All the zeroes of f(x) are, - 4, 3/2, - 5/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ f(x) = 9x³ + 45x² + 26x - 40
And, (x + 4) is a factor of f(x).
Now, Divide the function as;
⇒ x + 4 ) 9x³ + 45x² + 26x - 40 ( 9x² + 9x - 10
9x³ + 36x²
- -
------------------------
9x² + 26x
9x² + 36x
- -
-----------------------
- 10x - 40
- 10x - 40
------------------
0
Thus, All the factors of function f (x) is,
⇒ (x + 4) (9x² + 9x - 10)
⇒ (x + 4) (9x² + 15x - 6x - 10)
⇒ (x + 4) (3x(3x + 5) - 2(3x + 5))
⇒ (x + 4) (3x - 2) (3x + 5)
Thus, All the zeroes are,
⇒ x + 4 = 0 ⇒ x = - 4
⇒ 3x - 2 = 0 ⇒ x = 2/3
⇒ 3x + 5 = 0 ⇒ x = - 5/3
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* image is provided*
I know it might be hard to see but I really need help I’ll give points!!!!
Plssss help!!!!
From the data analytics of this table, the right statements are A,C and D.
What is called data in mathematics?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Given in the table of students which are watching movies or not
Yes No Total
Boys 6 8 14
Girls 9 7 16
Total 15 15 30
Statement (A): 27% of sampled students are boys who did not watch a movie?
27% of total students = 27 * 30/100
= 810/100
≈ 8 boys
So the statement (A) is true.
Statement (B): 30% of sampled girls watched a movie?
30% of sampled girl = 30 * 16/100
= 480/100
≈ 5 girls
So the statement (B) is false.
Statement (C): 50% of sampled students did not watch a movie?
50% of total students = 50 * 30/100
= 1500/100
= 15 students
So the statement (C) is true.
Statement (D): 57% of sampled boys did not watch a movie?
57% of total students = 57 * 14/100
= 798/100
≈ 8 boys
So the statement (D) is true.
SO that, the right statements are A,C and D.
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The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges $50 to mow a lawn that took him 1.5 hours to mow. Which equation models the amount in dollars, d, Troy charges when it take him, h, hours to mow a lawn? Group of answer choices h = 50d d = 75h d = 50h h = 75d
The equation d = (100/3)h models the amount in dollars, d, Troy charges when it take him, h, hours to mow a lawn.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given,
Troy charges $50 to mow the lawn that took him 1.5 hours to mow
Charges are proportional to time.
If charges are d and time is h
then,
Ratio of Charges to time
⇒ d/h = 50/1.5
⇒ d/h = 100/3
⇒ d = (100/3)h
Hence, d = (100/3)h is the equation that can be used to calculate the amount with time.
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Melissa is hosting a dinner party. She is making the main course and is assigning the invited guests to bring the following items: appetizer, side dish, salad, beverage, or dessert. Suppose there are nine guests invited to the party. Each is assigned to bring one of the items mentioned, and more than one guest can be assigned to an item so that each guest brings something to the dinner party.
a. Explain why assigning each guest an item to bring to the party is an example of a function.
Each guest being assigned to bring an item to the party is an example of a function because a unique output (the item to bring) is assigned to each input (the guest).
Why is this a function ?In this case, each guest is the input, and the item they are assigned to bring is the output. Each guest is assigned exactly one item, and there are no two guests assigned to bring the same item. This means that for each guest, there is a unique item that they are assigned to bring, and no two guests are assigned to bring the same item.
Therefore, the assignment of guests to items to bring to the dinner party is an example of a function because it assigns a unique output (the item) to each input (the guest), and it meets the mathematical definition of a function.
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5 is more than a number is greater than or equal to 27
5 more than a number is greater or equal to 27
The "number" can be represented as x.
[tex]\boxed{x+5\geq 27}[/tex]
The ratio of the measures of the angles in a triangle is 8:3:4. Find the measure of the largest angle.
BOTH QUESTIONS IN THE PICTURE
Will give brainliest !!!
Answer:
Only can do the first one
Let's call the measures of the angles in the triangle x, 3x, and 4x.
According to the ratio, we have:
x : 3x : 4x = 8 : 3 : 4
To find the value of x, we can set up a proportion:
8/x = 3/(3x) = 4/(4x)
Cross multiplying, we get:
8x = 12
So, x = 12/8 = 3
Therefore, the measures of the angles in the triangle are 3x, 3(3x), and 4(3x).
The measure of the largest angle is 4x = 4(3) = 12.
How do I solve this question?
The percentage of total budget for insurance, housing and entertainment is 3%. 13.3% and 4% respectively.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The total budget given is $4100 for the month.
The percentage of total budget for insurance is:
123/ 4100 (100) = 3%
The percentage of total budget for housing is:
574/ 4100 (100) = 13.3%
The percentage of total budget for entertainment is:
164/4100 (100) = 4%
Hence, the percentage of total budget for insurance, housing and entertainment is 3%. 13.3% and 4% respectively.
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of the 800 students at a certain college, 250 students live on campus and are more than 20 years old. how many of the 800 students live on campus and are 20 years old or less? (1) 640 students at the college are more than 20 years old. (2) 60 students at the college are 20 years old or less and live off campus.
As per the concept of permutation 100 out of the 800 students at the college live on campus and are 20 years old or less.
A permutation is the arrangement of objects in a specific order. In this problem, we are trying to find the number of students who live on campus and are 20 years old or less.
From the information given, we know that 250 students live on campus and are more than 20 years old. If there are 800 students in total at the college, then the number of students who are not living on campus is
=> 800 - 250 = 550.
We also know that 640 students at the college are more than 20 years old. This means that the number of students who are 20 years old or less is
=> 800 - 640 = 160.
Finally, we know that 60 students at the college are 20 years old or less and live off campus.
So, the number of students who live on campus and are 20 years old or less is
=> 160 - 60 = 100.
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The assets and liabilities of a doctor are listed below.
Home Value $492,456
Mortgage $287,763
Credit Card Balance $3,458
Owned Work Equipment $20,267
Car Value $15,981
Investments $62,309
Personal Loan $38,924
What is the total value of the doctor's capital assets?
$20,267
$62,309
$528,704
$591,013
Answer:
Hi! The answer is $591,013
aka D!
Step-by-step explanation:
A capital asset is property that is expected to generate value over a long period of time, such as a building, machinery, and vehicles.
Convert each equation to slope intercept form, then determine if the lines are parallel, perpendicular, or neither(intersecting).
A) 2x + 3y = 9
B) 2y - 3x = 8
The slope-intercept form of the equations are y = -2x/3 + 3 and y = 3x/2 + 4 and the line are perpendicular to each other.
What is the slope intercept form of an equation of a line?The meaning of slope intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given that two equations, we need to find their slope intercept form, and determine if the lines are parallel, perpendicular, or neither (intersecting).
The given equations are;
A) 2x + 3y = 9
B) 2y - 3x = 8
The general equation of a line, in a slope intercept form, is given by,
y = mx + c, where m is the slope of the line and c is the y-intercept,
A) 2x + 3y = 9
3y = 9-2x
y = -2x/3 + 3....(i)
B) 2y - 3x = 8
2y = 3x+8
y = 3x/2 + 4.....(ii)
Here, the slope are -2/3 and 3/2, we can say that both the slopes are negative reciprocal of each other,
We know that slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the given two line are perpendicular to each other.
Hence, the slope-intercept form of the equations are y = -2x/3 + 3 and y = 3x/2 + 4 and the line are perpendicular to each other.
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how many distinct rectangles are there with integer side lengths such that the numerical value of area of the rectangle in square units is equal to $5$ times the numerical value of the perimeter in units? (two rectangles are considered to be distinct if they are not congruent.)
There are a total of 5 distinct rectangles that can be formed whose area is equal to 5 times the numerical value of the perimeter.
The area of a rectangle is given by:
A = L*W, where L- length of rectangle and W- width of rectangle,
The perimeter of a rectangle is given by:
P = 2*(L + W)
Since area of rectangle in square units is equal to 5 times the numerical value of the perimeter of the rectangle, on substituting the perimeter in terms of the area, we get:
P = 2(L + W) = 2( √(A/5) * √(5A))
Since the length of the sides must be integers, the possible values of area can be 5, 25, 125, and so on.
For each value of A, there can only be one possible rectangle that is formed. Therefore, only 5 distinct rectangles with integer side lengths that can be formed which meets the provided criteria.
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What is -a^-2 if a=-5?
Answer:
-0.04ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
1/-25
Step-by-step explanation:
First we plug it in
-(-5)^-2
Then since the exponent is negative, we take the equation and put it under one which makes it a positive.
1/-(-5)^2
Then we solve the exponent
1/-(25)
Since it's a negative outside the parenthesis we treat it as multiplying it by -1 in which case we'd get
1/-25
Dana tried to evaluate an expression. Here is her work:
45 [(4 + 3) (60 ÷ 12 - 2)]
-
=
= 45 [7 (60+ 10)]
= 45 - [7.6]
= 45 - 42
= 3
Is Dana's work correct?
Step 1
Step 2
Step 3
Step 4
Dana is not correct, she has done mistake in the second step.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 45 [(4 + 3) (60 ÷ 12 - 2)]
45 [(4 + 3) (60 ÷ 12 - 2)]
The first step is 45 [7 (60÷ 10)], it is correct
The second step 45- [7.6] is wrong because 45 is a multiple of [7 (60÷ 10)]
45(42)
When we multiply 45 with 42 we get
1890
Hence, Dana is not correct, she has done mistake in the second step.
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There is a strong positive correlation between the number of umbrellas sold in a town and the water levels in nearby rivers.
What is a possible reason for why this correlation exists?
Question 9 options:
A melting glacier upstream of the rivers
A large number of tourists in the area
A new shopping mall opened in the area
High levels of rainfall
A possible reason for the strong positive correlation is high levels of rainfall. (fourth option)
What is correlation?Correlation is a measure used in statistics to measure the linear relationship that two variables have.
When two variables have a positive correlation, it means that the two variables move in the same direction. In this question, the number of umbrellas sold increase when water levels in streams increase. An reason for this could be that the increased water levels lead to higher rate of rainfall which would lead to people buying more umbrellas.
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evaluate the function when x = -2,0, and 5
f(x) = x + 6
The value of function at x = - 2 is, 4
The value of function at x = 0 is, 6
The value of function at x = 5 is, 11
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ f (x) = x + 6
Now, Substitute x = -2 in above equation,
⇒ f (x) = x + 6
⇒ f (-2) = -2 + 6
⇒ f (-2) = 4
Substitute x = 0 in above equation,
⇒ f (x) = x + 6
⇒ f (0) = 0 + 6
⇒ f (0) = 6
Substitute x = 5 in above equation,
⇒ f (x) = x + 6
⇒ f (5) = 5 + 6
⇒ f (5) = 11
Thus, The value of function at x = - 2 is, 4
The value of function at x = 0 is, 6
The value of function at x = 5 is, 11
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Please help thank u!!
Answer:
see below
Step-by-step explanation:
shift B right by 4units & up by 2 units to have point B overlap point A so the 2 circles center will be overlapped
What does a correlation coefficient of 0 indicate?
Answer:
the coefficient of 0 indicates that there is no relationship between the two values
. Seth’s father is thinking of buying his son a six-month movie pass for $40. With the
pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must
Seth attend in order for it to benefit his father to buy the pass?
Seth must attend the move 17 times
How to find the number of times Seth have to attendThe difference in price of matinee is
= price of matinee normally - price of matinee with movie pass
= 3.50 - 1
= 2.5
We divide to find the number of times
= 40 / 2.5
= 16
In other that Seth's father benefits Seth must attend at least 17 times
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the u shaped curve created by a quadratic equation
Answer: it is called a parabola
Step-by-step explanation:
Which statement is true about the triangle? Question 8 options: w = 99°, because 42 + 39 = 81 and 180 – 81 = 99. w = 261°, because 42 + 39 = 81 and 18 + 81 = 261. w = 81°, because 180 – (42 + 39) = 99 and 180 – 99 = 81. None of the above.
Answer c
w = 81°, because 180 – (42 + 39) = 99 and 180 – 99 = 81
Step-by-step explanation:
The statement which true about the triangle is a) w = 99°, because 42 + 39 = 81 and 180 – 81 = 99.
What is TriangleA triangle is a shape consisting of 3 sides and 3 vertices (180º total) of a straight line. As early as 300 BC, Euclid had come up with the concept that the sum of three angles is 180°. This makes great contributions to the concept of shapes, such as finding the lengths of their sides and angles.
A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry with vertices A, B and C represented as triangle ABC.
In Euclidean geometry, every three points define a unique triangle and a unique plane (that is, two-dimensional Euclidean space) when they do not collide. In other words, only one plane contains its sides, and every triangle contains many faces. If the whole geometry is just Euclidean planes, there is only one plane and everything is contained within it; however, in high-dimensional Euclidean space, this is no longer true.
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If 55% of a number is 176 and 35% of the same number is 112, find 90% of that number.
Answer:
288
Step-by-step explanation:
175 times 100 divided by 55 = 320
320 times .9 = 288
Answer: your answer would be 288
Step-by-step explanation:
9 subtracted from twice of x gives 5 time x
Answer:
x = -3.
Step-by-step explanation:
2x - 9 = 5x
2x - 5x = 9
-3x = 9
x = -3.
Estimate the number of rabbits at the farm in 2016
the Estimated number of rabbits will be 80 in the year 2016.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a table of Rabit at a zoo in the table below,
2008 14
2009 24
2010 30
2011 39
2012 45
2013 57
M: 2010.5 M: 34.8333
To estimate the number of rabbits in the zoo in 2016 we need to find the linear equation;
Sum of X = 12063
Sum of Y = 209
Mean X = 2010.5
Mean Y = 34.8333
Sum of squares (SSX) = 17.5
Sum of products (SP) = 143.5
Regression Equation = ŷ = bX + a
b = SP/SSX = 143.5/17.5 = 8.2
a = MY - bMX = 34.83 - (8.2*2010.5) = -16451.26667
ŷ = 8.2X - 16451.26667
For x = 2016
y = 8.2* 2016 - 16451.26667
y = 79.933 or 80
therefore, the Estimated number of rabbits will be 80 in the year 2016.
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Complete question:
a friend tells you that she has a total of three hours available to study for an exam next week. you should advise her to
You should advise her to divide the three hours into smaller, more manageable study sessions with breaks in between for maximum productivity and retention.
When studying for an exam, it's important to prioritize effectiveness over efficiency. Spending three hours straight on studying can lead to burnout and decreased retention. Instead, you can suggest dividing the time into shorter, more manageable study sessions of 50–60 minutes with 10-15 minute breaks in between. This way, your friend can focus on one topic at a time, recharge during the break, and avoid mental fatigue.
It's important to encourage your friend to take care of their physical and emotional well-being by eating well, getting enough sleep, and finding ways to reduce stress. These habits can help improve their overall focus and performance during their study sessions.
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I need help with this question
The mean absolute deviation of the numbers will be 3.5.
What is a mean absolute deviation?The average distance between the data points and a centre point is referred to as absolute deviation. (|xi - x|)/N is the formula for mean absolute deviation. N is the number of terms in the sample, where xi is the sample's individual value and x is the sample's mean or average.
Mean = ( 4 + 15 + 8 +4 + 6 + 11 + 1 + 7 + 3 1 ) / 10
Mean = 57 / 10
Mean = 5.7
The mean absolute deviations are calculated as:-
[tex]MAD = \dfrac{\sum{(X - \bar X)}}{n}[/tex]
MAD = 34 / 10
MAD = 3.4
Hence, the value of the mean absolute deviation is 3.4.
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Directions: Based on the information given in the following problem, compute the gross pay.
Regular hours worked: 40
Overtime hours worked: 8
Regular rate of pay: $7.75 per hour
gross pay: $
The gross pay based on the given information is $372.
What is gross pay?Gross Salary is the amount of salary after adding all benefits and allowances but before deducting any tax, Net Salary is the amount that an employee takes home.
Given that, regular hours worked: 40 and overtime hours worked: 8.
Regular rate of pay: $7.75 per hour
So, gross pay = 40×7.75+8×7.75
= $372
Therefore, the gross pay is $372.
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4. Ron is using the following formula to predict
the population of dolphins in the Galapagos
P = 2000(1.2)^t
Islands each year:
Question a): What is the initial value of this
exponential equation?
Question b): What is the constant percentage
growth rate of the loan per year?
Question c): What is the growth factor of the
loan per year?
The initial value is 2000
The constant percentage growth rate is 20%
The growth factor is 1.2
How to find the initial valueExponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, P = 2000(1.2)^t
the initial value = 2000
the base = 1.2
the exponents = t
The base is what says whether it will be an exponential growth or decay. For values of the base greater than 1 is exponential growth
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In the sport competition, France won more gold medals than Italy, who won more gold medals than Korea. If the total
number of gold medals won by these three countries is three consecutive integers whose sum is 39, find the number of
gold medals won by each.
The number of gold won by Korea is 12
The number of gold won by Italy is 13
The number of gold won by France is 15
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of gold won by Korea = x
Number of gold won by Italy = x + 1
Number of gold won by France = x + 2
Now,
The total number of gold medals won by these three countries is three consecutive integers whose sum is 39.
This means,
x + x + 1 + x + 2 = 39
3x + 3 = 39
3x = 39 - 3
3x = 36
x = 12
Thus,
Number of gold won by Korea = 12
Number of gold won by Italy = 13
Number of gold won by France = 15
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there are 48 students in the kennedy middle school student council. the number of 8th graders is 12 fewer than three times the number of 7th graders
Answer:
3 * 15 - 12 = 33 So, the equation is saying that the result of 3 times 15 minus 12 is equal to 33.
Step-by-step explanation:
Let's call the number of 7th graders "x". Then, the number of 8th graders is 3 * x - 12.
The total number of students in the student council is 48, so we can set up an equation:
x + (3 * x - 12) = 48
Expanding and simplifying:
4x - 12 = 48
Adding 12 to both sides:
4x = 60
Dividing both sides by 4:
x = 15
So, there are 15 7th graders and 3 * 15 - 12 = 33 8th graders in the Kennedy Middle School student council.
Answer: 36 8th graders and 12 7th graders
Step-by-step explanation:
48-12=36
36 divided by 3=12
With this information, 12 7th graders and 36 8th graders
a survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. half the complaints dealt with plumber a, who does 40% of the plumbing jobs in the town. find the probability that a consumer will obtain a an unsatisfactory plumbing job, given that the plumber was a. b a satisfactory plumbing job, given that the plumber was a.
The probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.
To find the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A, we first need to determine the proportion of plumbing jobs done by Plumber A that result in consumer dissatisfaction.
Given that half the complaints dealt with Plumber A and that Plumber A does 40% of the plumbing jobs in the town, we can calculate this proportion as follows:
Proportion of unsatisfactory plumbing jobs done by Plumber A = (Half the complaints / Total number of plumbing jobs done by Plumber A)
= (Half the complaints / 40% of the total plumbing jobs in the town)
= (Half of 10% / 40%)
= 10% / 2 / 40% = 1 / 4 = 0.25
Therefore, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25.
To find the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A, we subtract the probability of obtaining an unsatisfactory plumbing job from 1:
Probability of a satisfactory plumbing job given that the plumber was Plumber A = 1 - Probability of an unsatisfactory plumbing job
= 1 - 0.25
= 0.75
Therefore, the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.
In conclusion, given that Plumber A does 40% of the plumbing jobs in the town and that half the complaints dealt with Plumber A, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25, and the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75. These probabilities can be used to make informed decisions about which plumber to choose for plumbing jobs in the community.
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Proving Rectangles, Rhombi, and Squares in the Coordinate Plane
Classify as the most specific shape possible
1. A(8,3) B(7,8) C(2,7) D(3,2)
What formulas do I use to solve this? (My own question not in text)
The most specific shape is rhombus for the co-ordinates A(8,3) B(7,8) C(2,7) D(3,2).
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
We have four co-ordinates,
A(8,3) B(7,8) C(2,7) D(3,2).
The length of the segment AB = √{(8 - 7)² + (3 - 8)²} = √26 units.
The length of the segment BC = √{(7- 2)² + (8- 7)²} = √26 units.
The length of the segment CD = √{(2 - 3)² + (7 - 2)²} = √26 units.
The length of the segment AD = √{(8 - 3)² + (3 - 2)²} = √26 units.
That means, all the sides are equal.
Now, let the slope of AC = slope of BD
(7 - 3)/(2 - 8) ≠ (2 - 8)/(3 - 7)
The slope of the diagonal is not equal.
Therefore, the shape is rhombus.
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