given f(x)=x^2+2x-5 and the values of the linear function g(x) in the table, what is the range of (f+g)(x)
x: -6 -3 -1 4
g(x): 16 10 6 -4
Answers:
(infinity,1]
[-1,1]
R
Answers
The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.
What are a domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.
x -6 -3 -1 4
g(x) 16 10 6 -4
The function g(x) will be:-
g(x) = mx + c
m = ( 10 - 16 ) / ( -3 + 6 )
m = -6 / 3
m = -2
c = y - mx
c = 10 - 6
c = 4
g(x) = -2x + 4
The function ( f + g)(x) will be:-
( f + g)(x) = f(x) + g(x)
( f + g)(x) = x²+ 2x - 5 - 2x + 4
( f + g)(x) = x² - 1
At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).
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Related Questions
1
Select all quadrilaterals for which a diagonal is also a
line of symmetry.
(Select all that apply. )
trapezoid
isosceles trapezoid
parallelogram
rhombus
rectangle
square
Answers
Correct answer is parallelogram and rhombus.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.
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rectangle, rhombus
got it wrong on my test and was given the correct answers, so here they are.
In which direction must the graph of f(x) = 9x be shifted to produce the graph of g(x) = 9x + 7? a. up b. down c. left. d right
Answers
The translation or the graph must be shifted upwards by 7 units .
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The graph f(x)=9x
The required graph is given by g(x)=9x+7
A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.
Thus two transform the given graph into g(x) we have to translate the graph vertically or upwards by 7 units i.e f(x)=9x+7
where k=7
Hence, The translation or the graph must be shifted upwards by 7 units .
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Formulate a erie and how a proof by PMI to validate.
Give at leat one example each on the operation of function.
In at leat 50 word; What have you learned in GE4?
Answers
The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
Example of operation of function:
1. f(x) = x^2 + 3x - 2
When x = 3, f(3) = 3^2 + 3(3) - 2 = 14
2. g(x) = x^3 + 3
When x = 4, g(4) = 4^3 + 3 = 67
I have learned that GE4 is an introduction to mathematical proof and problem solving. We have gone through a variety of topics such as basic algebra, functions, and sets. We have also learned about the different approaches to problem solving, such as working backwards, proof by cases, and proof by PMI. I have also been introduced to the basics of logic and proof writing.
This answer explains the proof by PMI for the erie that if n is an odd number, then n^2 is an odd number. Two examples of operations of functions are also given. The student has learned that GE4 is an introduction to mathematical proof and problem solving, including basic algebra, functions, sets, and the different approaches to problem solving.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Which inequality shows the constraint on the amount of apples John has to make pies and cobblers?
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Answers
An inequality which shows the constraint on the amount of apple John has to make pies and cobblers is: D. 4x + 2y ≤ 16.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:
4x + 2y ≤ 16
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PLEASE HELP ASAP??!!
What is the end behavior of the function f(x) = −x³ + 2x² +1
As a approaches infinity, f(x) approaches infinity. As approaches negative
infinity, f(x) approaches negative infinity.
As a approaches infinity, f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches negative infinity.
As a approaches infinity. f(x) approaches negative infinity. As a approaches
negative infinity, f(x) approaches infinity.
As approaches infinity, f(x) approaches infinity. As a approaches negative
Answers
The end behavior of the function f(x) = −x³ + 2x² +1 is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
What is the end behavior of the function?Here we want to find the end behavior of the function below:
f(x) = −x³ + 2x² +1
Notice that the degree is odd, this means that the end behaviors are opposite in opposite values of x.
Because we have a negative sign on the term with the highest exponent, then as x tends to infinity, the function will tend to negative infinity.
And thus, because the degree is odd, the value of f(x) as x tends to negative infinity tends to positive infinity.
Thus we can write:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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Use technology to find points and then graph the function
y
=
−
x
+
1
+
5
y=−
x+1
+5 following the instructions below.
done plotting points
Plot at least four points from the table of values with integer coordinates on the axes below. Click a point to delete it.
Answers
The graph and the points are added as an attachment
How to determine the graph?From the question, we have the following parameters that can be used in our computation:
y = -x + 1 + 5
Evaluate the like terms
y = -x + 6
Set x = values from 0 to 3
So, we have
y = -0 + 6 = 6
y = -1 + 6 = 5
y = -2 + 6 = 4
y = -3 + 6 = 3
So, the points are (0, 6), (1, 5), (2, 4) and (3, 3)
Next, we plot the graph and the points
See attachment
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For each expression, circle any like terms and list any variables.
Answers
The final resultant expressions are 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expressions,
-2.5x+3.9 + 1.7x
3.9 + 1.7x-2.5x
3.9 - 0.8 x
1 1/2 + t + 2/3 s
= (2+1) / 2 + t+ 2/3 s
= 3/2 + t + 2/3 s
= 1.5 + t+0.66 x
15k+2/5 k -3m
k(15+2/5 ) - 3m
k (75 + 2 / 5 ) - 3m
77/5 k - 3m
Hence, The final resultant expressions 3.9 - 0.8 x , 1.5 + t+0.66 x ,
77/5 k - 3m
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For what value of x is JKLM a parallelogram?
4x + 13
4x-1
3x + 20
5X-8
Answers
To represents JKLM is a parallelogram the required value of x is equal to 7.
In the parallelogram JKLM,
Let us consider the measure of each side in form of 'x' is represented by :
JK = 4x + 13
KL = 4x - 1
LM = 3x + 20
MJ = 5x - 8
Opposite side of the parallelogram JKLM are congruent to each other.
JK = LM
⇒ 4x + 13 = 3x + 20
⇒ 4x - 3x = 20 - 13
⇒ x = 7
When
KL = MJ
⇒ 4x - 1 = 5x - 8
⇒ 5x - 4x = 8 - 1
⇒ x = 7
JK = 4(7) + 13
= 41
LM = 3(7) + 20
= 41
KL = 4(7) -1
= 27
MJ = 5(7) - 8
= 27
Therefore, the value of x which represents that JKLM is a parallelogram is equal to 7.
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simplify [17-8] - [13-4]
Answers
Answer:
0
Step-by-step explanation:
First, you do 17 - 8, which is 9 and then you do 13 - 4, which is 9. Then, you subtract 9 from 9, which gives you 0.
Question 19
Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years, and 2. 3%
thereafter.
Given that the interest is paid into his account monthly (and calculated monthly), work out how much money Luke
will have in his account after 6 years and 3 months.
Answers
As per the formula of compound interest the amount in his account after 6 year 3 months is $40,085.307
In math the term called compound interest is defined as when you earn interest on both the money you've saved and the interest you earn.
Here we know that Luke invests 34000 into an account that pays 3. 4% compound interest per annum for the first two years and 2. 3% thereafter.
Here we need to find the amount in his account after 6 years and 3 months.
Then it can be calculated as,
FV = PV(1 + i)ⁿ
Here we know that PV = 34000 and i = 3.4% for two years,
Then the FV is value is calculated as,
=> FV = 34000(1 + 3.4/100)²
=> FV = 34000 ( 1 + 0.034)²
=> FV = 36351.304
Similarly, the FV value of 4 years 3 months is calculated as,
=> FV = 36351.304(1 + 2.3/100)⁴°³
=> FV = 36351.304(1 + 0.023)⁴°³
=> FV = 40085.307
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7.Maddie performed a calculation on her calculator and received a result of 8E3.
What are the standard form and scientific notation for this value?
Select two answers: one for standard form and one for scientific notation.
Answers
The scientific notation of the given result is 8 x 10³
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
We are given that Maddie performed a calculation on her calculator and received a result of 8E3.
WE know that "E" means the power of ten
Therefore,
8E3 = 8 x 10³
This is the scientific notation.
For the standard form it should be 8,000.
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4. A 15-kg child is tossed up into the air by her parent. The child is 2.5 meters off the ground traveling 3 m/s.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
Answers
The object has both kinetic energy and potential energy.
The values of each type of energy the object has are KE = 67.5 J
GPE = 367.5 J
How to find the energy of the object?Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.
If a 15-kg child is tossed up into the air by her parent and the child is 2.5 meters off the ground traveling 3 m/s.
Then boy has kinetic energy due to his motion and also has potential energy due to his height.
Thus, M = 15-kg, h = 2.5 meters and V = 3 m/s
KE = 1/2(M)(V)² = 1/2 × 15 × 3² = 67.5 J
GPE = mgh = 15 × 9.8 × 2.5 = 367.5 J
KE + PE = 67.5 + 367.5 = 435 J
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Help please!! (5k + 2m)(3p + 4s)
Answers
. eight times the quotient of 6 and 3
Answers
Answer: 16
Step-by-step explanation:
8 * (6/3)
= 8 * 2
= 16
at time , a tank contains oz of salt dissolved in gallons of water. then brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. (a) how much salt is in the tank at an arbitrary time? 200-140e^(-t/25) oz. (b) how much salt is in the tank at time min?
Answers
The amount of salt in the tank is decreasing exponentially with time.
At time t, the amount of salt in a tank containing oz of salt dissolved in gallons of water can be calculated using the following formula:
Salt in tank (oz) = 200 - 140e^(-t/25)
For example, at time t = 10 min, the amount of salt in the tank is 200 - 140e^(-10/25) = 200 - 140(0.7787) = 124.42 oz.
This calculation assumes that brine containing oz of salt per gallon of brine is allowed to enter the tank at a rate of gal/min and the mixed solution is drained from the tank at the same rate. Thus, the amount of salt in the tank is decreasing exponentially with time.
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1. a certain college wants to estimate the amount of time students, who live off campus, spend commuting to classes each week. a random sample of 45 off-campus students is surveyed. a) identify the population and sample for this study. b) what data is being collected? what type of data is this? c) what type of study is this?
Answers
The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.
a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.
b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.
c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.
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Emma wants to paint her house light pink. She adds 6 cans of white paint to every 4 cans of pink
paint to make the desired color. How many cans of white paint will she need to mixed with 12 cans of
pink?
Answers
To find out how many cans of white paint Emma will need to mix with 12 cans of pink paint, we can use the proportion of white paint to pink paint that she is currently using: 6 cans of white paint to every 4 cans of pink paint.
We can set up an equation using the proportion:
white paint/pink paint = 6/4 =3/2
We know that Emma wants to use 12 cans of pink paint, so we can use this information to solve for the number of cans of white paint she needs:
white paint/pink paint = 3/2
white paint = (3/2) * pink paint
white paint = (3/2) * 12 cans
white paint = 18 cans
So Emma will need 18 cans of white paint to mix with 12 cans of pink paint to get the desired color.
If you guys can solve the sheet, I will crown your braincrown thing
Goodluck
Answers
The values of x from the given figures are 3 √29 and 24 respectively.
What is triangle ?
Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.
Given
In the figure,
The two given triangles are similar ,
So, in the first figure it is given that they are similar ,
√29 / 5 = x / 15
x = √29 * 15 / 5
x =√29 * 3
x = 3 √29
And in the second figure , here also they gave they are similar
so we get,
12 / 13 = x / 26
x = 12 * 26 / 13
x = 12 * 2
x = 24
Hence, The values of x from the given figures are 3 √29 and 24 respectively.
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Multiply.
(2x² - 4x)(6x² - 5x)
O A. 124-34x² + 20x
OB. 124-10x³ + 20x²
O C. 12x - 34x³ + 20x²
OD. 12-10x² + 20x
Answers
In each row decide whether the expression in column A is equivalent to the expression In column b. If they are not equivalent show how to change one expression to make them both equivalent. YAWL HELP URGENTLY IM GONNA CRY
Answers
I apologize for misunderstanding your question.
Regarding your new question, it depends on the specific expressions provided in column A and column B. Without knowing the exact expressions, I am unable to determine if they are equivalent or not. Additionally, if they are not equivalent, then to make them equivalent, you can use algebraic properties such as the commutative property, associative property, distributive property and simplification techniques to change one of the expressions so that it has the same value as the other expression for every input in their domain.
Please let me know the specific expressions you are working with and I will be happy to help you determine their equivalence and/or how to change one of the expressions to make them equivalent.
Answer:
SO bassically its is equivalent bc i seethat the dgene is really good
Step-by-step explanation:
1 + 1 =2w + 2x +2y = 3x and equiavelnt number
Your friend secretly chooses a number. She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27. What number did your friend choose?
Answers
Answer: 12
Step-by-step explanation:
Say that your friends number is x
She says that when you divide the number by 4, add 6, and then multiply by -3, the result is -27, so:
(x/4 + 6) * -3 = -27
We can solve the equation by first dividing by -3 on both sides:
x/4 + 6 = 9
Multiply both sides by 4:
x + 24 = 36
Subtract 24 from both sides:
x = 12
Double checking...
(12/4 + 6) * -3
= (3+6) * -3
= 9 * -3
= -27
Correct :>
So your friend chose the number 12
There is 3/4 of a large cake left over from a party. Pedro eats 1/2 of the cake that was left. How much cake did he eat?
Answers
Pedro ate 3/2 of the cake that was left.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part is denominator.
Consider a fraction 1/5.
Here, numerator is 1, denominator is 5
When certain thing is divided into 5 equal parts then each part of is represented by fraction 1/5
In this situation, there is 3/4 of a large cake left over from a party.
Pedro eats 1/2 of the cake that was left.
This means, Pedro eats half of the remaning cake.
We need to find the half of fraction 3/4
We divide fraction 3/4 by 2 in order to find the amount of cake he ate.
[tex]\frac{\frac{3}{4} }{2} \\\\=2\times \frac{3}{4} \\\\=\frac{3}{2}[/tex]
Thus he ate 3/2 of cake.
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The path of a volleyball thrown over a net is modeled with the function
A(x) = -0.02x2 + 0.6x + 5, where x is the horizontal distance, in feet, from the
starting point, and A is the altitude of the ball in feet. Write an equation that can be solved to find out how far the ball travels horizontally before it hits the ground. Then find the distance to the nearest foot.
equation:
distance:
Answers
The ball travel horizontally 37 feet before it hits the ground.
What is Distance ?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
we have;
A(x) = -0.02x2 + 0.6x + 5
where
The horizontal distance, x, is given in feet.
The ball's height is indicated by the symbol A ---> in feet.
The fact that
The ball's altitude was zero when it landed on the earth.
so,
For A(x)=0
-0.02x^2 + 6x +5 = 0
'
the quadratic equation to be solved
The equation solving formula for a quadratic equation of the type;
ax^2 + bx + c = 0
this equation is equal to ;
[tex]x = \frac{-b\pm \sqrt{b^{2}- 4ac } }{2a}[/tex]
we have ;
-0.02x^2 + 0.6x +5 = 0
So,
a = -0.02
b = 0.6
c = 5
Subsititue this values in the formula;
[tex]x = \frac{-0.6\pm \sqrt{0.6^{2} -4 *(-0.02)(5) } }{2*(-0.02)}[/tex]
[tex]x = \frac{-0.6\pm \sqrt{0.76 } }{-0.04}[/tex]
[tex]x = \frac{-0.6\pm \ 0.87 }{-0.04}[/tex]
[tex]x = \frac{-0.6\ + \ 0.87 }{-0.04}= -6.75[/tex]
[tex]x = \frac{-0.6\ - \ 0.87 }{-0.04}= 36.75[/tex]
therefore
The ball travel horizontally 37 feet before it hits the ground.
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what is the name for an equilateral triangle
Answers
Answer:
equiangular triangle
Step-by-step explanation:
Mr.Todd want to paint the outide of the birdhoue. How much paint doe he need to buy to cover the outide of the entire birdhoue( rounded to the nearet hundredth). Explain how much and how you know in at leat two entence.
Answers
The amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.
To calculate how much paint Mr.Todd needs to buy to cover the outside of the entire birdhouse, we must first know the dimensions of the birdhouse. Let's assume the birdhouse has the dimensions of 10 inches long, 8 inches wide and 6 inches tall, and each side requires 1 coat of paint. The total surface area of the birdhouse is then 10 x 8 + 10 x 6 + 8 x 6 = 176 inches squared. Next, we need to know the coverage of the paint, which we will assume is 250 square feet per gallon. Since 1 square foot is equal to 144 square inches, the coverage of the paint is 36000 square inches per gallon. To find out how many gallons of paint are needed to cover the birdhouse, we need to divide the total surface area of the birdhouse (176 square inches) by the coverage of the paint (36000 square inches per gallon). Therefore, the amount of paint needed is 176/36000 = 0.0049 gallons, which is equivalent to 4.9 milliliters, rounded to the nearest hundredth.
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How many times as long as a THimble jellyfish is a Lion's Mane jellyfish? Thimble jellyfish = 1 inch, Lion's mane jellyfish = 7 feet
Answers
84 inches times as long as a Thimble jellyfish is a Lion's Mane jellyfish.
Now, According to the question:
"Information available from the question"
A Thimble jellyfish is a Lion's Mane jellyfish.
Thimble jellyfish = 1 inch,
Lion's mane jellyfish = 7 feet
Convert feet into inches.
To calculate a value in feet to the corresponding value in inches, just multiply the quantity in feet by 12 (the conversion factor).
Here is the formula:
Value in inches = value in feet × 12
Formula: multiply the value in feet by the conversion factor '12'.
So, 7 feet = 7 × 12 = 84 inches.
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2. Mark is trying to fit a circular tabletop with a diameter
of 88 inches through a door. The width of the door is 36
inches and the height of the door is 84 inches. Will the
tabletop fit through the door?
Answers
Answer: lol no it won't
Step-by-step explanation:
In order to determine if the circular tabletop with a diameter of 88 inches will fit through the door, we must compare the dimensions of the tabletop to the dimensions of the door.
The width of the door is 36 inches and the height of the door is 84 inches. The diameter of the tabletop is 88 inches. To fit through the door, the tabletop's diameter must be less than or equal to both the width and the height of the door.
88 inches > 36 inches and 88 inches > 84 inches
In this case, the tabletop will not fit through the door because its diameter is larger than both the width and the height of the door.
An angle is two collinear rays with a common endpoint. Find an example that contradicts this definition. How would you change the definition to make it more accurate? Part B: Give an example of an undefined term and how it pertains to angles
Answers
For the definition "An angle is 2 collinear rays with a common endpoint" , then
(a) the contradictory example is "When two rays are collinear having a common end point; then the rays do not form an angle instead they form a line."
(b) the changed definition is , "An angle is formed at the intersection of two non-collinear rays that have the same endpoint " ;
(c) the example is "the Plane" .
The Angles are formed when the two straight lines or rays meet at a common endpoint.
Part(a) ;
An example which contradicts this definition of angles is "When two rays are collinear with a common endpoint; the rays do not form an angle ,instead they form a line" because when all the points of two lines are collinear then all the points of the two lines will be overlapping .
Part(b) ;
The change that need to be made in the definition of angle is "An angle is formed at intersection of two non-collinear rays which have same endpoint ".
Part(c) ;
The Example of the undefined term is :
Undefined terms do not have a formal definition; an example of this is "the plane" . The plane pertains to the angles because the plane determines the parameter to be measured.
The given question is incomplete , the complete question is
An angle is two collinear rays with a common endpoint.
(a) Find an example that contradicts this definition.
(b) How would you change the definition to make it more accurate ?
(c) Give an example of an undefined term and how it pertains to angles .
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Find the area of the polygon with the given vertices. $K(-3,3),L(3,3),M(3,-1),N(-3,-1)$
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The area of the polygon is 24 unit².
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
We have four coordinates of vertices given, K(-3,3), L(3,3), M(3,-1), N(-3,-1).
So the polygon must be a quadrilateral.
Length of KL = [tex]\sqrt{(3--3)^{2} + (3-3)^2 }[/tex] = [tex]\sqrt{6^2}[/tex] = 6
Length of LM = [tex]\sqrt{(3-3)^2+(-1-3)^2}[/tex] = [tex]\sqrt{(-4)^2}[/tex] = 4
Length of MN =[tex]\sqrt{(-3-3)^2+(-1--1)^2}[/tex] = [tex]\sqrt{(-6)^2}[/tex] = 6
Length of NK = [tex]\sqrt{(-3--3)^2+(3--1)^2}[/tex] = [tex]\sqrt{4^2}[/tex] = 4
So we get that, opposite sides are having equal length.
So the polygon must be a rectangle.
Area of the rectangle = Length × Width
= 6 × 4
= 24 units²
Hence the area of the polygon with the given vertices is 24 unit².
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21•15 equals
(20+1)•15
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21 x 15 = 21 x 15