Which is a rational function?
A. Y= 2/x
B. Y=x^2 - x + 4
C. Y= x-3^x/x^2
D. Y= x-5/2
A rational function is the algebraic expression y = 2 / x. (Correct choice: A)
What function is a rational function?
Rational functions are algebraic expressions, whose form is described below:
R(x) = P(x) / Q(x)
Where:
P(x) - Numerator polynomic function.Q(x) - Denominator polynomic function.Please notice that Q(x) must be a polynomial whose grade is greater than zero.
Polynomials are algebraic expressions of the form:
P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.
Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.
To learn more on rational functions: https://brainly.com/question/8177326
#SPJ1
please help with geometry proof
Answer:
a and c are both congruent to each other i just learned about rhombuses the other day so if a and c are congruent then b and d are congruent too
Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).
Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:
F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)
We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:
105 = (R + F) * 3
Now we can substitute the first equation into the second equation:
105 = (R + (R + 5)) * 3
Simplifying and solving for R, we get:
R = 20 mph
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).
Learn more about velocity through:
https://brainly.com/question/18084516
#SPJ1
It is industry norms and key business ratios Dunn and Bradstreet reported that Q1 Q2 and Q3 were 2037 gasoline service stations sales to inventory ratios or 24 833.4 and 53.8 respectively from this we can conclude that what percentage of these service stations have sales to inventory ratio
From the inventory ratios of 24 8, 33.4 and 53.8 of Dunn and Bradstreet report. It can be concluded that
50% of these service station had sales to inventory ratios of 53.8 or moreHow to find the correct statement about the reportsThe problem is seeking expression of ratios in percentage
Ratios represents part or share of a whole while percentage refers to a fraction of hundred
Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up
= 24 8 + 33.4 + 53.8
= 108
Expressing as ratio 53.8 a percentage, we have
= 53.8/108 * 100
= 0.4981 * 100
= 49.81%
approximately 50%
We can therefore say that inventory of 53.8 or more is 50%
Learn more about percentage at:
https://brainly.com/question/24304697
#SPJ1
156x2.2=?????Help fast
Answer:
343.2
Step-by-step explanation:
156 × 2.2
= (156 × 22)/10
= 3432/10
= 343.2
1.2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
whats the answer?
Answer:
3(y^2 + 1) + 2(y+4)
Step-by-step explanation:
2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
= 2y^2 + y^2 + 6y - 4y + 8.9 - 8.6
= 3y^2 + 2y + 8(9-6)
= 3y^2 + 2y + 24
= 3y^2 + 2y + 3.2.2.2
= 3(y^2 + 1) + 2(y+4)
What is the area of the circle if BC = 6cm?
Answer:
[tex]A=9\pi cm^{2}[/tex][tex]=28.27cm^{2}[/tex]
Step-by-step explanation:
If BC= 6
then r = BC/2 = 6/2 = 3cm
[tex]A=\pi r^{2} =\pi (3)^{2} =9\pi[/tex]
[tex]A=28.27cm^{2}[/tex]
Hope this helps
evaluate 5² + 7 - 3 +4
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5² + 7 - 3 + 4
Simplify the expression, then we have
⇒ 5² + 7 - 3 + 4
⇒ 25 + 7 - 3 + 4
⇒ 36 - 3
⇒ 33
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
A student is graduating from college in 12 months but will need a loan in the amount of $10,958 for the last two semester. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 3.85%, compounded monthly, and a grace period of six months from time of graduation
PLUS loan: annual interest rate of 4.15%, compounded monthly, with a balance of $11,421.51 at the time of repayment
Which loan will have a higher balance, and by how much at the time of repayment?
Answer:
To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.
The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.
The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:
Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)
Plugging in the given values, we have:
Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16
The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.
The balance of the PLUS loan at the time of repayment can be calculated using the same formula:
Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54
Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.
Step-by-step explanation:
Find the length of AB.
The length of AB in the line segment is 21 units.
How to find the length of a line segment?A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.
Therefore, let's find the length AB, in the line segment AC.
Hence,
AC = AB + BC
AC = 23
AB = 2x + 7
BC = 3x - 19
Therefore,
23 = 2x + 7 + 3x - 19
23 = 5x - 12
23 + 12 = 5x
35 = 5x
divide both sides by 5
x = 35 / 5
x = 7
Therefore,
AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21
learn more on line segment here:https://brainly.com/question/9536205
#SPJ1
In Circle O, mAB = 72. Find m
Check the picture below.
Carlos measures an angle x. He then finds that the complement of the angle is 35 degrees. A. What is the measure of angle x? B. What is the supplement of angle x?
Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.
Describe complimentary angles.A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way
Here,
Given : complementary angle one of the angle is 35°
=> x+ 35° = 90°
=> x = 55°
Let y be the supplement of angle x
=> x+ y = 180°
=>55° + y =180°
=>y =125°
Therefore , the solution of the given problem of angle comes out to be
x = 55° and y =125°.
To know more about complementary angles visit:
https://brainly.com/question/5708372
#SPJ1
[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
Answer:
A sample of helium was compressed at 35 °C from a volume of 0.5 L
to 0.25 L where the pressure is 500 mmHg. What was the original pressure?
Step-by-step explanation:
name all the terms realted to subtraction
Answer:
Other words for subtraction:
taking away
withdrawal
abstraction
removal
discounting
Step-by-step explanation:
PLEASE HURRY I WILL GIVE BRAINLY PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.
c = 87
c = 8.5
c = 35
c = 10
Answer:c=35
Step-by-step explanation:
i just did this
A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together in decigrams? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
1,021 decigrams
10,210 decigrams
102,100 decigrams
1,021,000 decigrams
Answer:
102200
Step-by-step explanation:
564+458= 1022
1 decagram=100 decigram
So multiply the sum by 100
1022*100=102200
You deposit $250 in an account that earns simple interest at an annual rate of 2.2%.
How much money is in the account after 4 years?
Answer: $272
Step-by-step explanation: you would multiply 250 * 0.022 = 5.5
then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272
Five student government officers want to go to the state convention. It will cost them $115 for registration, $365 for transportation and food, and $55 per person for the hotel. There is $485 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $6 per car, how many cars must they wash in order to have enough money to pay for the trip?
Answer:
45 cars
Step-by-step explanation:
115+365+(55*5) = 755
755 - 485 =270
270/6 = 45
24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
Answer:
y-int = 0
slope = -1
equation: y = -x
Step-by-step explanation:
The line crosses the y-axis at y = 0, so the y-intercept is 0.
Go from (0, 0) to (-1, 1).
slope = m = rise/run = 1/(-1) = -1
y = mx + b
y = -x
y-int = 0
slope = -1
equation: y = -x
In 3 billion repetitions of an experiment, a random event occurred in 500 million cases.
The probability of the event is 1.
True or False
The probability of the event is 0.
True or False
What is the expected probability of this event?
What is the expected probability of the complement of the event?
Answer:
The probability of the event is 1. False
The probability of the event is 0. False
What is the expected probability of this event?
The probability of the event is (500 million successful events) / (3 billion total repetitions) = 0.1667 or 16.67%.
What is the expected probability of the complement of the event?
The complement of the event is the event not happening. The probability of the event not happening is (3 billion total repetitions - 500 million successful events) / (3 billion total repetitions) = 0.8333 or 83.33%.
Uday Tahlan
which is the highest 4,16,77 and lowest
Answer:
highest 77 and lowest is 4
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.
The probability of drawing a bag with bad potatoes is less than 1.
True or False
The probability of drawing a bag with good potatoes is greater than 0.
True or False
What is the probability of drawing a bag with bad potatoes?
What is the expected probability of the complement of the event?
Answer:
The probability of drawing a bag with bad potatoes is less than 1. True
The probability of drawing a bag with good potatoes is greater than 0. True
What is the probability of drawing a bag with bad potatoes?
The probability of drawing a bag with bad potatoes is (2 bad bags) / (20 total bags) = 0.1 or 10%.
What is the expected probability of the complement of the event?
The complement of the event of drawing a bag with bad potatoes is drawing a bag with good potatoes. The probability of drawing a bag with good potatoes is (18 good bags) / (20 total bags) = 0.9 or 90%.
Uday Tahlan
his mapping shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (2, 4), (negative 3, 0), (negative 1, negative 1), (4, 3). When f(x)=4, what is the value of x? 0 2 3 4
when f(x)=4, then the value of x is 2
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs:
The ordered pairs are (2, 4), (-3, 0), (- 1, -1), (4, 3)
We need to find value of x when f(x)=4
In the (x, y) ordered pair the x place represents the domain value and y place represents the range.
In the order pairs we have to look for the y value which has 4.
The corresponding element of 4 is the x value
So the value of x is 2 if f(x)=4
Hence, when f(x)=4, then the value of x is 2
To learn more on Functions click:
https://brainly.com/question/21145944
#SPJ1
if (x+A)^2 -3 = x^2 + 4x + B. Find the value of A and B
The values of A and B are 2 and 4 respectively.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the equation as -
(x + A)² - 3 = x² + 4x + B
We can write the given equation as -
(x + A)² - 3 = x² + 4x + B
x² + A² + 2Ax = x² + 4x + B
A² + 2Ax = 4x + B
A² + 2Ax = B + 4x
Equating both sides, we get -
A² = B
and
2A = 4
A = 2
Then B will be equivalent to 4.
B = 4
Therefore, the values of A and B are 2 and 4 respectively.
To solve more questions on expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
What does 69 divided by 310.5 equal in decimal form?
Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.
The design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz can be Illustrated through a coin.
How to design the simulation?Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.
He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.
Learn more about simulation on:
https://brainly.com/question/15892457
#SPJ1
Which of the following functions describes the graph of g(x)? (5 points)
Rational function with one piece decreasing from the left asymptotic to the line y equals 2 and going through a hole at the point negative 2 comma eight-fifths and going down through the point 2 comma 0 asymptotic to the line x equals 3 and another piece decreasing from the left asymptotic to the line x equals 3 and going through the point 5 comma 3 going up to the right asymptotic to the line y equals 2
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus 5 x plus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus 5 x plus 6 end quantity
The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that,
The function g(x).
The graph of a function never touches the x = 1 line
At x = -1 there will be a vertical asymptote.
At x = -2 there will be a horizontal asymptote.
The equation of the function g(x) will be:
g(x) = (2x + 4)/(x + 1)
The equation of rational function is g(x) = (2x + 4)/(x + 1)
Therefore, g(x) = (2x + 4)/(x + 1) is correct.
Learn more about a function on https://brainly.com/question/12431044
#SPJ1
Solve each equation for both variables help please 15 points
Answer:
I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!
Which absolute value function, when graphed, will be
wider than the graph of the parent function, f(x) = |x|?
On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.
What are similar angles?Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.
Given:
m ∠1 = m ∠2
m ∠2 = m ∠4
We have to prove that m ∠ABC = m ∠EDC
∠EDC = ∠3 + ∠4
m ∠ABC = m ∠1 + m ∠2
m ∠EDC = m ∠3 + m ∠4
m ∠1 + m ∠2 = m ∠3 + m ∠4
m ∠ABC = m ∠EDC
Hence, by using the given information we can prove that
m ∠ABC = m ∠EDC.
To know more about similar angles visit:
brainly.com/question/27996834
#SPJ1
draw and divide a rectangle to show each product use a distributive property to find the product 5×14
The product of 5 and 14 using the distributive property is 70.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
For three numbers a, b and c, Distributive property states that,
a (b + c) = a b + a c
We have to find the product 5 × 14 using distributive property.
5 × 14 = 5 (12 + 2)
Using distributive property,
5 × 14 = (5 × 12) + (5 × 2)
= 60 + 10
= 70
Hence using distributive property, we can find the product of 5 and 14 as 70.
To learn more about Multiplication, click on the link given below :
https://brainly.com/question/28335468
#SPJ1