asymptote at x = 3, we have that a factor of the denominator of the function is (x - 3)
With a hole at (1, -5), we have, (x - 1) in both the numerator and the denominator and when x = 1, f(x) = -5
The general form of the function can be presented as follows;
f(x) = ((x + 9)·(x - 1))/((x - 3)(x - 1)) = (x² + 8·x - 9)/(x² - 4·x + 3)
Given that the power of the numerator and the denominator are equal, the horizontal asymptote occur at ratio of the leading coefficient of the numerator and the denominator which from the above equation is 1/1 = 1
The horizontal asymptote occur at y = 1
Please find attached the graph of the function created with Microsoft Excel
PLEASE ANSWER THISSS
Answer:
78.5 ft
Step-by-step explanation:
You had the right answer
Hope you got the clarification you needed! :)
Brainliest pls
Paul is locked out of his house. An 18-ft ladder is outside and an upstairs window is open. Paul read the safety warning on the ladder recommending it be placed six feet away from the wall. He placed the ladder according to the warning and it reached the base of the window. How high is the base of the window off the ground?
Answer:
17.0 ft
Step-by-step explanation:
Let h be the height of the base of the window from the ground, L be the length of the ladder = 18 ft and d be the distance of the ladder from the wall = 6 ft. Now, these three lengths form a right-angled triangle with the length of the ladder, L as the hypotenuse side.
So, using Pythagoras' theorem,
L² = h² + d²
So, h = √(L² - d²)
Substituting the values of L = 18 ft and d = 6 ft, we have
h = √((18 ft)² - (6 ft)²)
= √(324 ft² - 36 ft²)
= √288 ft²
= 16.97 ft
≅ 17.0 ft
Russell caught 9 butterflies for his science project in the first week. He caught 13 butterflies in the second week. What is the percent increase in the number of butterflies Russell caught from the first week to the second week? Round your answer to the nearest whole number.
Answer:
44 Percent Increase
Step-by-step explanation:
Hope This Helps :)
Dr. Concha Gómez is an Italian, Cuban American who received a Ph. D. in Mathematics at the University of California at Berkeley. Dr. Gomez currently works at the University of
Wisconsin where she teaches her students how to find the solutions to a quadratic function. To start, she asks her students to find the factors for the quadratic expression,
7z^2 -38z + 15.
Select the factors of this quadratic expression.
Answer:
7z - 3 and z - 5
Step-by-step explanation:
The factors of the given quadratic expression is (z-5((7z-5).
The given quadratic expression is 7z² -38z + 15.
What is the quadratic expression?An expression of the form ax² + bx + c, where a ≠ 0 is called a quadratic expression. In other words, any expression with the variables of the highest exponent or the expression's degree as 2 is a quadratic expression.
The given quadratic expression 7z² -38z + 15 can be solved as follows:
Using spitting middle term
7z² -35z-3z + 15
= 7z(z-5)-3(x-5)
= (z-5((7z-5)
Therefore, the factors of the given quadratic expression is (z-5((7z-5).
To learn more about the quadratic expression visit:
https://brainly.com/question/14083225.
#SPJ6
Which is the better value, 2 books for $18 or 6 books for $45? Explain. {hint: make two tables; compare} (1 pt.) RP.1.3 b a.2 books for $18 because each book costs $9 and 6 books for $45 because each book costs $9.50 b.2 books for $18 because each book costs $8 and 6 books for $45 because each book costs $9.50 c.6 books for $45 because each book costs $7.50 and 2 books for $18 because each book costs $9 d.6 books for $45 because each book costs $9 and 2 books for $18 because each book costs $9.50 answer fast please
Answer:
I am a little confused by your question but if you were getting less it would be the first but more would be the second
Step-by-step explanation:
Answer:
c. 6 for 45 b/c each costs 7.50 and 2 for 18 b/c each book costs 9
Step-by-step explanation:
If you divide the amount of money by the number of books then you will find how much each book costs individually. If you wanna spend less money per book, then you 6 books for 45 is a better deal
Mike has a certain amount of money and is given $25.25 more money. Anthony has three times the total that mike has plus $5.48 extra dollars. Their combined total is $261.23. Write an equation and solve it to determine how much each of them has.
Answer:
Mike has =$63.94
Anthony = $197.3
Step-by-step explanation:
Step one:
let the certain amount that Mike has be x
so
in all Mike has = (x+25.25)
Anthony has
3(x+25.25)+5.48
we are told that the total amount for both Mike and Anthony is
$261.23
so
(x+25.25)+3(x+25.25)+5.48=261.23
open bracket
x+25.25+3x+75.75+5.48=261.23
collect like terms
x+3x+25.25+75.75+5.48=261.23
4x+106.48=261.23
4x=261.23-106.48
4x=154.75
divide both sides by 4
x=154.75/4
x=38.69
Hence,in all
Mike has = (38.69+25.25)
Mike has =$63.94
Anthony has
=3(38.69+25.25)+5.48
=3(63.94)+5.48
=191.82+5.48
=$197.3
Lorena is trying to choose between two different savings accounts at H-Town Bank. She will deposit $3,500 dollars and will leave the money in the account for 12 years. There will be no additional money deposited or withdrawn from the account. Advanced Savings Account. Initial Deposit three thousand five hundred. Account earns 5 percent simple interest. Premier Savings account. Initial Deposit three thousand five hundred. Account earns four point five percent interest compounded annually. Which statement about the accounts will be true at the end of 12 years?
Answer:
GET REKTTKTKTTK
Step-by-step explanation:
SJDHDIAJSJSJSJAJ
please help me I dont want to do it and I am on a timed thing
Answer:
-1
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
-5 -15 = -20
-20+4 = -16
-16+15 = -1
Therefore, -5-15+4+15 = -1
Need solved asap please.
Answer:
Cost of one cheap golf ball is $0.75 and one expensive golf ball is $2.00
Step-by-step explanation:
Let,
x be the price of one cheap golf ball
y be the price of one expensive golf ball
According to given statement;
6x+4y=12.50 Eqn 1
4x+3y=9.00 Eqn 2
Multiplying Eqn 1 by 4
4(6x+4y=12.50)
24x+16y=50.00 Eqn 3
Multiplying Eqn 2 by 6
6(4x+3y=9.00)
24x+18y=54.00 Eqn 4
Subtracting Eqn 3 from Eqn 4
(24x+18y)-(24x+16y)=54.00-50.00
24x+18y-24x-16y=4.00
2y=4.00
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{4.00}{2}\\y=2.00[/tex]
Putting y=2.00 in Eqn 1
6x+4(2.00)=12.50
6x+8.00=12.50
6x=12.50-8.00
6x=4.50
Dividing both sides by 6
[tex]\frac{6x}{6}=\frac{4.50}{6}\\x=0.75[/tex]
Hence,
Cost of one cheap golf ball is $0.75 and one expensive golf ball is $2.00
John and his mother are trying to determine the dimensions of their new curtains. They know that the area of the fabric they have available is y^2-10y+25 square inches. Which of the following are possible dimensions of the curtains, in inches?
A.
(y – 1)(y – 10)
B.
(y – 25)(y – 1)
C.
(y – 5)(y – 5)
D.
(y + 5)(y – 5)
Answer:
the answer is C . (y-5)(y-5)
Step-by-step explanation:
i just did it in edge
I NEED HELP ASAP??
Does this table represent a proportional relationship?
Cans of 5| 10| 6| 9| 2|
paint (x)
Bird houses 15|30|18| 27| 6
painted (y)
Your answer:
pleaseeeeee helpppppppppp
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
This is the answer because:
1) Mean - add all the numbers and divide by with how many numbers you added.
2) The numbers are: 7,9,10,5,8,3,7
3) 7 + 9 + 10 + 5 + 8 + 3 + 7 = 49
4) 49 ÷ 7 = 7
Therefore, the answer is 7.
Hope this helps! :D
what is the best estimate for V18
Answer:
34/8-16/3-14/9
Step-by-step explanation:
Every year, the amount of CO2 in the atmosphere increases by a factor of
CHICKEN WING + CHICKEN WING EQUALS WHAT?
A) CHICKEN WANG
B) UR STOOPID
C) I HAVE NO CLUE
D) DOUBLE CHICKEN WINGS
Answer:
hot dog and baloney
Step-by-step explanation:
can someone answer this please
Answer:
The coordinates of point P are (1, -1)
Step-by-step explanation:
If the point (x, y) reflected about the x-axis, then its image is (x, -y)To find the image of a point reflected about the x-axis change the sign of its y-coordinateThe rule is R x-axis → (x, -y)If the point (x, y) reflected about the y-axis, then its image is (-x, y)To find the image of a point reflected about the y-axis change the sign of its x-coordinateThe rule is R y-axis → (-x, y)→ Assume that the coordinates of point P are (x, y)
∵ The coordinates of point P are (x, y)
∵ The rule of the reflection is R y-axis (P)
∴ Its image = (-x, y)
∵ The image = (-1, -1)
→ Equate the two images
∴ (-x, y) = (-1, -1)
∴ -x = -1
→ Divide both sides by -1
∴ x = 1
∵ y = -1
∴ The coordinates of point P are (1, -1)
Which equation could be used to solve for a value, x, that is equal to 5 times the sum of x and 12?
x = 5x = 12
5x = x + 12
x = 5(x + 12)
x = x + (5)(12)
.
Marshall gave the cashier $100 to pay for 4 new video games. The cashier gave him $4.08 in change. Each video game cost the same amount.
What is the cost in dollars and cents for each video game?
PLZZZZ HELP
Answer:
I would say it's $23.98
Step-by-step explanation:
If you do 100-4.08, you get 95.92 and since there's 4 video games, divide 95.92 by 4 and you get 23.98
Answer:
$23.98 or 2398 cents
Step-by-step explanation:
If the cashier gave $4.08 back, that means that he spent 100-4.08 on the 4 games.
$100 = 4 games + $4.08
4 games = $95.92
$95.92/4 = $23.98
Hope That Helps.
If f(x) = 4x+7 and g left parenthesis x right parenthesis space equals fraction numerator 1 over denominator 2 x end fraction w h a t space i s space t h e space v a l u e space o f space left parenthesis f over g right parenthesis left parenthesis 5 right parenthesis ?
Answer:
270
Step-by-step explanation:
its on my test this is the right answer
Please Please Please help
I’ll give brainliest to first correct answer!!
Calculate the slope of line m
Answer:
6,6
Step-by-step explanation:
a
Answer:
it´s freaking 4
Step-by-step explanation:
What is the slop of 1x+3
Answer:
The slope of 1x+3 is 1
Step-by-step explanation:
Y= mx+b
M= slope
B= Y-Intercept
What are the points of the inverse graph of the graph listed below
Answer:
5 and -1.5 i believe
Step-by-step explanation:
Help please fast ahh
Answer:
the 2nd one
Step-by-step explanation:
-12 may be more in positive numbers but it is less in negative numbers
PROBLEM 24
Can you write the equations for this word problem? Having trouble figuring out how to write the problem from a word problem.
Answer:
23. 22x + 15y = 228
x + y = 11
Step-by-step explanation:
I can't really figure out the other two, I'll let you know if I get it though D: Really sorry, I wish I could help you more. Good luck man.
1. Calculate the value of x in the following diagram. 53 - Y IN Q 5x 18
Answer:
x = 7
Step-by-step explanation:
QY = 5x
YZ = 18
QZ = 53
Thus:
QY + YZ = QZ (segment addition postulate)
5x + 18 = 53
5x = 53 - 18 (subtraction property of equality)
5x = 35
Divide both sides by 5
x = 7
Factor the expression 5x+15
Answer:
5(x+3)
Step-by-step explanation:
Find the Greatest Common Factor (GCF).
GCF = 55
2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
5(\frac{5x}{5}+\frac{15}{5})5(
5
5x
+
5
15
)
3 Simplify each term in parentheses.
5(x+3)5(x+3)
Factor 5 out of 5x + 15.
5 (x + 3)
-7+82*78-67^6+5-4/6=?
sufferrrrrrrrrr!
Answer:
-90458375775.7
Step-by-step explanation:
yes
-3/8(x-24)+x=19 i need a answer ASAP!
Answer:
x = 16
Step-by-step explanation:
Problem: -3/8(x-24)+x=19
Distribution:
-3/8x + 9 + x = 19
5/8x = 19 - 9
5/8x = 10
x = 10 • 8/5
x = 16
What is the linear equation that represents the value shown below?
X l Y
0 l 6
1 l 10
2 l 14
3 l 18
4 l 22
-------------------------------------------------------------------------------------------------------------------
y = 6x + 10
y = 4 + 6x
y = 10x
y = 6 + 4x
Answer:
The linear equation that represents the value shown below is [tex]\mathbf{y=4x+6}[/tex]
Option D is correct option.
Step-by-step explanation:
We need to find the linear equation that represents the value shown below.
X l Y
0 l 6
1 l 10
2 l 14
3 l 18
4 l 22
The equation will be of form [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
We need to find slope and y-intercept.
Finding slope
Using points (0,6) and (1,10) we can find slope by formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{10-6}{1-0}\\ Slope=\frac{4}{1}\\Slope=4[/tex]
So, we get slope m = 4
Now finding y-intercept
When x=0, the value of y is y-intercept
So, y-intercept b = 6
So, the equation having slope m= 4 and y-intercept b=6
[tex]y=mx+b\\y=4x+6[/tex]
So, The linear equation that represents the value shown below is [tex]\mathbf{y=4x+6}[/tex]
Option D is correct option.