Final answer:
A rational function with vertical asymptotes at x = 3 and x = -4, x-intercepts at x = -1 and x = 5, and a horizontal asymptote at y = 6 is constructed by using factors that make the denominator zero at the vertical asymptotes and the numerator zero at the x-intercepts, with a constant ratio to define the horizontal asymptote.
Explanation:
To construct a rational function that meets the specified criteria, we need to ensure that the function has the correct vertical and horizontal asymptotes as well as the specified x-intercepts. A vertical asymptote occurs where the denominator of the rational function is equal to zero, whereas x-intercepts occur where the numerator is equal to zero.
The horizontal asymptote represents the end behavior of the function as x approaches infinity.
Step-by-step construction of the rational function
For vertical asymptotes at x = 3 and x = -4, the denominator must be zero at these points. So, we can use factors (x - 3) and (x + 4) in the denominator.
For x-intercepts at x = -1 and x = 5, the numerator must be zero at these points. Thus, we can use factors (x + 1) and (x - 5) in the numerator.
To incorporate a horizontal asymptote at y = 6, we need the degrees of the numerator and denominator to be the same, and the leading coefficients must have a ratio that equals 6. To achieve this, we introduce the constant 6 in the numerator.
The resulting rational function, considering all the conditions above, is:
f(x) = 6(x + 1)(x - 5) / ((x - 3)(x + 4))
2) Oliver is determining the number of cats in his math class. Oliver is collecting what kind of data? A) bivariate B) categorical C) qualitative D) quantitative
gas costs $2.53 per gallon in May. In September, gas cost $3.05 per gallon. What was the percent change in the cost of a gallon of gas?
Answer:
20.6%
Step-by-step explanation:
To calculate the percentage of how much increase, we must first know how much is the difference in the price of May with that of September.
That difference will represent how many $ increase the gallon
[tex]3.05-2.53=0.52[/tex]
We know that a $ 0.52 increase now we must calculate to what percentage of the initial price this value is equivalent to know in what percentage the price of May increased.
[tex]2.53 \longrightarrow 100\%\\0.52 \longrightarrow x\\x=\frac{(0.52)(100)}{2.53} \\x=20.6\%[/tex]
It takes a person 30 minutes to gather 1 basket of fruit. Working at the same rate, how many baskets can 25 people gather in 8 hours?
.04 is 1/10 of what number
Answer:
0.4
Step-by-step explanation:
Let x be 1/10 of 0.04.
1/10 of x would be [tex]\frac{1}{10}x[/tex].
We can represent our given information in an equation as:
[tex]\frac{1}{10}x=0.04[/tex]
Let us solve for x.
[tex]10*\frac{1}{10}x=10*0.04[/tex]
[tex]x=0.4[/tex]
Therefore, 0.04 is 1/10 of 0.4.
Trent hikes up a hill at 4 km/h. He hikes back down at 6 km/h. The hiking trip took 3 hours. How much time did it take Trent to hike up the hill? Write an equation you can use to solve for t, the time it took him to climb up the hill
t = time to hike up the hill
3-t is the time to hike down the hill
so 4t = 6(3-t)
4t = 18-6t
10t = 18
t = 18/10 = 1.8 hours to hike up the hill
1.8 hours = 1 hour 48 minutes
Answer:
The time it took him to climb up the hill is 1.8 hours.
Step-by-step explanation:
Here, t represents the the time it took him to climb up the hill,
Total time taken by it = 3 hours,
Thus, the time taken by it to climb down the hill = ( 3 - t ) hours.
Since, Trent hikes up a hill at 4 km/h,
⇒ Total distance covered by it to climb up = 4 t (Distance = Speed × Time)
Since, Trent go down a hill at 6 km/h,
⇒ Total distance covered by it to go down = 6(3-t)
We know that,
Total distance covered by it to climb up = Total distance covered by it to go down
⇒ 4t = 6(3-t)
Which is the required equation.
⇒ 4t = 18 - 6t
⇒ 10 t = 18
⇒ t = 1.8
Hence, the time it took him to climb up the hill is 1.8 hours.
13.1 miles in 58 minutes and 23 seconds; 30 yards in 4.8 seconds. Which is faster
1 mile = 1760 yards
13.1 * 1760 = 23056 yards / 58.38 = 394.93 yards per minute
394.93/60 = 6.58 yards per second
30/4.8 = 6.25 yards per second
13.1miles in 58 minutes 23 seconds is faster
Which of the ratios below can be used to finish the proportion
5/12 = ... ?
Select all correct answers.( The slashes are fraction bars not division signs!!)
(A) 0.25/0.6 (B) 40:96 (C) 1/2 over 1 and 2/5 (D) 1.5:3.6 (E) 1/3 over 0.8
Thanks so much I don't get this!
Which of the following best describes the square root of 12
if the amount of white sugar were increased by a factor of 2 1/2, in cups how much white sugar would there be
A. 2 1/2
B. 2 3/5
C. 1 2/3
D. 1 3/5
To find the amount of white sugar if it were increased by a factor of 2 1/2, multiply the original amount by 2 1/2. The answer is A. 2 1/2 cups.
Explanation:To find the amount of white sugar if it were increased by a factor of 2 1/2, we need to multiply the original amount by 2 1/2. Let's assume the original amount is x. Multiplying x by 2 1/2 gives us:
x × 2 1/2 = x × 2 + x × 1/2 = 2x + (1/2)x = (4/2)x + (1/2)x = (5/2)x
So, the amount of white sugar after it is increased by a factor of 2 1/2 is (5/2)x cups. This is equivalent to 2 1/2 times the original amount of white sugar. Therefore, the answer is A. 2 1/2 cups.
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owen's bedroom has a perimeter of 46 feet if the length is 11 feet, what is the width of the bedroom anwer
To start off, identify your equation. You know P= 46, and L= 11, so you need to find W=. To do that, first you need to double your length, and width. So, L now equals 22, and W now equals 2W. Now, add W, and L, and it will need to be the original number. Simply subtract 22, from your product, and divide by two, and you'll have W. Here's what the equation should look like.
(2 * 11) + 2W= 46
22 + 2W= 46
46 - 22= 24
2W= 24
W= 12 ft. Or, the width is 12 feet.
Which graph represents the inequality y<−1+2x?
math question down below
Mr nielson works 154 hours each month He works 8 months each year. How many hours does Mr nielson work each year
20 POINTS AND BRAINIEST ANSWER
Mr. Chen goes to the post office to buy small and large boxes. He needs at least 4 small boxes. Altogether, he will buy no more than 15 boxes. The post office has 10 small boxes and 9 large boxes in stock.
The graph shows the feasible region, where x represents the number of small boxes and y represents the number of large boxes.
Which ordered pairs meet all the constraints and make sense in context of the situation?
Select each correct answer.
6,9
7,10
8,6
9,8
The correct answer is
8,6 & 6, 9
Answer:
The correct options are 1 and 3.
Step-by-step explanation:
It is given that x represents the number of small boxes and y represents the number of large boxes.
The post office has 10 small boxes and 9 large boxes in stock.
He needs at least 4 small boxes.
[tex]4\leq x\leq 10[/tex]
He will buy no more than 15 boxes.
[tex]6+9=15\leq 15[/tex]
[tex]8+6=14\leq 15[/tex]
Therefore options 1 and 3 are correct.
[tex]x+y\leq 15[/tex]
[tex]7+10=17>15[/tex]
[tex]9+8>15[/tex]
Therefore options 2 and 4 are incorrect.
Samuel is saving to buy a watch that costs 169 this is $48 more than 4 times what he saved last month how much did he save last month?
the bike course is 80 miles long and I have ridden 44 miles of the course. what percentage have avridden?
Alicia wants to cover a section of her wall that is 2 feet wide and 12 feet long with mirrors.Each mirror tile is 2 feet wide and 1.5 feet long.How many mirror tiles does she need to cover that section?
The two shapes have the same area. Work out the perimeter of the rectangle.
What is the value of 6 cubed?What is the value of 6 cubed?
12
36
72
216
The value of 6 cube or 6×6×6 or 6³ is 216.
What is a perfect square number?A perfect square number when taken the square root of it results in an integer.
Numbers that are not perfect squares when taken the square root of it are irrational numbers.
One method of obtaining square roots for perfect squares is prime factorization.
Now, A perfect cube number is which when taken cube root results to an integer.
A number multiplied by itself by twice results in a cube of that number.
Therefore, The value of 6 cube would be 6 multiplied twice to itself, which is, = 6×6×6 = 36×6 = 216.
It can also be written as exponent form which is, 6³.
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how many pairs of intersecting line segments does a cube have?
I need help with the rest of those problems? the ones that are blank.
In un rettangolo la somma delle sue dimensioni misura 154 cm e queste sono una i 5/6 dell'altra.Calcola l'area del rettangolo.
L'area del rettangolo in questione è 6449.5 cm quadrati, calcolata risolvendo l'equazione che unisce le due lunghezze date.
Explanation:In questo problema matematico, siamo interessati a trovare l'area di un rettangolo. Sappiamo che la somma delle lunghezze dei due lati del rettangolo è 154 cm e che un lato è 5/6 della lunghezza dell'altro .
Possiamo iniziare ponendo x come la lunghezza più corta e 5x/6 come la lunghezza più lunga, in quanto è 5/6 della lunghezza di x. Sommando questi due valori, otteniamo l'equazione: x + 5x/6 = 154. Risolvendo questa equazione, otteniamo x = 88 cm.
Il lato più lungo del rettangolo sarà quindi 5/6 * 88, che è uguale a 73.33 cm. Per calcolare l'area del rettangolo, moltiplichiamo la lunghezza con la larghezza: 88 cm * 73.33 cm = 6449.5.
Quindi, l'area del rettangolo è 6449.5 cmquadrati.
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in 1525 German print-maker Albrecht Durer first used the word net to describe a printed pattern that folds up into a three dimensional shape. Why do you think he choose to use the word net?
Albrecht Dürer used the term 'net' to describe a pattern because of its geometric nature and the way it mirrors a literal fishing net, which can be both flat and three-dimensional. His background in printmaking and geometry likely influenced this descriptor, showing his dedication to precision and instruction in visual arts.
The term net used by Albrecht Dürer in 1525 refers to a pattern that when folded, creates a three-dimensional shape. Dürer, a prominent figure in the Northern Renaissance, was a master in various forms of visual art. He possessed expertise in painting, printmaking, and had an understanding of geometrical principles as well as the new technology of print. The use of the word 'net' to describe a flattenable 3D pattern aligns with Dürer's keen attention to detail, precision, and geometry in his artworks. His choice of the term could have been inspired by the resemblance of the interconnected lines in a pattern to a fishing net, which can be spread out flat but typically exists in a more complex, three-dimensional form.
Through his prints and craft manuals, Dürer contributed to the dissemination of knowledge on artistic techniques and the use of geometry in art. His detailed illustrations often acted as visual instructions, which would align with the concept of a 'net' aiding in the construction of a three-dimensional understanding of shapes and forms. The term might have been quite intuitive for someone with Dürer's graphical sensibility, as it connects the craft of design with a term that people could visualize and comprehend easily.
How to label tables with unit rates
Grace earn seven dollars for each car she washes she also save $25 for a weekly earnings this week she wants to have at least $65 in spending money how many cars would you wash right and solve an Equality to represent the situation interpret the solution contacts
It will be -12 degrees tonight. The weatherman predicts it will be 25 degrees warmer by noon tomorrow. What will be the temperature be by noon tomorrow?
which is an equation of the line with x-intercept 2 and y-intercept 12
The equation of the line having The x-intercept of the line is 2, The y-intercept of the line is 12, is y = -6x + 12.
What is a line?Lines are defined as objects with an infinite length and no width, depth, or curvature. Lines are one-dimensional objects even though they can occur in contexts that are two, three, or higher dimensional.
A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction.
Given:
The x-intercept of the line is 2,
The y-intercept of the line is 12,
Write the equation of the line as shown below,
y = m x + 12
Here, m is the slope,
At y = 0 we get the x-intercept, so
0 = m × 2 + 12
m = -12 / 2
m = -6
Thus, the equation of the line is y = -6x + 12.
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Solve 8w – 3r = 45 for r
x^2+xy=20 and y^2+xy=30 what is xy?
Find the area of a circular park whose radius is 4.9 meters?
Answer:
75.4296 meters
Step-by-step explanation:
Use the circle area equation: pi(r)^2 to do 4.9^2 multiplied by pi