Therefore, the solution of the given problem of function comes out to be [tex]f^{-1}[/tex] = x+ 6 /7.
Describe function.Mathematics includes the study of numbers, equations and associated structures, forms and the environments in which they occur, quantities and their changes, and spatial relationships. A function is an association between such a set of inputs, each of which has an output. Simply described, a function is an association between the inputs and outputs in which each input results in a single, distinct result. Each operation has a domain and a scope, which are also referred to as codomains.
Here ,
In our case, f(x) = y = 7x-6.
The following procedures must be taken in order to determine the inverse function of the given function:
First, x and y must be switched, thus
x= 7y-6
We must add 6 to both sides in order to solve for y in the following step.
x+6=7y
7 divided by both sides, that is
y = x+ 6 /7
Therefore, the solution of the given problem of function comes out to be
[tex]f^{-1}[/tex] = x+ 6 /7.
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What are 2 examples of composite number?
Composite numbers are whole numbers that contain more than two elements.. Examples of composite numbers include 36 and 42. These numbers are divisible by more than just 1 and themselves. 36 is divisible by 1, 2, 3, 4, 6, 9, 12, and 18. 42 is divisible by 1, 2, 3, 6, 7, 14, and 21.
Example 1: To find the factors of 36
Step 1: Start by dividing 36 by 2, which gives us 18.
Step 2: Divide 18 by 2, which gives us 9.
Step 3: Divide 9 by 3, which gives us 3.
Step 4: Divide 3 by 3 which gives us 1.
Step 5: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.
Example 2: To find the factors of 42
Step 1: Start by dividing 42 by 2, which gives us 21.
Step 2: Divide 21 by 3, which gives us 7.
Step 3: Divide 7 by 7 which gives us 1.
Step 4: The factors of 42 are 1, 2, 3, 6, 7, 14, and 21.
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Question Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. f(x)=x4−6x3−8x+48; x−6
Answer:
(x-2)(x²+2x+4)(x-6)
Step-by-step explanation:
6 | 1 -6 0 -8 48
_____6_0_0_-48__
1 0 0 -8 | 0
As we can see, our remainder is 0, so x-6 is indeed a factor of the polynomial. Also, we can see that the factored polynomial is [tex]x^4-6x^3-8x+48=(x^3-8)(x-6)=(x-2)(x^2+2x+4)(x-6)[/tex]
Which inequalities are true? Check all that apply. You
can use the tool on the right to help you.
5/6 > 4/6
3/8< 5/8
4/5 <2/5
4/7> 6/7
2/31/3
The true inequalities are:
5/6 > 4/6
3/8< 5/8
2/3 > 1/3
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
5/6 > 4/6
0.833 > 0.667
so, this inequality is true.
3/8 < 5/8
0.375 < 0.625
so, this inequality is true.
4/5 < 2/5
0.8 < 0.4
so, this inequality is false.
4/7 > 6/7
0.571 > 0.857
so, this inequality is false.
2/3 > 1/3
0.667 > 0.333
so, this inequality is true.
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The table shows a linear function. What is the rate of change?
Hours
Pay
1
18
1.5
23
2
28
2.5
33
3
38
Answer:
rate of change = 5
Step-by-step explanation:
the slope m gives the measure of the rate of change of the function
calculate the slope m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]
with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table
m = [tex]\frac{18-38}{1-3}[/tex] = [tex]\frac{-20}{-2}[/tex] = 5
then rate of change = 5
A number, x, rounded down to 1 significant figure is 40
Write down the error interval for x.
Please explain How you got the answer and thanks so much in advance
Error interval is 35 ≤ x < 45.
Error intervals working?
Error intervals work by providing a range of values within which the true population value is likely to fall, with a certain level of confidence. The most common level of confidence used is 95%, which means that if the survey or experiment were conducted multiple times, the true population value would fall within the error interval 95% of the time.
We are looking at a rounded value when we employ error intervals. The range of values that were possible before the number was rounded is described by an error interval.
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is 35 ≤ x < 45.
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
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The sum of the interior angles of a polygon is 20 x 180.
Work out the number of sides of the polygon.
sides
So the polygon has 22 sides.
A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle with three sides is an example of a polygon.
The sum of the interior angles of a polygon can be calculated using the formula:
(n-2) * 180 = sum of the interior angles
Where n is the number of sides of the polygon.
We know that the sum of the interior angles is 20*180, so we can substitute this into the formula:
(n-2) * 180 = 20 * 180
Solving for n, we get:
n = (20 * 180) / 180 + 2
n = 20 + 2
n = 22
So the polygon has 22 sides.
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1. Which word doe not have a imilar meaning to - condemn
critique
diparage
criticize
cenure
Among the given four options, the word that doesnot have similar meaning to condemn is "critique".
What is the meaning of word condemn?The word "condemn" means to express strong disapproval or criticism of something or someone, often in a formal or official manner. It can also mean to pronounce a judgment of guilt, especially in a court of law. It implies a severe judgment or punishment. Condemn also implies the declaration of something being morally wrong or unacceptable. It is a strong word that carries a sense of condemnation or blame.
Make two sentences using the word condemn.The sentences are given below:
The judge condemned the defendant for his crimes, sentencing him to life in prison.The community condemned the company for their unethical business practices and called for a boycott.The word that does not have a similar meaning to "condemn" is "critique".
"Condemn" means to express strong disapproval of something or someone, often in a formal or official manner.
"Criticize" means to express disapproval or to find fault with something or someone
"Censure" means to express strong disapproval or criticism of something or someone, typically in a formal or official manner.
"Disparage" means to speak or write about in a negative way; to belittle or criticize.
"Critique" means to evaluate (a work of art, literary work, etc.) in terms of its strengths and weaknesses; to give an analysis or evaluation of something."Critique" is different because it is an analysis or evaluation of something, whereas the other words are about expressing disapproval or criticism.
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Simplify: [tex]\frac{10m}{5m}[/tex]
Answer:
2
When you cancel out the m (cause its the common factor) the only thing left is to simplify 10/5 which is 2.
26. Pregnancy length The length of human pregnancies from conception to birth
follows a Normal distribution with mean 266 days and standard deviation 16 days.
Choose a pregnant woman at random. Let X = the length of her pregnancy.
(a) Find P(X2 240) and interpret the result.
(b) What is P(X> 240)? Explain.
(c) Find the value of c such that P(X ≥ c) = 0.20. Show your work.
There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the the value of c such that P(X ≥ c) = 0.20 is 279.44
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
Given that Mean (μ) = 266
and Standard deviation(σ) = 16
The z-score is the value decreased by the mean divided by the standard deviation:
z = (x−μ)/σ = (240−266)/16
≈−1.63
Determine the corresponding probability using the normal probability table in the appendix:
P (X ≥ 240)
= 1 - P (X < 240)
= 1 - P(Z < -1.63)
= 1 - 0.0516
=0.9484
(a) There is a chance of about 94.84% that the pregnancy last at least 240 days
(b) P (X ≥ 240) = 0.9484
(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.
The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04
thus, the z-value is z=0.84.
x = μ+zσ = 266+0.84*(16 )
=279.44
The the value of c such that P(X ≥ c) = 0.20 is 279.44
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There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the the value of c such that P(X ≥ c) = 0.20 is 279.44
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
Given that Mean (μ) = 266
and Standard deviation(σ) = 16
The z-score is the value decreased by the mean divided by the standard deviation:
z = (x−μ)/σ = (240−266)/16
≈−1.63
Determine the corresponding probability using the normal probability table in the appendix:
P (X ≥ 240)
= 1 - P (X < 240)
= 1 - P(Z < -1.63)
= 1 - 0.0516
=0.9484
(a) There is a chance of about 94.84% that the pregnancy last at least 240 days
(b) P (X ≥ 240) = 0.9484
(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.
The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04
thus, the z-value is z=0.84.
x = μ+zσ = 266+0.84*(16 )
=279.44
The the value of c such that P(X ≥ c) = 0.20 is 279.44
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Using data from 1944 through 2000, the histogram shows the number of years that had a particular number of hurricanes reaching the East Coast of the U.S. For example, in 14 of those years there was exactly one hurricane each year that reached the East Coast of the U.S. What is the median number of hurricanes per year reaching the East Coast from 1944 through 2000
The median number of hurricanes per year reaching the East Coast from 1944 through 2000 is two.
What is median number?Median number is the middle value of a set of numbers. It is the number found at the midpoint of a sorted data set, when all the numbers are arranged in numerical order from lowest to highest. The median number is used to determine the average of a set of numbers, and is often used to represent the central tendency of the data. To calculate the median, first arrange the numbers from lowest to highest, then locate the middle value. If there is an even number of values, the median is the average of the two middle numbers.
This is calculated by taking the middle value of the data set. In this case, there were 18 years with one hurricane, 16 years with two hurricanes, 13 years with three hurricanes, and six years with four hurricanes. Thus, the median number of hurricanes in this data set is two.
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Can u please help.......
Using the centroid P on the triangle, the value of QN is 25.5 and PN is 8.5
What is Centroid of a TriangleThe centroid of a triangle is a point located at the intersection of the three medians (the lines that connect the vertices to the midpoints of the opposite sides). The centroid divides each median in two segments that have the same length. It is the center of gravity of the triangle and is the point at which the triangle's three medians intersect.
The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
In this triangle, the centroid is at P and the QP is 17.
a) QN
The distance between QP is two-thirds the length of QN
The length of QP = 17
QP = 2/3 QN
17 = 2/3 QN
QN = (3 * 17) / 2
QN = 25.5
b) PN
The distance between PN is calculated as;
PN = QN - QP
PN = 25.5 - 17
PN = 8.5
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ASAP 100 POINTS PLUS BRAINLIEST
A local rent-to-own business has a television set advertised with a purchase price of $1,095. 0. Calculate the APR if the finance terms are $29. 99 per week for 73 weeks. Round the final answer to the nearest tenth. (4 points)
73. 4%
71. 4%
81. 2%
Based on the provided information, the APR is 71.4%.
Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by
APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100
The finance terms in the given case is $29.99 per week for 73week. Hence,
Total amount paid = 29.99*73 = $2,189.27
Loan principal = $1,095
Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27
Fees = 0 (as it not mentioned in the question)
Number of days in loan terms = 73*7 = 511 days
Substituting the values in the formula,
APR = ((1094.27/1095)/511) * 365 * 100
APR = 71.4%
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A whale descends from the surface of the water at a rate of 22 feet per minute.
What is the position of the whale relative to the surface after diving for 3
minutes?
Answer:
66
Step-by-step explanation:
22 per minute
? Per 3 minutes
22 x 3 = 66
Answer: The position of the whale relative to the surface of the water can be determined by multiplying the rate at which it descends (22 feet per minute) by the amount of time it has been descending (3 minutes).
Position = Rate x Time
Position = 22 feet/minute x 3 minutes = 66 feet
So, after diving for 3 minutes, the position of the whale relative to the surface of the water is 66 feet.
It means the whale descended for 66 feet from the surface level of the water.
Please keep in mind that this information is assuming a linear motion, without taking into account any other factors that could affect the whale's descent such as currents or obstacles in the water.
Step-by-step explanation:
Determine whether the graph of the given equations are parallel, perpendicular, or neither
Answer:
7) perpendicular
8) perpendicular
Step-by-step explanation:
If the equations are in the form:
y = mx + b
(they all are in this form in these questions)
the m, the number in front of the x, is the slope.
If the slopes are the "negative reciprocals" (opposite signs and flipped over from each other) of each other, then the lines are perpendicular.
You can also do a quick check by, if the m values are multiplied together you should get -1.
1/3 • - 3 = -1
1 • -1 = -1
1/3 and -3 have opposite signs and are reciprocals (flipped over)
1 and -1 are opposite signs. It isn't very obvious maybe that they are reciprocals, but they are. Like 1/1 flipped over is 1/1.
What is the formula of polynomial?
The general formula of a polynomial is:
P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
A polynomial is a mathematical expression consisting of variables (such as x), coefficients, and exponents. The general formula of a polynomial is P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0. Here, a_n, a_(n-1), ... , a_2, a_1, and a_0 are coefficients, and n is the degree of the polynomial. The highest exponent in the polynomial is the degree of the polynomial. For example, in the polynomial 3x^2 + 5x – 8, x^2 is the highest exponent, so the degree of the polynomial is 2. The coefficient of the highest exponent is known as the leading coefficient. In the example above, 3 is the leading coefficient. Polynomials can be used to represent a variety of functions, from simple linear equations to complex curves.
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A $73 ceramic vase costs $78.84 after sales tax is figured in. What is the sales tax percentage?
Answer:
8%
Step-by-step explanation:
78.84 - 73 = 5.84
Tax = $5,84
5.84 / 73 = 0.08
0.08 * 100 = 8%
Answer:
8%
Step-by-step explanation:
1. Set up the equation represented
[tex]$78.84 = \frac{x}{100}(73) + 73[/tex]
x is the sales tax percentage. hence, we have to solve for x.
[tex]$78.84 = \frac{x}{100}(73) + 73[/tex]
[tex]$78.84 = \frac{73x}{100} + 73[/tex]
[tex]5.84 = \frac{73x}{100}[/tex] . . . . . . . . . . . . . . subtract both sides of the equation by 73
[tex]584 = 73x[/tex] . . . . . . . . . . . . . . multiply both sides by 100
[tex]8 = x[/tex] . . . . . . . . . . . . . . . . . . divide both sides by 73
∴ There was an 8% sales tax on the ceramic vase.
PLEASE MARK BRAINLIEST IF THIS HELPED YOU. THANKS.
if logx 27 +logy 4 =5 and log x 27 -logy 4=1 find x and y
Answer:
[tex](x,y)\rightarrow(3,2)[/tex]
Step-by-step explanation:
I assume you mean [tex]\log_x(27)+\log_y(4)=5[/tex] and [tex]\log_x(27)-\log_y(4)=1[/tex]:
[tex]\biggr(\log_x(27)+\log_y(4)\biggr)-\biggr(\log_x(27)-\log_y(4)\biggr)=5-1[/tex]
[tex]2\log_y(4)=4\\\log_y(4)=2\\4=y^2\\2=y[/tex]
[tex]\log_x(27)+\log_y(4)=5\\\log_x(27)+\log_2(4)=5\\\log_x(27)+2=5\\\log_x(27)=3\\27=x^3\\3=x[/tex]
The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
The total cost of an item that sells for $12 is $12.96
How to determine the total cost of an item that sells for $12?From the question, we have the following parameters that can be used in our computation:
Selling price = $12
Sales tax = 8%
The total cost of an item that sells for $12 is then calculated as
Total cost = Selling price * (1 + Sales tax)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 12 * (1 + 8%)
Evaluate
Total cost = 12.96
Hence, the total cost is $12.96
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What are the coordinates of point (x,y) when it is reflected across the line y=−x?
The coordinate of the reflection is (-y, -x)
How to determine the coordinate of the reflectionFrom the question, we have the following parameters that can be used in our computation:
Point = (x, y)
Reflection: Across the line y=−x
Using the above as a guide, we have the following:
The reflection of a point over the line y = -x implies that, the x-coordinate and y-coordinate change places Then they are negated (the signs are changed)So, we have
Image = (-y, -x)
Hence, the image is (-y, -x)
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Adrian has $1 worth of nickels and dime. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Adrian has. Define the variables that you use to write the system.
Answer: We can use two variables, x and y, to represent the number of dimes and nickels Adrian has, respectively.
We know that Adrian has twice as many nickels as dimes, so we can write the equation:
y = 2x
We also know that the total value of the coins is $1, and since nickels and dimes have different values, we can write the equation:
0.05y + 0.1x = 1
So the system of equations is:
y = 2x
0.05y + 0.1x = 1
These equations can be solved simultaneously to find the number of nickels and dimes that Adrian has.
Step-by-step explanation:
Answer: X+ywwiww asksn q9ru3
Step-by-step explanation:
88-2
1. Write the equation of the mirror line for the segment with endpoints (5, 4) and (-1, -1).
2. Find the reflection of the point A(3, -2) through the mirror line of y = 1/2x − 1.
The price of an article is fixed at a certain percent above the cp and sold it at 5% discount . If the cp is rs16000 and sp is rs20900 with 10% vat ,how much percentage is mp more then cp ?
Markup price is 30% more then Cost price.
What is VAT?The selling price includes a VAT (which is a form of tax) and a discount.
A Vat is a form of tax which increases the price of a good and a discount reduces the price.
The marked price is mp = cp(1 + 5%) = 1.50cp
The selling price is sp = mp(1 -10%) = 0.90mp
The gain is profit =sp -cp
= (0.90(1.50cp)) -cp
= cp(0.90·1.50 -1)
= 0.04cp
Mark up = (selling price - cost price) / cost price
(20900 - 16,000) / 16,000 = 0.306 = 30.6 %
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someone help me
Plsss
Answer:
Step-by-step explanation:
oh thats easy its 2
Annie and Bonnie are running laps around a 400-meter oval track. They started together, but Annie has pulled ahead, because she runs 25% faster than Bonnie. How many laps will Annie have run when she first passes Bonnie
Bonnie will complete four laps before being passed by Annie because she runs an additional quarter lap for every lap she completes. This indicates that Annie and Bonnie are on an equal footing, and Annie must complete an additional lap to pass Bonnie. Annie will have completed five laps after that.
What unitary method examples are there?We can use the unitary method to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.
What circumstances allow us to use the unitary method in our daily lives?The unitary method can be used to calculate how many kilometres a car will travel on one litre of gas if it travels 44 km on two litres of fuel. In other words, the unitary method is the process by which we determine the value of a single unit and then use that information to determine the values of multiple units.
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please help if you know the answer i need to get my grade up
Work hard to get all your work done and still have time to study.
How can you request a grade increase?Highlight your drive to improve. It is critical that your lecturer recognizes your desire to enhance your course performance. During your meeting, ask the professor for advice on how to enhance future assignments. “I’m really committed to improving my grade in this course,” try stating.
Say what you feel is wrong with your grade calmly and professionally. Present additional examinations and assignments that indicate your abilities, and provide a solution that you believe is feasible. Be persuading and confident, but don’t think you know more or better than your teacher.
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How do you solve a math problem step by step?
Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.
There are few basic steps to be followed while solving any mathematics problem:
1. Read and understand the problem.
2. Identify what is given and what is needed to solve the problem.
3. Choose an appropriate strategy to solve the problem.
4. Carry out the strategy.
5. Check your answer to make sure it is correct.
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A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the cat cover in taking 12 steps
According to unitary method, cat takes 12 steps to cover 9 feet.
How do you translate distance in steps?Measure your stride length or assume that it is 2.2 feet for women and 2.5 feet for men to determine it. Add the stride length to the number of steps, for example, 2.2 feet multiplied by 1,000 feet equals 2,200 feet. The answer is 2,200 ft / 5,280 0.42 mi when expressed in miles.
Given, it takes a dog three steps to cover the same distance as a cat four steps.
4 steps of a cat = 3 steps of a dog
12 cat steps equal (3/4)*12 to 9 dog steps.
Additionally, a dog's step covers one foot.
The dog moves nine feet in nine steps.
So a cat takes 12 steps to cover 9 feet.
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Philip is having a party and wants to spend less than $572. He has already spent $500. The only item left on his list is sodas, which cost $8 per case. How many cases of soda, x, can Philip purchase and stay under his budget? Select the number line that includes the largest number of cases of soda that Philip can purchase and still stay under his budget.
Answer:
x = 8
Step-by-step explanation:
572 - 500 = 72
72 / 8 = 9.
But in order to spend less than 572, he has to buy 8 cases. If he buys 9 cases he will be exactly 572.
Answer:
9 or fewer cases
Step-by-step explanation:
Solving a two step equation:
First, determine how much he has left to spend
572 - 500 = 72
He has 72 dollars left to spend on soda
Each case is 8 dollars.
Divide how much he has to spend by the cost of each case
72/8 = 9
He can buy up to 9 cases and stay under budget.
Is 4x² 3x 7 a polynomial in one variable?
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
what is polynomial ?A polynomial is an expression in mathematics made up of variables (sometimes referred to as indeterminates) and coefficients that only employs the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that combines variables, constants, and exponents utilizing addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
given
'x' is the only variable in the provided polynomial. As a result, the polynomial 4x² - 3x + 7 has one variable.
The following list includes a few examples of polynomials with one variable: x+2. x2+3x+2.
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Where is quadrant 4?
The fourth quadrant, often known as Quadrant IV, is the bottom right quadrant. The x-axis in this quadrant is positive, whereas the y-axis is negative.
Two-dimensional Cartesian axes separate the plane into four infinite areas known as quadrants, each of which is bordered by two half-axes. These are frequently numbered 1 through 4.
90° arc; one-fourth of a circle. the region enclosed by such an arc and two sketched radii, one at each extreme. a component of a machine that has a quarter-circle form.
The x- and y-coordinates are both positive in quadrant I.
The x-coordinate is negative and the y-coordinate is positive in quadrant II.
The x- and y-coordinates are positive in quadrant III.
Quadrant IV: The x-coordinate is positive and the y-coordinate is negative.
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