Consider the function
f(x) = [tex]\frac{x-3}{x-4}[/tex]
Domain of the function = All real numbers except , x≠4 .
[tex]y=\frac{x-3}{x-4} \\\\ xy - 4y = x-3 \\\\ x y -x= 4 y-3\\\\ x=\frac{4 y-3}{y-1}[/tex]
Range = All real numbers except , y≠1 .
Horizontal Asymptote= Since the degree of numerator and denominator of rational function is same , So Divide coefficient of x in numerator by divide coefficient of x in denominator.
So Horizontal Asymptote , is : y=1
To get vertical asymptote, put
Denominator =0
x-4=0
x=4 , is vertical asymptote.
Domain = All real numbers except vertical Asymptote
Range = All real numbers except Horizontal Asymptote
Final answer:
The vertical asymptotes of a rational function can be found by determining the roots of the polynomial in the denominator, while the horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches infinity. The asymptotes are closely related to the function's domain and range.
Explanation:
Vertical asymptotes of a rational function can be determined by finding the roots of the polynomial in the denominator. Each root corresponds to a vertical asymptote. For example, if the polynomial has a factor of (x - 2), then there is a vertical asymptote at x = 2.
On the other hand, horizontal asymptotes of a rational function can be found by analyzing the behavior of the function as x approaches positive or negative infinity. If the leading terms of the numerator and denominator have the same degree, then the function will have a horizontal asymptote. For instance, if the leading terms are both x^2, then the horizontal asymptote will be y = 0.
The domain of the function is the set of all valid inputs, while the range is the set of possible outputs. The vertical asymptotes and the behavior of the function as x approaches infinity are closely related to the domain, while the horizontal asymptotes are related to the range.
State the postulate or theorem that proves that x||y.
A.converse of the consecutive interior angles theorem
B.converse of the alternate interior angles theorem
C.converse of the corresponding angles postulate
D.converse of the alternate exterior angles theorem
The theorem that proves x is parallel to y is the Converse of the Alternate Interior Angles Theorem, which states that if alternate interior angles are congruent, the lines are parallel. The correct answer to the question of which postulate or theorem proves that x is parallel to y is B. Converse of the Alternate Interior Angles Theorem.
Explanation:According to this theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The other options, such as the converse of the corresponding angles postulate or the converse of the consecutive interior angles theorem, are related but specifically address different sets of angles formed when two lines are cut by a transversal.
In geometry, it is crucial to apply the correct postulates or theorems to prove specific properties, like parallel lines. The reliability of these mathematical proofs, like those in trigonometry or physics, comes from the logical sequence of applying these fundamental principles accurately.
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the bryant family reuion and the jordan family reunion both include a visit to the zoo desert archers different amounts for children and adults in the following system A represents the cost of an adult ticket and C represents the cost of a child ticket. The first equation in the system represents the amount of money the Bryant family spends and the second equation represents the amount of money that the Jordan family spends
12a + 16c =176
10a + 8c =120
Which of the following statements are true?
A. the Bryants take 12 adults and 16 children to the zoo
B. There is a total of 22 children at the reuions
C.There is a total of 18 people at the Jordans reuion
D.16 represents the cost of a child ticket for the Bryant reuion
E. 10 represents the cost of an adult ticket for the Jordan family
F. The Bryant family spends $120 on tickets for the children and adults
G. Together the family spends $296
❗PLEASE HELP❗
Answer:
D. 16 represents the cost of a child ticket for the Bryant reunion.G. Together the family spends $296Step-by-step explanation:
To find the right answer we have to solve the system of equation:
[tex]\left \{ {{12a+16c=176} \atop {10a+8c=120}} \right.[/tex]
If we multiply the second equation by -2, we could eliminate the c-variable and solve for a-variable:
[tex]\left \{ {{12a+16c=176} \atop {-20a-16c=-240}} \right.\\-8a=-64\\a=\frac{-64}{-8}=8[/tex]
Now, we replace this value in one equation to obtain the other value:
[tex]10a + 8c =120\\10(8)+8c=120\\80+8c=120\\8c=120-80\\c=\frac{40}{8}=5[/tex]
So, the solution of the system is [tex](8,5)[/tex], which means that there are 8 adults and 5 children.
Also, according to the linear expressions The Bryants spend $12 per adult and $16 per child, and a total amount of $176. The Jordan family spend $10 per adult and $8 per child, and a total amount of $120. Both families together spent $296.
Therefore, the right answers are D and G
the cost of a pencil is 25 cents more than the cost of an eraser. if the cost of 8 pencils and 10 erasers is 12.80 dollars, find the cost of each
At the halftime show, a marching band marched in formation. The lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. What were the coordinates of the drummer's final position? (3 points)
Answer:
a) The answer is: (x + a, y + b)
b) The answer is: (-1, -2)
The initial coordinates are:
(x, y) = (-2, -5)
should be the answer.
Let's find a and b.
a is a distance in x direction: a = 1
b is a distance in y direction: b = 3
The final position is:
(x + a, y + b) = (-2 + 1, -5 + 3) = (-1, -2)
Step-by-step explanation:
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and x are related by the equation.
What is the change in the total cost for each book printed?
What is the cost to get started (before any books are printed)?
Equation: y=1250+25x
In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)
(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?
To calculate the probability of getting a blackjack from a single well-shuffled deck, you must consider the probability of drawing an Ace and then a 10-value card or vice versa, and add those probabilities together. The same process applies to two decks with adjusted numbers. You will then round the final probabilities to four decimal places.
Explanation:To answer the question of the probability of getting a blackjack in a single deck, consider that there are 4 aces in a deck and 16 cards that are either a face card or a 10 (each suit has 4 such cards - Jacks, Queens, Kings, and 10s). When one card is drawn, the remaining cards are one fewer, so we need to adjust our probability for the second card.
Calculate the probability of drawing an Ace first and then a card with a value of ten: P(Ace first, then 10) = (4/52) × (16/51).Calculate the probability of drawing a 10-value card first and then an Ace: P(10 first, then Ace) = (16/52) × (4/51).Add the two probabilities together for the final answer.For the probability of a blackjack from two decks, follow the same steps, but adjust the numbers for a 104-card deck.
P(Ace first, then 10) = (8/104) × (32/103).P(10 first, then Ace) = (32/104) × (8/103).Add the two probabilities together for the final answer.After doing the calculations, we round the probabilities to four decimal places as instructed.
the sum of two numbers is s.if one of the numbers is n,the second number can be expressed as
1. s+n
2. s÷n
3. s-n
4. n-s
Given that two numbers sum to 's', and one of the numbers is 'n', the other number can be expressed as 's - n'. In essence, if you subtract 'n' from the sum 's', you obtain the second number.
Explanation:The student's question relates to expressing one number in terms of another when their sum is given. Given that the sum of the two numbers is s and one of the numbers is n, the second number can be expressed as s - n. This is because when two numbers add to give 's', subtracting one of the numbers (n, in this case) from 's' would give the other number.
For instance, if s = 10 and n = 3, then the second number would be 10 - 3 = 7. Hence, the correct answer from the options provided would be 3. s - n.
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Find the amount of simple interest earned after 2 years on $480 invested at a 7% annual interest rate?
Using the simple interest formula, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.
Finding Simple Interest on an Investment
To calculate the simple interest earned after 2 years on a $480 investment at a 7% annual interest rate, you can use the simple interest formula: Interest = Principal times Rate times Time.
The principal (P) is the initial amount of money, which in this case is $480. The rate (R) is the annual interest rate expressed as a decimal, so 7% becomes 0.07. The time (T) is the number of years the money is invested or borrowed, which is 2 years in this scenario.
Using the simple interest formula:
Interest = 480 times 0.07 times 2
Interest = 33.6 times 2
Interest = $67.20
Therefore, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.
Write the following in terms of sin(θ) and cos(θ); then simplify if possible.
cos(θ) + sin(θ)cot(θ) = ...?
Naomi draws a portion of a figure as shown. She wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
Answer:
In FLVS it is the third option
Step-by-step explanation:
Hope this helps :)
I need help on the back side
Expressions cannot _____.
be evaluated
be solved
be simplified
have variables
Answer:
B. be solved
Step-by-step explanation:
What is 598% divided by 26%
What is 0.853 to the nearest tenth?
The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:
What is the youngest age for which the average income of a lawyer is $450,000?
Round to the nearest year.
To find the youngest age for a lawyer to have an average income of $450,000, you solve the income function equation and round to the nearest year.
Explanation:The youngest age for which the average income of a lawyer is $450,000 can be found by solving the given function:
I(x) = 10000 + 2000x
Given I(x) = $450,000, the equation becomes:
450,000 = 10000 + 2000x2000x = 440,000x = 220Rounded to the nearest year, the youngest age would be 220 years old.
The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function w(x)=x^2/2(1-x), where x is a number between 0 and 1 known as the traffic intensity. Find the average number of vehicles waiting if the traffic intensity is 0.92. ...?
To find the average number of vehicles waiting at a traffic intensity of 0.92, we substitute 0.92 into the function w(x) = x² / (2(1-x)) to arrive at the answer 5.29.
Explanation:The average number of vehicles waiting in line is modeled by the function w(x) = x^2 / (2(1-x)) where x represents traffic intensity. The question is asking us to calculate the average number of vehicles waiting when the traffic intensity is 0.92. By plugging this value into the function, we get w(0.92) = 0.92^2 / (2(1-0.92)), which simplifies to w(0.92) = 0.8464 / 0.16. The result is 5.29, so the average number of vehicles waiting would be 5.29 when the traffic intensity is 0.92. To find the average number of vehicles waiting when the traffic intensity is 0.92, we substitute the value of x into the given function w(x)=x^2/2(1-x). In this case, x=0.92. So, the average number of vehicles waiting can be found by evaluating w(0.92).
w(0.92) = (0.92)^2 / 2(1 - 0.92)
w(0.92) = 0.8464 / (2 * 0.08)
w(0.92) = 10.58
Therefore, when the traffic intensity is 0.92, the average number of vehicles waiting is approximately 10.58.
The hypotenuse of a 45°-45°-90° triangle measures 128 cm.What is the length of one leg of the triangle?
Answer:
Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
In 45°−45°−90° triangle
Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]
then,
the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]
The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg. ....[1]
Given: length of hypotenuse = 128 cm.
then,
from [1] we have;
128 = [tex]\sqrt{2}\cdot x[/tex]
or
[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]
Simplify:
[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.
Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.
The ratio of two numbers is 1 to 4, and the sum of the numbers is 45. What is the smaller number?
10
9
8
7
9 i think
What is closer to 1/3 0.3 0.33 or 0.333
what are the x and y intecepts of the graph of the equation 6x - 5y=3
PLEASE HELP PLEASE PLEASE
When the following expression is written in simplest form, what is the coefficient of the variable term?
-2.5y + 8y - 10.5y
3 out of 4 students surveyed in a school said they will vote for nuncio for class president predict how many of the 340 students in the school would vote for nuncio
To predict the number of votes for Nuncio for class president, multiply 3/4 (or 0.75) by the total number of students (340), resulting in a prediction that 255 students would vote for Nuncio.
To predict how many of the 340 students in the school would vote for Nuncio for class president, we need to understand the proportion that we got from the survey. Since 3 out of 4 students said they would vote for Nuncio, this is the same as 75% or 0.75 when expressed as a decimal.
We then apply this proportion to the total number of students in the school:
Convert the fraction 3/4 to a decimal: 3 ÷ 4 = 0.75.
Multiply the total number of students by the decimal: 340 students × 0.75 = 255 students.
Therefore, we predict that 255 of the 340 students would vote for Nuncio for class president.
If B=A, where on the number line will B appear?
A.to the right of A
B.in exactly the same location as A
C.to the left of A
(04.02 LC)
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r,
Which ratio is equal to b:q? (1 point)
b:a
c:r
r:a
q:c
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that triangle ABC is similar to triangle PQR.
In triangle ABC, AB=c, BC=a, and AC=b.
In triangle PQR, PQ=r, QR=p, PR=q.
The corresponding sides of similar triangles are proportional.
Since [tex]\triangle ABC\sim \triangle PQR[/tex], therefore their corresponding sides are proportional.
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]
It meas the ratio c:r = a:p = b:q.
Therefore the correct option is 2.
4 is equivalent to how hundreths
Three-fourths of a number increased by one-fifth is no less than seven-eighths.
Which equation represents this problem?
Answer:
yea, most likely it´s 3/4 y + 1/5 ≥ 7/8
Step-by-step explanation:
What is the answer to the riddle 20 30 x 0 1 the real answer..?
PEMDAS- [Parenthese, Exponents, Multiplication, Division, Addition, Subtraction.]
Since there is no Parentheses, nor Exponents, you have to go straight to multiplication. Then to addition
30+30×0+1
30×0=0
30+0+1=31.
I hope my answer has come to your help. God bless and have a nice day ahead!
The population of foxville is about 12 times 10 to the power of 3. which is another way to write this number
Answer:
The population of foxville is 12000.
Step-by-step explanation:
It is given that the population of foxville is about 12 times 10 to the power of 3.
Population of foxville = [tex]12\times 10^3[/tex]
[tex]12\times 10^3[/tex] is a scientific notation of a number.
We need to write this number in another way.
[tex]12\times 10^3=12\times 1000[/tex]
[tex]12\times 10^3=12000[/tex]
Therefore, the population of foxville is 12000.
Round to the nearest tenth 848.607