The 10th term of the arithmetic sequence is T₁₀ = a + 9d. a is the first term and d is the common ratio.
What is a sequence?
A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined as the number of items.
An arithmetic sequence follows a pattern.
Arithmetic progression or arithmetic sequence is a number sequence in which the difference between subsequent terms is constant.
The formula for nth term of the sequence is
Tn = a + (n - 1)d
Where a is the first term, d is the common ratio, and n is the number of terms.
Putting n = 10 in Tn = a + (n - 1)d
T₁₀ = a + (10- 1)d
T₁₀ = a + 9d
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Shawn found a deal for a kayak trip to see the bioluminescent
jellyfish in the Indian River Lagoon. The deal said it was 40%
of the regular price. Shawn paid $267 for 5 adults. What was
the regular cost of the kayak trip for 1 adult?
A. 32.04
B. $53.40
C. $89.00
D. $133.50
When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
Shawn spent $267 on five persons,
$267 / five equals $53 (or 40%, or 40/100, or two out of five),
= $ 53.
When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.
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Hurry - please help!!!!!!!!
Answer:
false
Step-by-step explanation:
I think it's false but I don't really remember, but I would go with someones else answer cause I'm not sure
The linear function f is defined as f(x)= -2x+3 consider the graph y =f(x)
On solving the provided question, we can say that the linear function is f(x) = -2x +3 and by the graph y = f(x) = -1
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
here,
the linear function is f(x) = -2x +3
and by the graph y = f(x) = -2x +3 = -2(2) + 3 = -4+3 = -1
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Unit 11 volume and surface area homework 2 area of sectors
Answer:
2. KI = 20 ft 119 M K 4. YZ = 14.2 m 2 6. PO = 2.8 in R 311 8. WZ = 5.3 km w z 108
Step-by-step explanation:
how do write 3n - 6 as a phrase in words
Resolve F2 into components along the u and v axes determine the magnitudes of these components.
Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.
According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.
For the given diagram, first, draw the vector components. Then, by sine law, we get,
[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]
Now, substitute the value of F₂, and we get,
[tex]F_u=F_2=\mathrm{150\;N}[/tex]
Now, solve for [tex]F_v[/tex], we get,
[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]
The required answers are 150 N and 77.64 N.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Using the information provided on the graph, draw the line the line that is perpendicular to line segment AB and passes through point P
The required equation of the line is given as y = 5x -6.
Given that,
To determine the equation of a line passing through the point P(9, -8) and perpendicular to the line AB y = 3x + 6.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the given line
y = 3x + 6.
m = 3
The equation of the perpendicular line is given as,
y - y₁ = -1/m (x - x₁)
Substitute the value in the above equation,
y + 8 = -1 / 3 (x - 9)
y = -x/3 + 3 - 8
y = -x/3 - 5
Thus, the required equation of the line is given as y = -x/3 - 5.
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Which of the following are square roots of the number below? Check all that
apply.
529
A. 5291/2
B. 23
C. -23
D. 1058
E. -5291/2
The final statement is: The square roots of 529 are [tex]529^{1/2}[/tex] -23 and 23
What is Square Root?The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √16 = 4. The radical symbol is also called a root symbol or surds.
Given here: The number 529 and to find its square root equivalent.
We know 529=23² and (-23)²=529
Also √529= [tex]529^{1/2}[/tex]
Thus these are the square root equivalent of the number 529
Hence, The square roots of 529 are -23,23 and [tex]529^{1/2}[/tex]
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Hurry! Please Help = 2 questions
Answer:
true because i guessed and got it right trust me
Describe and correct the error in graphing the inequality. 10. x≤ -3 y
We plotted the inequality given in question as a solid line in the graph.
What does mean by graph of inequality?
In mathematics, graph of inequality means graphical representation of unequal comparison regarding an expression. Inequality having ≤ and ≥
sign is shown as a solid line. Other inequality while plotting is shown as a dotted line.
What is the graph of the inequalities given in question and error?
we are given an inequality x≤ - 3y
As per the rules of solving an inequality, we need to start with an isolated variable from the left side.
we notice, x is located on the left side.
the value of x must be less than or equal to -3 y. So, the graph of the inequality is located on the negative X coordinate, and it is a straight solid line. We know, the sign ≤ or ≥ indicates that inequality of the graph will be a solid line.
if we look at the graph given in question, we find that the line is drawn as a dotted line but we have less than or equal sign. So, the graph is needed to correct.
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Morgan says the 1/2+1/4 equals two or six used to drop menus to explain why Morgan is incorrect Morgan is incorrect because to have sex is 1/2 1/2+1/4 must be 1/2
Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.
What is composite number?Prime numbers can really be expressed as the sum of two different numbers. The sum of two or more numbers is what is referred to as a composite number. Examples of prime numbers include 2,3,5,71,11 since they only have two factors, one and itself. Examples of composite numbers include 4,6,8,10,12 since they contain more than two contributing variables.
Here,
we can see Morgan's claim that any numbers with a 2 in the place of a one are composite numbers.
We can conclude that Morgan is correct given the prior description of composite numbers by stating that all numbers with a 2 in the place of a one are composite numbers.
In actuality, any even integer—aside from 2—is a composite number.
Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.
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Pls help its in the attached image only two problems
The Congruent Triangles figure are attached below.
What is Congruency?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
The following the Congruent properties:
SSS, or Side Side Side. SAS, or Side Angle Side. ASA, or Angle Side Side. AAS, or Angle Angle Side. HL, or Hypotenuse Leg, for right triangles only.Given:
1. ΔFUN and ΔCAR
If the both triangles are congruent then
FU = CA
UN = AR
NF = RC
and, <FUN = <CAR, <UNF = <ARC and <NFU = <RCA.
This is because Congruent Triangles have Corresponding Side and angles equal in length.
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A mountain is 12,790 feet above sea level, and a valley is 368 feet below sea level. What is the difference in elevation between the mountain and the valley?
Answer:
The difference in elevation between the mountain and the valley is 13,158 feet.
12,790 feet (mountain elevation) - (-368 feet (valley elevation)) = 13,158 feet
Step-by-step explanation:
Assistance is needed please thank you easy! simple interest problem
A. The interest Bianca earned for a period of 3 years is $382.50. The correct option is B. $382.50
B. The number of years Bianca kept the account open is 11 years
Calculating simple interestFrom the question, we are to calculate how much interest Bianca will earn for a period of 3 years
From the simple interest formula, we have that
S.I = PRT
Where S.I is the simple interest
P is the principal
R is the rate
and T is the time
From the given information
P = $3,000
R = 4.25% = 0.0425
T = 3
Therefore,
S.I = $3,000 × 0.0425 × 3
S.I = $382.50
B.
From the given information, Bianca receives $4,402.50 when she closes the account
Thus,
The simple interest = $4,402.50 - $3,000
Simple interest = $1402.5
We are to calculate how many years Bianca kept the account open. That is, T
Using the formula,
S.I = PRT
$1402.5 = $3000 × 0.0425 × T
$1402.5 = $127.5 × T
T = $1402.5/$127.5
T = 11
Hence, the time is 11 years
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Graph the linear inequality y < 1/2x + 2 using slope-intercept form.
Given inequality:
y < 1/2x + 2To graph it first, consider line:
y = 1/2x + 2Find two points on the line.
Let them be x- and y-intercepts:
x = 0 ⇒ y = 1/2*0 + 2 = 2, so the point is (0, 2)y = 0 ⇒ 0 = 1/2x + 2 ⇒ 1/2x = - 2 ⇒ x = - 4, the point is (- 4, 0)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < \dfrac{1}{2}x+2[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=\dfrac{1}{2}x+2[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=\dfrac{1}{2}(0)+2 =2\implies (0, 2)[/tex]
[tex]x=4 \implies \dfrac{1}{2}(4)+2=4 \implies (4,4)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 2) and (4, 4).Draw a dashed straight line through the points.Shade under the dashed line.Solve the following equation. 2(y +4) = 3(2y -4) SHOW YOUR WORK
Answer:
y = 5
Step-by-step explanation:
2(y + 4) = 3(2y - 4)
2y + 8 = 6y - 12
-4y = -20
y = 5
Entry load and exit load are both calculated as a % of the
The "net asset value" is used to compute both entry load as well as exit load as a percentage.
Define the term Entry load and exit load?Entry load is the sum of money or fee that an investor must pay to join a scheme or a company as an investment.
Exit loads are fees or amounts collected from investors for quitting a plan or a corporation as a shareholder.
In other words, the per-unit cost would be 10.1 rupees if the NAV are 10 rupees or the entry load is 1%. Simply put, when units are allocated, the entry load is added to the NAV. The price at which the company is anticipated to be sold is known as the Exit Value (EV) or Terminal Value. This is typically computed using the Venture Capital technique as a multiple of a company's revenues during the year of sale.Thus, the "net asset value" is used to compute both entry load as well as exit load as a percentage.
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The points on the number line are opposite numbers. The tick marks represent
intervals of 1 unit.
Label 0 at the correct spot on the number line.
Label the point plotted to the right of 0.
Label the point plotted to the left of 0.
Picture will be inserted below
The points on the number line are opposite numbers, so that the required answer is as attached.
What is a number line?A number line is a straight line which extends from negative infinity to positive infinity on which the position of all directed numbers can be located.
Directed number are numbers with sign, which shows its direction i.e negative or positive.
In the given question since the points are opposite numbers, then we have single number but opposite in directions. Therefore there must be at equal distance to point 0 on the number line.
Considering the given conditions in the question, the opposite numbers are; -5 and +5. While the point 0 is the midpoint between -5 and +5.
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Using the calculations for each ingredient:
How much did Hector's homemade sandwich cost?
That’s the picture of the prices please help this is due today!!
On solving the provided question we can say that to plot data - dread = $0.16; Turkey = $1.24; Cheese = $0.30
what is plotting data?The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.
to plot data -
dread = $0.16
Turkey = $1.24
Cheese = $0.30
Lettuce = $0.06
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[tex]\frac{1-5}{6-3} =\frac{-4}{3} =[/tex]
The value of the given fraction is -1.33.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
Given is an expression in fractions of the form,
(1 - 5) / (6 - 3) = (-4) / 3
Actually we got an improper fraction here.
Improper fractions have larger value on the numerator than the denominator.
If we need the answer in decimal form, just divide the number 4 by 3 and give negative sign for the answer.
So here the given answer is -1.33.
Hence the decimal form of the fraction (-4)/3 is -1.33.
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A company sells floats for children An equation model their profit P=4x-10000 where x is no of floats sold if 5000 are sold out what is company profit
Based on the equation that models the company's profit as P = 4x - 10,000, if 5,000 units are sold, the company's profit is $10,000.
What is a profit equation?The profit equation shows the difference between the revenue and the costs during a financial period.
The revenue is a product of the units sold and the number of units.
Equation Model:Profit, P = 4x - 10,000
Number of units sold = x
If 5,000 units are sold:
The profit = $10,000 (4 x 5,000 - 10,000)
Check:
Total revenue = $20,000 (4 x 5,000)
Unit selling price = $4
Number of units sold = 5,000
Total costs = $10,000
Thus, using the profit equation, the company generated a profit of $10,000 from selling 5,000 floats for children.
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Alex and Monte are shopping for new clothes. Alex says to Monte, "If you give me $12, we will have an equal amount of money." Monte responds, "That may be true, but if you give me $6, I will have twice as much as you.
The question is a word problem, where; the amount of money Alex has is the same as the amount Monte will have if he gives Alex $12, and the amount of money Monte will have will be twice the amount with Alex if he receives $6 from Alex, indicating that the amount of money Alex has is $30, while the amount of money with Monte is $54.
What is a word problem?A word problem is a verbal presentation of a mathematical or science question, using words and sentences, rather than numbers and symbols, and for which the solution is found mathematically, or by using standard scientific steps.
Let x represent the amount of money Alex has, and let y represent the amount of money Monte has, we get;
x + 12 = y - 12...(1)
2·x = y + 6...(2)
Adding 12 to both sides of equation (1), we get;
x + 12 + 12 = y - 12 + 12
x + 24 = y - 0 = y
x + 24 = y
y = x + 24
Plugging in the value of y into equation (2), we get;
2·x = y + 6
2·x = x + 24 + 6 = x + 30
2·x = x + 30
Subtracting x from both sides of the above equation, we get;
2·x - x = x + 30 - x
x = x - x + 30 = 0 + 30
x = 30
The amount of money Alex has, x = $30
y = x + 24
Therefore; y = 30 + 24 = 54
The amount of money Monte has, y = $54
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Kelly rolled scores of 254, 202, 284, 269, 151, 258 and 202 in a recent tournament. What was the mean, median and mode of her scores?
Answer:
See below!
Step-by-step explanation:
Data:254, 202, 284, 269, 151, 258, 202
Mean:The sum of data divided by the number of data is called mean.Mean of the data:
[tex]\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}[/tex]
Median:The middle value of the data is median.Median of data:
Arrange the data in increasing order.
151, 202, 202, 254, 258, 269, 284
The middle value = 254
So,
Median = 254Mode:The frequently occurring value in the data is known as mode.Mode in data:
The mode, here, is 202. (occurring 2 times.)
So,
Mode = 2[tex]\rule[225]{225}{2}[/tex]
Gilda's sponge cake is three times as long as it is wide. The sponge cake is 18 inches long. Use n to represent the cake's width.
The width of the cake is 54 inches
How to determine the width of the cakefrom the question, we have the following parameters that can be used in our computation:
Gilda's sponge cake is three times as long as it is wide. The sponge cake is 18 inches longThe above parameters mean that
Length = 18
Width = 3 * Length
So, we have
n = 3 * length
substitute the known values in the above equation, so, we have the following representation
n = 3 * 18
Evaluate
n = 54
Hence, the width is 54 inches
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Complete question
Gilda's sponge cake is three times as long as it is wide. The sponge cake is 18 inches long. Use n to represent the cake's width.
Determine the width of the cake
The width of the cake which is represented as n would be = 54 inches
How to calculate the width of the cake?The length of the sponge cake that is owned by Gilda = 18 in.
The width of the sponge cake owned by Gilda (n) = 3( length)
That is;
n = 3( 18)
n = 54 inches.
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Pls help me solve these. They are due today 11:50pm
Answer:
1) 64, 2) 65536, 3) 5--------------------------------
Solve each equation.
1)
[tex]3\sqrt[3]{x} =12[/tex][tex]\sqrt[3]{x} =4[/tex][tex]x = 4^3=64[/tex]2)
[tex]\sqrt[3]{4x} +3=67[/tex][tex]\sqrt[3]{4x} =64[/tex][tex]4x=64^3[/tex][tex]4x=262144[/tex][tex]x=262144/4[/tex][tex]x=65536[/tex]3)
[tex]\sqrt[3]{5x+2} -3=0[/tex][tex]\sqrt[3]{5x+2}=3[/tex][tex]5x+2=3^3[/tex][tex]5x+2=27[/tex][tex]5x=25[/tex][tex]x=5[/tex]Madeline spends all of her spare money on widgets, which cost $2 each, and gizmos, which cost $2 each. What is her opportunity cost if Madeline buys 12 widgets? opportunity cost:
The opportunity cost of Madeline based on the information would be 8 units of gizmos .
What is the opportunity cost of Madeline?The benefit or gain that a person might have obtained or earned if he or she had not chosen the current alternative is known as opportunity cost.
Madeline has spent $24 ($2 x 12) on the widgets in this question since she purchased 12 of them at a cost of $2 each. In this case, her opportunity cost would be the gadgets she could have purchased, which works out to $24 / $3 = 8 units.
Therefore, the opportunity cost is 8 units.
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Find the slope of the line that passes through points 2, -8 and the origin using m=rise/run
Answer:
-4
Step-by-step explanation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-8)}{0-2}=\frac{8}{-2}=-4[/tex]
The slope of the line that passes through the points (2, -8) and the origin is calculated using the formula m = rise/run, which gives -4.
Explanation:In this Mathematics problem, we are asked to find the slope of the line that passes through two points using the formula m = rise/run, where 'm' is the slope. The points provided are (2, -8) and the origin, which is (0, 0).
To find the slope (rise/run), we can subtract the y-values (rise) and the x-values (run) of the two points, respectively. So, the formula becomes: m = (-8 - 0) / (2 - 0) => m = -8/2 = -4.
Therefore, the slope of the line that passes through the points (2, -8) and the origin is -4.
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Bismuth-214 has a half life of approximately 20 minutes. Find
the amount of bismuth-214 left from a 30-gram sample after 1 hour
One of the common terms for exponential decay is half-life, which refers to the period of time it takes for a quantity to fall by an exponential rate and halve its initial value.
What is meant by exponential decay function?In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. It can be written as [tex]y = a(1 - b)^x[/tex], where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.
The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.
The time it takes for a quantity to drop by an exponential rate to halve its initial value is known as the half-life, which is one of the popular words used to describe exponential decay.
Each 20 minutes there is 1/2 as much one hour is 3 half lives :
start 30 then 15 then 7.5 then 3.75 gm
30(1/2)3 = 3.75 gm
The complete question is;
Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left from a 30-gram sample after 1 hour.
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Determine if the scenario involves mutually exclusive events
You roll a fair six-sided die. The die shows an even number or a number less than three.
A) Not mutually exclusive
B) Mutually exclusive
2 is a common sample in the 2 events, therefore they are not mutually exclusive.
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will discover the likelihood of outcomes for a random experiment using this fundamental probability theory, which is also applied to the probability distribution.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.
If we roll a dice which is fair
Events that we get to shw even are = {2, 4, 6}
Events that we get when getting less that 3 = {1, 2}
So, 2 is a common sample in the 2 events, therefore they are not mutually exclusive.
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During a series of plays in a football game, a running back carried the ball for the yardages given by 6, -3, 2, -1, 7,
-4, and -2. Find his total yards and his average yards per carry.
The total yards for the running back was
(Simplify your answer.)
Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.
Define area.Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.
Here,
We find w = 56, which indicates that the parallelogram has a length of 56 yards.
Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.
The rectangle's length is shown to be 118 yards.
The size of the playing area is accordingly 118 yard by 56 yards.
As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.
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