The length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.
how to determine the length of the boundary wall ?To determine the length of the boundary wall that needs to be raised, we need to know which part of the stadium the wall will enclose.
If the wall is to be raised along the length of the stadium (i.e., the longer side), then the length of the wall will be equal to the length of the stadium, which is 125 meters.
If the wall is to be raised along the width of the stadium (i.e., the shorter side), then the length of the wall will be equal to the width of the stadium, which is 85 meters.
If the wall is to enclose the entire stadium, then we need to find the perimeter of the stadium and add the length of the wall that will enclose the remaining side.
Perimeter of the stadium = 2 x (length + width)
Perimeter of the stadium = 2 x (125 + 85) = 420 meters
To enclose the remaining side, we need to add a wall of length 125 - 85 = 40 meters.
Therefore, the length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.
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In ΔLMN, the measure of ∠N=90°, NM = 28, LN = 45, and ML = 53. What is the value of the sine of ∠M to the nearest hundredth?
researchers observed 50 random people brush their teeth and recorded the number of seconds each person spent brushing. from the sample, they found a mean time of 41.5 seconds. further, their calculations revealed that this estimate is within a margin of error of 2.45 from the true average time that all people spend brushing their teeth. write the interval estimate that will estimate the true average time that people spend brushing their teeth. write your answer using inequality notation:
Answer:
The interval estimate is:
41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45
or
38.05 ≤ true average time ≤ 44.95
Inequality notation:
[38.05, 44.95]
The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.
Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:
(sample mean) ± (margin of error)
Substituting the given values, we get:
41.5 ± 2.45
Simplifying, we get:
[39.05, 43.95]
Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.
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7. William's father wants to buy a new glass top for the desk in his
home office. The dimensions of the top of the desk are shown.
If glass is $0.06 per square inch, how much will the new glass top
cost for his desk? Round to the nearest hundredth if necessary.
If glass is $0.06 per square inch, the new glass top will cost $80.64.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and express relationships between variables. It involves the use of letters and symbols to represent numbers and quantities, and the use of equations and inequalities to solve for unknown values.
Algebra is used to solve a wide range of mathematical problems, including linear equations, quadratic equations, polynomial equations, and systems of equations. It is also used to study functions, which are mathematical relationships between variables that can be represented by graphs or equations.
Algebraic concepts and techniques are used in many fields, including engineering, physics, finance, and computer science. For example, in engineering, algebra is used to model physical systems and to analyze their behavior, while in finance, algebra is used to calculate interest rates, loan payments, and other financial transactions. In computer science, algebra is used to design and analyze algorithms and data structures.
The area of the glass top required for the desk can be found by multiplying the length and width of the desk:
Area = 48 in x 28 in = 1344 square inches
The cost of the glass top can be found by multiplying the area by the cost per square inch:
Cost = 1344 sq in x $0.06/sq in = $80.64
Therefore, the new glass top will cost $80.64.
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what is the correct expression of the null hypothesis for the alternative hypothesis: the percentage of internet users who use the internet for shopping is greater than .40?
The null hypothesis for the alternative hypothesis "the percentage of internet users who use the internet for shopping is greater than 0.40" can be expressed as:
H0: p ≤ 0.40
Here, H0 represents the null hypothesis and p represents the proportion of internet users who use the internet for shopping.
The null hypothesis states that the percentage of internet users who use the internet for shopping is less than or equal to 40%.
In hypothesis testing, we collect data and analyze it to determine whether we can reject the null hypothesis or not.
If the data provides strong evidence against the null hypothesis, we reject it and accept an alternative hypothesis that suggests there is a significant relationship or difference.
However, if the data is not strong enough to reject the null hypothesis, we fail to reject it, but we cannot conclude that the null hypothesis is true.
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do sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers? the appropriate test of hypothesis would be select one: a. a one-tailed test b. a two-tailed test c. cross-sectional d. participant observation
The appropriate test of hypothesis in this case would be a two-tailed test.
Why the test of hypothesis would be a two-tailed test?A two-tailed test is used when the hypothesis being tested is that there is a difference between the groups being compared, but the direction of the difference is not specified. In this case, the hypothesis being tested is whether sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers.
The hypothesis does not specify the direction of the difference, only that there is a difference. Therefore, a two-tailed test would be appropriate to determine whether there is a significant difference in the number of pregnancies among teenagers who have access to sex education classes and free clinics compared to those who do not have access.
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Ms. Wilson's taxable income is $36,201. She is filing as single,
and she has already paid $5344 in federal taxes.
What will she receive or pay after she figures her taxes for the
year?
A. She will receive a refund of $245.
B. She will pay $245.
C. She will pay $258.
D. She will receive a refund of $258.
Ms. Wilson will receive a amount given by option D. She will receive a refund of $258.
Total taxable income of Ms. Wilson's = $36,201
Status filled by Ms. Wilson is Single.
Amount already paid as federal tax = $5344
From the table,
Taxable amount to be paid by single .
Range of income is 36,200 to 36250 is equal to $5086
Here federal tax paid by Ms. Wilson is higher then tax to be paid.
This implies,
She will receive a refund.
Refund amount = Federal tax amount - Tax to be paid
Substitute the value we have,
⇒Refund amount = $5344 - $5086
⇒Refund amount =$258
Therefore, the Ms. Wilson will receive her refund represented by option D. She will receive a refund of $258.
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What is the value of the third quartile of the data set represented by this box plot?
The third quartile (Q3) of this data set is 29.
What is data set?A data set is a collection of data that is organized. It is typically structured to allow for easy access and manipulation of the data. It is generally composed of a set of values, observations, or measurements that are related to each other and that can be used to analyze and interpret information. Data sets may include variables, such as names, numbers, addresses, and dates, or they may include images, audio, or video. Data sets can be used for academic research, business analysis, or other purposes.
To calculate Q3, we divide the set into four quarters. The first quarter (Q1) is the set of values from the smallest to the median, which is 18.
The second quarter (Q2) is the set of values from the median to the third quartile, which is 29. The third quarter (Q3) is the set of values from the third quartile to the largest value, which is 36.
The fourth quarter (Q4) is the set of values from the largest value to the smallest value, which is 12. Therefore, the third quartile (Q3) of this data set is 29.
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complete questions as follows-
A rectangle garden has a length of 42cm and a width of 36 cm. of fencing cost 4.00$ a meter. how much will it cost to fence the garden? grade 5 math
Answer:
$624
Step-by-step explanation:
The width is the smaller side and there are four sides to a rectangle so 2 sides are 36 cm and 2 sides are 42cm. The perimeter formula follows this P=(L+W)*2 so plugging the variables (42+36)*2= 156. So there are 156 meters of fencing and each meter costs $4.00. Thus, 156*4=$624
Help please! No silly answers. Correct answers please, thank you.
A linear function has one independent variable and one dependent variable..
therefore, all are linear except y=x²-6
a study is conducted to examine the relationship between family status and school performance. the sample is selected by randomly choosing every 5th child from the list of children at the abc elementary school. data are collected from the school record for each child. family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. school performance is measured by a student math test and a student reading test that are administered to the child in april. each test includes 20 questions. each correct answer is worth five points. q 1 question 1 what is the study design? select one: a. quasi-experimental study b. cross-sectional study c. pre-experimental study d. cohort study e. case-control study f. experimental study
The study design described is a cross-sectional study.
The study design in this scenario is a cross-sectional study. The study aims to examine the relationship between family status and school performance. The sample is selected by randomly choosing every 5th child from the list of children at the ABC elementary school. Data is collected from the school record for each child, and family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. The school performance is measured by administering a student math test and a student reading test to the child in April, with each test including 20 questions and each correct answer being worth five points.
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The equation of line A is y = 7x + 12.
Line B is parallel to line A and passes through the point (2, 24).
What would be the solution to the system of equations represented by line A and line B?
A. R=7, y=61
B. The system of equations has an infinite number of real solutions.
C. The system of equations has no real solutions.
D. r=4,y=38
This equation is clearly not true, which means there is no real value of x that satisfies it. Therefore, the system of equations represented by line A and line B has no real solutions, the correct option is C.
Line A has a slope of 7, which means any line parallel to it will also have a slope of 7. Therefore, line B can be represented by the equation y = 7x + b, where b is the y-intercept that we need to find.
We know that line B passes through the point (2, 24), so we can substitute these values into the equation to get:
24 = 7(2) + b
Simplifying the right side gives:
24 = 14 + b
Subtracting 14 from both sides gives:
b = 10
Therefore, the equation of line B is y = 7x + 10.
Now we need to find the point of intersection between line A and line B, which is the solution to the system of equations represented by these two lines. To accomplish this, we can put the two equations equal to one another and find x:
7x + 12 = 7x + 10
Subtracting 7x from both sides gives:
12 = 10
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The ratio of mercy’s present age to her mom’s present age 2:3. If their combined age is 50 years, how old is mercy and her mom 7 years from now?
Mercy will be 27 years old, and her mom will be 37 years old, 7 years from now.
To find Mercy's and her mom's ages, follow these steps:
1. Set up an equation: Let Mercy's age be 2x and her mom's age be 3x.
Their combined age is 50 years, so the equation is 2x + 3x = 50.
2. Solve the equation: Combine the terms on the left side to get 5x = 50.
Then, divide both sides by 5 to find x = 10.
3. Find their present ages: Mercy's age is 2x = 2(10) = 20 years old, and her mom's age is 3x = 3(10) = 30 years old.
4. Find their ages 7 years from now:
In 7 years, Mercy will be 20 + 7 = 27 years old, and her mom will be 30 + 7 = 37 years old.
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When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 140 lb and 201 lb. Weights of women are now normally distributed with a mean of 162 and a standard deviation of 46 lb . Complete parts (a) through (c) below.
Answer:
(a) What percentage of women would not be able to use the original ejection seats designed for men?
To answer this question, we need to find the percentage of women whose weight is outside the range of 140 lb to 201 lb, which is the weight range for which the original ejection seats were designed. We can do this by standardizing the weight distribution of women using the formula:
z = (x - μ) / σ
where z is the standard score, x is the weight of a woman, μ is the mean weight of women, and σ is the standard deviation of the weight of women.
Substituting the given values, we get:
z = (140 - 162) / 46 = -0.478
z = (201 - 162) / 46 = 0.848
Using a standard normal table or a calculator, we can find that the percentage of women whose weight is below 140 lb (corresponding to a z-score of -0.478) is 31.45%. Similarly, the percentage of women whose weight is above 201 lb (corresponding to a z-score of 0.848) is 19.34%. Therefore, the percentage of women who would not be able to use the original ejection seats designed for men is:
31.45% + 19.34% = 50.79%
(b) What weight range would accommodate 99.7% of the female pilots?
To find the weight range that would accommodate 99.7% of the female pilots, we need to find the z-scores that correspond to the 0.15% and 99.85% percentiles of the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -2.97 and 2.97, respectively.
Substituting these z-scores into the standardization formula, we get:
-2.97 = (x - 162) / 46
x = 63.88 lb
and
2.97 = (x - 162) / 46
x = 260.12 lb
Therefore, the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb.
(c) What percentage of women would need ejection seats redesigned for them?
To find the percentage of women who would need ejection seats redesigned for them, we need to find the percentage of women whose weight is outside the weight range that would accommodate 99.7% of the female pilots. Using the values from part (b), we can see that the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb. Therefore, the percentage of women who would need ejection seats redesigned for them is:
100% - 99.7% = 0.3%
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x and x < 5
What is the inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
Option 1: x < 5 – This is one of the correct representations. It is obtained by solving the inequality as follows:
-3(2x – 5) < 5(2 – x)
-6x + 15 < 10 – 5x (Distribute on the left and right sides)
-x < -5
x > 5 (Multiply both sides by -1 and reverse the inequality)
Option 2: -6x – 5 < 10 – x – This is not a correct representation. It is obtained by distributing on the left side but incorrectly distributing on the right side.
Option 3: -6x + 15 < 10 – 5x – This is one of the correct representations. It is obtained by distributing on the left and right sides, and then simplifying.
Option 4: x + 6 < 5x – 10 – This is not a correct representation. It is obtained by incorrectly distributing on the right side.
As for the number line representations:
The number line from negative 3 to 3 in increments of 1 with an open circle at 5 and a bold line starting at 5 and pointing to the right represents the solution x < 5, which is correct.
The number line from negative 3 to 3 in increments of 1 with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left does not represent the correct solution. There is no negative solution to this inequality, so there should not be an open circle or a bold line pointing to the left.
Hence, The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x and x < 5
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find the answer (2√x) × (3³√x)
Answer:
6x^(3/2)
Step-by-step explanation:
To simplify the expression (2√x) × (3³√x), we can first use the properties of exponents to rewrite the cube root as a fractional exponent:
3³√x = x^(1/3)^3 = x^(1)
Using this, we can rewrite the expression as:
(2√x) × (3³√x) = 2x^(1/2) × 3x^(1)
To multiply these two terms, we can add the exponents since the bases are the same:
2x^(1/2) × 3x^(1) = 6x^(1/2 + 1) = 6x^(3/2)
Therefore, the simplified expression is 6x^(3/2).
How many solutions does the equation have?
y+7=y–3
Responses
no solutions
no solutions
1 solution
1 solution
many solutions
Answer:
no solutions
Step-by-step explanation:
y + 7 = y - 3 ( subtract 7 from both sides )
y = y - 10 ( subtract y from both sides )
0 = - 10 ← false statement
this false statement indicates the equation has no solution
Please help and explain
Answer:
A. 500 yards
Step-by-step explanation:
By the Pythagorean Theorem:
[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]
The distance from the park to Anita's house is 5 blocks, which is
5 blocks × 100 yards/block = 500 yards.
Answer:
A. 500 yards
Step-by-step explanation:
1 block = 100 yards
one leg: 4*100= 400 yards
second leg: 3*100= 300 yards
hypotenuse:
pythagorean theorem
hypotenuse ^2 = (one leg)^2 + (second leg)^2
hypotenuse ^2= (400)^2 + (300)^2
hypotenuse ^2 = 160,000 + 90,000
hypotenuse = sqrt(250,000)
hypotenuse = 500 yards
find the value of x.
Answer:
x = 55°
Step-by-step explanation:
Inscribed Angle Theorem says that the angle inside the circle is equal to 0.5 times the measurement of the arc it span. For example, the 70° spans 140° of the arc.
Create two equations to solve for x and r.
x = 0.5r
2r + 2(70) = 360
2r + 140 = 360
2r = 220
r = 110
x = 0.5 * 110
x = 55°
Eden brings a 0.75-quart bottle of sports drink to each softball practice. At her first practice, she drank 12 bottle of sports drink. At her second practice, she drank the entire bottle. How many quarts of sport drink did she consume during both practices?
Eden consumed a total of 9.75 quarts of sports drinks during both practices.
Eden brings a 0.75-quart bottle of sports drink to each softball practice. At her first practice, she drank 12 bottles of sports drinks. This means she drank a total of:
12 bottles x 0.75 quarts/bottle = 9 quarts
At her second practice, she drank the entire bottle, which is another 0.75 quarts.
Therefore, the total amount of sports drinks Eden consumed during both practices are:
9 quarts + 0.75 quarts = 9.75 quarts
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Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.
The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."
To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:
Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:
[tex]4x^2 - 20x + 25 = 0[/tex]
This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:
[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]
Substituting the values of a, b, and c, we get:
x = (-(-20) ± - 4(4)(25))) / 2(4)
x = (20 ± sqrt(400 - 400)) / 8
x = 5/2
Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.
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find the number of integers between 2000 and 5000 which no digit is repeated if the integers are divisible by 5
Answer:
Step-by-step explanation:
PLEASE HELP ME SOO FAST I BEG
Answer: 63
Step-by-step explanation:
tan(B) = 10/5
B = tan^-1 (10/5)
B = 63.43 ≈ 63
A bag contains 6 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.
To find the probability of drawing three green marbles from the bag, we need to use the formula for calculating the probability of multiple independent events. The probability of multiple independent events occurring together is the product of the individual probabilities of each event.
Let's first calculate the probability of drawing a green marble on the first draw. We have a total of 6 + 4 + 7 = 17 marbles in the bag, and 7 of them are green. So the probability of drawing a green marble on the first draw is:
P(green on first draw) = 7/17
After we draw a green marble on the first draw, we have 16 marbles left in the bag, including 6 red marbles and 4 blue marbles. Since we don't replace the marble after we draw it, the probability of drawing a green marble on the second draw is:
P(green on second draw) = 6/16
Finally, after we draw a green marble on the second draw, we have 15 marbles left in the bag, including 5 green marbles. So the probability of drawing a green marble on the third draw is:
P(green on third draw) = 5/15
To find the probability of drawing three green marbles in a row, we need to multiply these probabilities:
P(three green marbles) = P(green on first draw) x P(green on second draw) x P(green on third draw)
P(three green marbles) = (7/17) x (6/16) x (5/15)
Simplifying this expression, we get:
P(three green marbles) = (7 x 6 x 5) / (17 x 16 x 15)
P(three green marbles) = 0.0735
Therefore, the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.
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ay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
Answer:
The answer is 8
Step-by-step explanation:
Let total number of rides be represented by x
And total amount spent on the ride and entry fees be y
Entry fees of the park = $10.50
Also, Charge for each ride is given to be $4.50
So, The linear function which describes the situation :
y = 10.50 + 4.50x
Now, Its given that Jay spent a total of $46.50 in the park
So, to find total number of rides taken substitute y = 46.50 in the above linear equation.
⇒ 46.50 = 10.50 + 4.50x
⇒ 4.50x = 36
⇒ x ≈ 8
Thus, Number of rides taken = 8
4.44 a company produces a computer battery that it claims last for 8 hours on a single charge with a standard deviation of 20 minutes. a random sampling of seven batteries are tested and found to have a sample standard deviation of 29 minutes. what is the chi-squared value and the predicted level of significance as represented by the test?
In order to determine the chi-squared value and the predicted level of significance as represented by the test, we need to conduct a hypothesis test. We will use the chi-squared test for a population variance. The null hypothesis is that the population variance is equal to 20 minutes squared (the square of the standard deviation), and the alternative hypothesis is that the population variance is greater than 20 minutes squared.
Therefore, the chi-squared value is calculated as:χ2 = (n - 1) × s2 / σ20where n is the sample size, s is the sample standard deviation, and σ0 is the hypothesized population standard deviation. Substituting the values given in the question, we get:χ2 = (7 - 1) × 29² / 20²= 21.19.
The degrees of freedom for this test are df = n - 1 = 6.Using a chi-squared distribution table with 6 degrees of freedom, we can find the predicted level of significance. For a chi-squared value of 21.19 and 6 degrees of freedom, the level of significance is less than 0.005. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population variance is greater than 20 minutes squared.
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help asapp will give brainliest!!
Answer:
x+48=180-2x (straight lines sum is 180 and corresponding angles)
x+2x=180-48
3x=132
x=44°
Pls Answer Fast!!!! Whoever gets it correct first I will give a brainly.
Answer:
Step-by-step explanation:
use a calculator it's free
Any help with this ???
Answer:
a) 2 new printers
b) 11 min
Step-by-step explanation:
Given:
5 old printers take 30 min to produce a batch of comic books
4 new printers take 18 min to produce a batch of comic books
.
a) First, we need to find how long does one old and new printer take to produce a batch of comic books:
.
Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):
.
1 old printer does the job in:
5 × 30 = 150 min
1 new printer does the job in:
4 × 18 = 72 min
.
Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):
6 old printers would take:
150 / 6 = 25 min
2 new printers would take:
72 / 2 = 36 min
.
25 < 36
That means, 2 new printers would do this job faster
.
b) In order to find how much less time would this take, we have to subtract:
.
36 - 25 = 11 min
help asapp!!!!!!!!!!
the volume of the conical section is approximately 604.8 cubic inches. we need to use volume formula of conical section to get the answer
what is conical section ?
A conical section is a geometric shape formed by the intersection of a plane with a cone. A cone is a three-dimensional geometric shape that has a circular base and tapers to a point, while a plane is a two-dimensional flat surface that extends infinitely in all directions.
In the given question,
To find the volume of a conical section, we need to use the formula:
Volume = (1/3) x π x r² x h
where r is the radius of the circular base of the cone, h is the height of the conical section, and π is the constant pi (approximately 3.14159).
In this case, we are given the diameter of the base of the cone, which is 12 inches. We can use the formula to find the radius:
r = d/2 = 12/2 = 6 inches
We are also given the height of the conical section, which is 14 inches. We can now plug these values into the formula:
Volume = (1/3) x π x r² x h
Volume = (1/3) x π x 6² x 14
Volume = (1/3) x π x 36 x 14
Volume = 604.8 cubic inches (rounded to one decimal place)
Therefore, the volume of the conical section is approximately 604.8 cubic inches.
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Try It
Complete the square.
y²-20y
Find the missing term that completes the square.
y²-20y +
(Simplify your answer. Type an integer or a fraction.)
we can represent this as a trinomial with a perfect square:(y-10)²-100
PRECISE SQUARE TERMINAL: WHAT IS IT?
A quadratic expression that can be factored into a binomial squared is a perfect square trinomial. When it is factored, it follows a pattern where the first and last terms are monomial perfect squares and the middle term is the product of the first two. A given trinomial is not a perfect square trinomial if the pattern does not fit for it1.
For instance, the trinomial x2+6x+9 is a perfect square trinomial since it factors into (x+3)². The square of x is represented by the first term, x², and the square of 3 by the last term, 9. Its result 2(x)(3) is twice as long as the middle term 6x.
Y has a coefficient of -20. A fraction of -20 is -10.
-10 is squared to give 100.
As a result, we can add and take 100 to finish the square.
It is necessary to add and subtract the square of the y-half coefficient's in order to finish the square for y²–20y.
y²-20y+100-100
=(y-10)²-100
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