The equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
According to the question,
We have the following information:
The product of two consecutive odd Integers is 143.
Now, let's take the smaller integer to be x.
Now, next consecutive odd integer:
(x+2)
So, we have the following expression:
x(x+2) = 143
[tex]x^{2} +2x = 143\\[/tex]
[tex]x^{2} +2x -143 = 0[/tex]
[tex]x^{2}[/tex]+13x-11x-143 = 0
Taking x as the common factor from first two terms and -11 from the last two terms:
x(x+13)-11(x+13) = 0
(x-11)(x+13) = 0
x-11 = 0 and x+13 = 0
x = 11 or x = -13
Next odd integer = 13 or -11
Hence, the equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
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5. Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay
race. Chris runs his part of the race in 12.35 seconds, Kiona takes
13.12 seconds, and Seiko takes 11.91 seconds.
a. The team wants to break the school record of 48.92 seconds. How
fast will Dwayne have to run?
Dwayne have to complete the race in 11.53 second or the speed of Dwayne is 11.53 second/ 100 meter.
What is speed of an object?
Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. The formula for speed is straightforward: time divided by distance.
Given that Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay
race. Chris runs his part of the race in 12.35 seconds, Kiona takes
13.12 seconds, and Seiko takes 11.91 seconds.
The total time that is taken by Chris, Kiona, and Seiko is (12.35 + 13.12 + 11.91) seconds = 37.38 seconds.
The team wants to break the record of 48.92 seconds.
To break the record, they should complete the race in 48.91 seconds.
Thus Dwayne have to run 100 meters in ( 48.91 - 37.38) = 11.53 seconds.
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 60% pure antifreeze. the company want to obtain 180 gallon of a mixture that contain 35% pure antifreeze. how many gallon of water and how many gallon of the premium antifreeze solution must be mixed
The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable w represent the gallons of water.Let the variable p represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
w + p = 180 ....equation 1.
0.60p = 0.40(180) ....equation 2.
From equation 2, we have:
0.60p = 0.40(180)
0.60p = 72
Premium antifreeze, p = 72/0.60
Premium antifreeze, p = 120 gallons.
For the gallons of water, we have:
w + p = 180
Water, w = 180 - p
Water, w = 180 - 120
Water, w = 60 gallons.
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Sarah ran 7/8 of the distance around the school track. Jacob ran 2/3 of Sarah‘s distance what fraction of the total distance around the tractor Jacob run?
Jacob run 7/12 of the total distance around the school track.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
Given: Sarah ran 7/8 of the distance around the school track.
Jacob ran 2/3 of Sarah‘s distance.
To find what fraction of the total distance around the track Jacob ran, we will find when solving 2/3 of 7/8 or symbolically
[tex](\frac{2}{3})(\frac{7}{8}) = \frac{14}{24} = \frac{7}{12}[/tex]
Hence, Jacob run 7 / 12 of the total distance around the school track.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Employee Number Years Worked 1 8 2 13 3 15 4 3 5 13 6 28 7 4 8 12 9 4 10 26 11 29 12 3 13 10 14 3 15 17 16 13 17 15 18 15 19 23 20 13 21 12 22 1 23 14 24 14 25 17 26 16 27 7 28 27 29 18 30 24 The data shows the number of years that 30 employees worked for an insurance company before retirement. is the population mean for the number of years worked, and % of the employees worked for the company for at least 10 years. (Round off your answers to the nearest integer.)
The population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.
The mean is calculated by dividing the number of employees by the number of years of service. The total number of years of service is 417, hence the average will be
The average years worked = 417/30 = 13.9 ≈ 14 years
The % of workers who have worked there for at least ten years is calculated by calculating the number of employees who have ten or more years of service and dividing that number by the total number of employees.
The final result is presented as a percentage will be:
(10 years or more)/(total number) = 22/30 = 0.73 = 73%
Thus, the population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.
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Question 4 of 10
If f(x) = 2(x)² +5√(x+2), complete the following statement (round your
answer to the nearest hundredth):
f(0) =
The function of f(0) =7.0710.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(x) = 2(x)² +5√(x+2)
f(0) = 2*0 +5√2
f(0) = 7.0710
Hence the value will be 7.0710.
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Write (-4x^2ya^3)^2 as a monomial in standard form.
Answer:
[tex]16a^6x^4y^2[/tex]
Step-by-step explanation:
To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])
Using that rule, we get:
[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].
This can be simplified to
[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],
which can be written as:
[tex]16a^6x^4y^2[/tex]
using the commutative property of multiplication.
This table gives a few (x, y) pairs of a line in the coordinate plane.
x
Y
-54
-21
-40
-14 -26
- 28
What is the y-intercept of the line?
The y-intercept of the line is y = 2
What is an intercept?
A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
Here,
A linear function has the following equation:
y = mx + b
Where m is the slope and b is the y-intercept, which is the value of y when x = 0.
We have given three points:
(-28, -54)
(-21, -40)
(-14, -26)
We use two of them to construct a system, to find values for m and b.
(-28, -54)
This means that when x = - 28 , y = - 54
so, y = mx + b
- 54 = - 28m + b
28m = b + 54
m = (b + 54)/28
Now, we have x = -21, y = -40
so, y = mx + b
- 40 = - 21m + b
we put the value of m here
- 40 = - 21 {(b + 54)/28} + b we get,
7b - 1134 = - 40 × 28
b = 2
Hence, the y-intercept of the line is y = 2
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Answer:
(0,2)
Step-by-step explanation:
khan academy
10% of your grade is participation, 30% is class work/homework, 60% is test /projects. a student had an average of 100 for participation, 95 for class work/homework and 75 for test/projects. What the is the grade in the class?
The overall weighted average grade for this student in the class is 83.5%.
How is the weighted average grade computed?The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.
The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.
Grade Average Class Grade
Participation 10% 100 10% (10% x 100%)
Classwork/Homework 30% 95 28.5% (30% x 95%)
Test/projects 60% 75 45% (60% x 75%)
Total grade in class 83.5%
Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.
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If you want easy access to your money for paying bills, eating out, etc, it is best to use a ____________ account.
If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.
What is checking account?A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.
For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.
It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.
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A food company stores grain in a hopper. The hopper is 12 feet in diameter and holds 2024.5 cubic feet of grain. When turned on, the hopper empties grain at a constant rate of 42 cubic feet per second. About how long does it take for the hopper to empty all the grain?
The hopper will empty all of the grain in approximately 48.2 seconds .
Total amount of grain in the hopper = 2024.5 cubic feet
Rate at which the grain is emptied = 42 cubic feet /second.
Time taken to empty the grain
= 2024.5 / 42
= 48.202...
≈ 48.2 seconds
The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.
Hence the hopper will empty all the grain in about 48.2 seconds.
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somebody answer, please?
The table displays data collected, in meters, from a track meet.
one fourth 6 2 4
3 two thirds one third nine halves
What is the median of the data collected?
2.5
4.5
2
3
The median of the data collected from a track meet is 2 meters.
What is median?The median is the middle number in a sorted, ascending or descending list of numbers.
To calculate the median of the given date, we folloe the steps below.
Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2
Step 1: Rearreange the date in accending order.
1/3, 1/2, 2/3, 1, 2, 3, 4, 4, 6Step 2: Pick the middle of the number in the arranged data
Median = 2 meters.Hence, the median of the data collected is 2 meters.
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Answer:
2.5
Step-by-step explanation:
a property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance for each distance between 2 points on the map.
10 cm
= __ cm
If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm
How to find the actual distance on a scale of 1 :1000information gotten from the question
a scale of 1:1000
2 points on the map 10 cm = ?
Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image
A map has a scale of 1 : 1000
the scale factor is 1/1000 then 10/?
1/1000 = 10/?
cross multiplying gives
? = 10 000 cm
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 90 %, σ is not known, and the histogram of 52 player salaries (in thousands of dollars) of football players on a team is as shown.
The correct statement regarding the critical value of the t-distribution is given as follows:
a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]
Which distribution should be used?What defines which distribution should be used is whether the population standard deviation is known, as follows:
If the population standard deviation σ is known, then the z-distribution is used.If the population standard deviation σ is not known, then the t-distribution is used.As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.
The critical value is obtained using a t-distribution calculator, considering that:
The confidence level is of 90%.The amount of degrees of freedom, which is one less than the sample size, is of 52 - 1 = 51.Hence it is given as follows:
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Use the number line below, where RS
I need help with this please help me
Which set of fractions is ordered from least to greatest?
A) 5/8, 8/12, 3/4
B) 8/12, 5/8, 3/4
C) 3/4, 5/8, 8/12
D) 5/8, 3/4, 8/12
The arrangement of the fraction from least to greatest is A. 5/8, 8/12, 3/4.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator, as well as the denominator, are both integers
The fraction can be changed to percentage to make it easier.
5/8 = 5/8 × 100 = 62.5%
8/12 = 8/12 × 100 = 66.7%
3/4 = 3/4 × 100 = 75%
The arrangement is 5/8, 8/12, 3/4.
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Is 3 4/9 greater than 3 4/5?
for every 4 male birds in a cage there are 6 females what is the ratio of males to females
The ratio of males to females in the cage is 2:3.
According to the question,
We have the following information:
For every 4 male birds in a cage there are 6 females.
The ratio of males to females = Number of males in the cage: number of females in the cage
Ratio of males to females = 4:6
We can convert this ratio into the simplest form by dividing both the numbers by 2 and this will also be the equivalent ratio of this obtained ratio.
Ratio of males to females = 2:3
Hence, the ratio of males to females in the cage is 2:3.
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An interest survey was taken at a summer camp to plan leisure activities. The results are given in the tree diagram.
The tree diagram shows campers branching off into two categories, prefer outdoor activities, which is labeled 80%, and prefer indoor activities, which is labeled 20%. Prefer outdoor activities branches off into two sub-categories, prefer hiking, which is labeled 70%, and prefer reading, which is labeled 30%. Prefer indoor activities branches off into two subcategories, prefer hiking, which is labeled 20%, and prefer reading, which is labeled 80%.
What percentage of the campers prefer outdoor activities and reading?
24%
30%
56%
80%
The percentage of the campers prefer outdoor activities and reading is A. 24%.
What is the percentage?From the information, the tree diagram shows campers branching off into two categories, prefer outdoor activities is labeled 80%, and those who prefer reading, which is labeled 30%.
Therefore, percentage of the campers prefer outdoor activities and reading will be:
= Percentage for outdoor × Percentage of reading
= 80% × 30%
= 24%
In conclusion, the correct option is A.
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Answer: 56% i did the test
Step-by-step explanation:
1. Which function below is an exponential function?
Answer:
D
Step-by-step explanation:
The sum of two numbers is
36. Three times the smaller plus
twice the larger is 87. Find the
two numbers.
Answer:
2 and 43.5
Step-by-step explanation:
Help. I'll mark as brainlist.
Answer: 22 square unit
Step-by-step explanation:
As each small square represents one square unit, we can count the squares and get the answer easily.
leo
toring
29
Due Dec 6 by 11:59pm
Question 13
Ch. 9 Quadratics Homework (Copy)
Score: 12/17 12/17 answered
▼
The width or short side is
The length or long side is
Points 20
Submit Question
The length of a rectangle is 6 feet longer than it is wide. If each side is increased 6 feet, then the area is
multiplied by 2. What was the size of the original rectangle?
<
Submitting an external too
The width or short side is 12 feet
The length or long side is 18 feet
What is Area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.
Let Width= x feet
so, as per question Length = x+6 feet
Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]
According to the question each side is increased 6 feet
New Length = x+12 feet
New Width = x+6 feet
New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>
Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]
x+12=2x
x=12 feet
so, original width = 12 feet
original length = 18 feet
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If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible
volume of the box.(include units)
solve for each proportion
Answer:
r = 20/7
x = 13.5
Step-by-step explanation:
Hello!
7)Solve for r by cross-multiplying:
[tex]\frac r2 = \frac {10}7[/tex][tex]r*7 = 10 * 2[/tex][tex]7r = 20[/tex][tex]r = \frac{20}7[/tex]The value of r is 20/7.
8)Solve for x by cross-multipying:
[tex]\frac 94 = \frac x6[/tex][tex]9*6 = 4*x[/tex][tex]4x = 54[/tex][tex]x = 13 \frac12[/tex]The value of x is 13.5.
Answer:
7) r = 20/7 8) x = 27/2Step-by-step explanation:
7) r/2 = 10/7, value of r?
→ r/2 = 10/7
→ r = (10/7) × 2
→ r = (10 × 2)/7
→ [ r = 20/7 ]
Hence, value of r is 20/7.
8) 9/4 = x/6, value of x?
→ 9/4 = x/6
→ x/6 = 9/4
→ x = (9/4) × 6
→ x = (9 × 6)/4
→ x = 54/4
→ [ x = 27/2 ]
Hence, value of x is 27/2.
If < 1 and <2 are complementary, and m< 1 = 42°, find m< 2.
Answer:
m< 2= 48°
Step-by-step explanation:
Complementary angles sum up to 90 degrees
We know that m< 1 = 42°
All we have to do is subtract 90 from 42 to find m< 2:
m< 2= 90 - 42
m< 2= 48°
Hope this answers your question :)
Periodic Inventory Using FIFO, LIFO, and Weighted Average Cost Methods The units of an item available for sale during the year were as follows: Jan. 1 Inventory 16 units at $31 $496 Aug. 13 Purchase 14 units at $33 462 Nov. 30 Purchase 13 units at $35 455 Available for sale 43 units $1,413 There are 21 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using the (a) first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal places and your final answer to the nearest whole dollar). a. First-in, first-out (FIFO) $fill in the blank 1 b. Last-in, first-out (LIFO) $fill in the blank 2 c. Weighted average cost
The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:
a) first-in, first-out (FIFO) method: $719
b) last-in, first-out (LIFO) method: $661
c) weighted average cost method: $690
What does the ending inventory cost?The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.
Some of the inventory methods include:
First-in, First-outLast-in, First-outWeighted AverageSpecific Identification.Date Activities Units Unit Cost Total
Jan. 1 Inventory 16 $31 $496
Aug. 13 Purchase 14 $33 462
Nov. 30 Purchase 13 $35 455
Available for sale 43 $1,413
Average cost = $32.86 ($1,413 ÷ 43)
Ending inventory 21
Units sold = 22 (43 - 21)
a) FIFO:
Ending inventory = $719 (13 x $35 + 8 x $33)
Cost of goods sold = $694 ($1,413 - $719)
b) LIFO:
Ending inventory = $661 (16 x $31 + 5 x $33)
Cost of goods sold = $752 ($1,413 - $661)
c) Weighted Average:
Ending inventory = $690 (21 x $32.86)
Cost of goods sold = $723 (22 x $32.86)
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As a member of the hiking club, you have paid
a total of $51 after 4 months and a total of $105
after 10 months. What is the linear equation in
slope-intercept form that models this situation.
The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
In the question ,
it is given that ,
a member of hiking club paid $51 for 4 months ,
let the number of months be represented on x coordinate , and
the amount paid be represented on y coordinate .
So , the point becomes (4 , 51).
also given that you pay a total of $105 after 10 months ,
the second point becomes (10 , 105).
to find the equation in slope intercept form , we need slope ,
So , Slope = (105-51)/(10-4)
= 54/6
= 9
So , the equation having the point (4,51) and slope as 9 , in slope intercept form is
(y - 51) = 9(x - 4)
y - 51 = 9x - 36
y = 9x - 36 + 51
y = 9x + 15
Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
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The sum of four consecutive numbers is thirty-two. Find the largest number. (show work)
9.5 is the largest number
Consecutive numbers are the number will follow each other in order.
The difference between every two numbers is one. if n is the number so, the consecutive number will be n+1,n+2 , . . . . . .
Let four consecutive numbers be a , a+1 , a+2 , a+3
where a+3 will be largest number
Given the sum of these is 32
a + a +1 +a + 2 + a +3 = 32
=> 4a + 6 = 32
=>4a = 26
=> a= 26/4
=> a = 6.5
putting the values,
consecutive number will be = 6.5 , 7.5 , 8.5 , and 9.5
9.5 is the largest number
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For a $250,000 mortgage, with an interest rate of 6% paid over 25 years, the monthly payment is $1,610.75. After one month, what is the balance of the loan?
Round your answer to the nearest dollar.
Do NOT round until you calculate the final answer.
The balance on the loan after a month is $623389.25.
How to calculate the interest?The following can be deduced from the information given:
Principal = $250000
Time = 25
Rate = 6%
Interest = (Principal × Rate × Time) / 100
Interest = (250000 × 6 × 25) / 100
Interest = $375000
The total amount will be:
= Principal + Interest
= $250000 + $375000
= $625000
The balance of the loan will be:
= Amount - One month payment
= $625000 - $1,610.75
= $623389.25
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Compare the following functions:
Function A: y = 4x −5
Function B: _______.
What is the slope/rate of change of Function A? ______.
What is the slope/rate of change of Function B between f(0) and f(1)? ______.
What is the slope/rate of change of Function B between f(1) and f(2)? ______.
What is the slope/rate of change of Function B between f(2) and f(3)? _____.
The slope of Function A is _______.
The slope of Function B is _______.
The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;
The slope of function A is 4
The slope of function B are;
Between f(0) and f(1), the slope is 1
Between f(1) and f(2), the slope is 3
Between f(2) and f(3), the slope is 5
What is the slope of a graph of a function?The slope is found by the ratio of the rise to the run of the graph.
The function A is; y = 4·x - 5
Function A is of the form y = m·x + c
Where;
m = The slope of the function = 4
Therefore;
The slope of function A is 4
The first difference of the values of function B is not a constant.
The value of f(0) in function B is 0
The value of f(1) in function B is 1
The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)
Which indicates that m = (1 - 0)/(1 - 0) = 1
The slope of function B between f(1) and f(2) is found as follows;
f(2) = 4, f(1) = 1, from which we get;
m = (4 - 1)/(2 - 1) = 3
The slope between f(2) and f(1) is 3
The slope of the function B between f(2) and f(3) is found as follows;
f(2) = 4, f(3) = 9, from which we get;
m = (9 - 4)/(3 - 2) = 5
The slope of the function B between f(2) and f(3) is 5
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