ANSWER:
[tex](x+1)^2+(y+6)^2=36^{}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where (h, k) is the center and r is the radius } \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} (x-(-1))^2+(y-(-6))^2=6^2 \\ (x+1)^2+(y+6)^2=36^{} \end{gathered}[/tex]Manny opened a savings account 7 years ago the account earns 9%interest compounded monthly if the current balance is 400.00 how much did he deposit initially
We have the following:
The formula for compound interest is as follows
[tex]\begin{gathered} A=P(1+r)^t \\ \end{gathered}[/tex]A is amount (current balance 400), P is the principal ( deposit initially), r is the rate (0.07) and is the time ( 7 years)
replacing:
[tex]\begin{gathered} 400=P(1+0.07)^{7^{}} \\ P=\frac{400}{(1.07)^7} \\ P=249.09 \end{gathered}[/tex]Which means that the initial deposit was $ 249.09
Two students are painting strips of wood to make scenery for the school play. Henry has painted 14 strips of wood. He can paint 3½ strips of wood per minute. Sandy has painted 10 strips of wood. She can paint 4 strips of wood per minute. After how many minutes will both students have painted the same number of strips of wood? Let m represent the number of minutes. Select the correct values to write an equation to represent the situation.
The number of minutes when they would both paint the same strip of wood is 8 minutes.
In how many minutes would they paint the same strip of wood?The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)
14 + (3½x m)
14 + 3½m
The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)
10 + (4 x m)
10 + 4m
When both people paint the same strip of wood, the two above equations would be equal.
10 + 4m = 14 + 14 +3½m
4m - 3½m = 14 - 10
0.5m = 4
m = 4 / 0,5 = 8
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graph the function y=sqrt(x+6)+2. which point lies on the graph
Explanation
We are given the following function:
[tex]y=\sqrt{x+6}+2[/tex]We are required to graph the function.
Using a graphing calculator, we have:
Hence, the answer is (-2, 4).
The last option is correct.
2. Simba pays $15 per month
for the phone he bought. His cell phone plan costs $49
per month and includes 15GB of
data. He also pays $5 for each additional 1GB
of data he uses over the 15GB limit. Using x to represent the GB of data
he uses over 15 GB, write an equation to represent Simba's monthly cell
phone bill and determine how much he will pay if one month he uses
23GB of data.
The equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
What is an linear equation is one variable?
An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation
We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.
He pay additional $5 for 1 gb data after 15gb data limit got over
Let the number of gb's used be x
Hence the total bill will be given by the equation
B= 15+49+5x
B= 64+5x
If he uses 23 gb of data the first 15 Gb are covered in his phone plan
And he has to pay $5 for each gb
The total cost is 8*5=$40
Hence the total phone bill is B=64+40
B=$104
Hence the equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
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6. Tyrion's hourly rate is $16 an hour. He worked for 30 hours this week. 5 of those hours wereon a holiday, and his company pays twice the hourly rate for holidays. What was the total on hispaycheck? Show your calculations.
the area of a triangular wedge is 90 square inches the height is 18in what is the base
it is given that,
the height of the wedge is h = 18 in
the area of the wedge is A = 90 square in.
we know that the area of a triangle is
A = 1/2 x base x height
put values,
90 = 1/2 x base x 18
90/18 = 1/2 x base
5 = 1/2 x base
base = 5 x 2
base = 10 inches,
thus, the base of the wedge is 10 inches,
the question is y=4m=2x=3solve for b
y=mx+b
replacing y=4, m=2, x=3 in the equation:
4=2(3)+b
then
b=4-2(3)=4-6=-2b=-2Put these numbers in order from least to greatest. -27/36, 6, 18/40, 5/20
We have four numbers. We have to know that negative numbers are "smaller" than positive numbers, and when numbers are far away from zero are even "bigger".
The least number is -27/36. It is a negative number.
We can also see that we have some fractions. A fraction is a part of "a whole".
So, as we can see 6 is not a fraction. Therefore, 6 is the greatest number from this list.
So we have the least and the greatest: -27/36 and 6, respectively.
We also need to compare 18/40 and 5/20. What fraction is bigger?
In order to compare them, we need to have two fractions with the same denominator. Then, the fraction with the greatest numerator is "bigger" than the other fraction.
Let us see:
If we divide the numerator and the denominator of 18/40 by 2, we have:
18/2 = 9
40/2 = 20
Then, the equivalent fraction is 9/20 (or 9/20 is equivalent to 18/40). Now, we can compare them:
9/20 and 5/20. So, which one is the greatest? The one with the greatest numerator: 9/20.
Our final list is this way, from least to the greatest as follows:
-27/36, 5/20, 18/40 (9/20), 6.
What is 150% of 38.
We are asked to find 150% of 38
Step 1:
Convert the 150% to decimal by removing the % sign which means dividing by 100.
150/100 = 1.5
Step 2:
Now simply multiply the decimal percentage with the number 38
1.5×38 = 57
Therefore, 150% of 38 is found to be 57
Find the distance between the two points. 16.) (-4,2), (5,1)
distance is 9.055
Explanation:Given:
Two points; (-4, 2) and (5, 1)
To find:
the distance between two points
We will apply the formula for distance between two points:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} x_1=-4,y_1=2,\text{ }x_2=5,\text{ }y_2\text{ = 1} \\ distance\text{ = }\sqrt{(1-2)^2+(5-(-4))^2} \\ distance\text{ = }\sqrt{1\text{ + 9}^2} \\ distance\text{ = }\sqrt{82} \\ distance\text{ = 9.055} \end{gathered}[/tex]Factor.2n2 + 7n + 5
The first step to factor this expression is to find its roots (the values of 'n' that makes this expression equals zero)
To find the roots, we can use the quadratic formula:
(Using the coefficients a=2, b=7 and c=5)
[tex]\begin{gathered} n_1=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-7-\sqrt{49-40}}{4}=\frac{-7-3}{4}=\frac{-10}{4}=\frac{-5}{2} \\ n_2=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-7+3}{4}=\frac{-4}{4}=-1 \end{gathered}[/tex]So the roots of the expression are -5/2 and -1. Now, we can write the expression in this factored form:
[tex]\begin{gathered} a(n-n_1)(n-n_2) \\ 2(n+\frac{5}{2})(n+1) \\ (2n+5)(n+1) \end{gathered}[/tex]So the factored form is (2n+5)(n+1)
help i’ll greatly appreciate it :)
Answer: i think B
Step-by-step explanation:
im not that sure tho
А ВC D0 2 4 68 10 12Which point best represents V15?-0,1)A)point AB)point Bpoint CD)point D
We have to select a point that is the best representative of the square root of 15.
We can calculate the square root of 15 with a calculator, but we can aproximate with the following reasoning.
We know that 15 is the product of 3 and 5. If we average them, we have 4.
If we multiply 4 by 4, we get 16, that is a little higher than 15.
If we go to the previous number (3) and calculate 3 by 3 we get 9, that is far from 15 than 16.
So we can conclude that the square root of 15 is a number a little less than 4.
In the graph, the point B is the one that satisfy our conclusion, as it is a point in the scale that is between 3 and 4, and closer to 4.
The answer is Point B
“John is buying carpet for his house. He pays $1.30 per square foot for the first 1000 square feet. He pays $1.00 peradditional square foot after 1000 square feet.Part A: Write an equation for the total price when John buys less than 1000 square feet of carpet. Let c representthe amount of carpet needed in square feet, and p represent the total price in dollars.Enter vour equation in the first response boxPart B: John calculates that the total price will be $1500. How many square feet of carpet will he buy?Place your answer in the second response box”
EXPLANATION:
Given:
We are told that John pays $1.30 per square foot for the first 1000 square feet of carpet he buys. Then he pays $1.00 per additional square foot after the first 1000 square feet.
Required:
We are required to write an equation to represent the total price when he buys less than 1000 square feet.
Step-by-step solution;
Take note that he pays $1.30 per square foot for the first 1000 square feet. The amount spent, that is the price would be represented by p while, c would represent the amount of carpet to be bought.
Hence, for buying less than 1000 square feet;
[tex]p=1.30c[/tex]Next we note that John calculates that the total price would be $1500.
If John pays the amount of $1.30 for the first 1000 square feet, then he would have paid;
[tex]p=1.30(1000)[/tex][tex]p=1300[/tex]However, we are told that John calculates a total of $1500. This simply means that he will buy more than 1000 square feet of carpet.
He is going to spend an extra $200 (that is 1500 minus 1300). The cost of any extra foot after the first 1000 is $1.00. That means;
[tex]Extra\text{ }carpet=\frac{200}{1.00}[/tex][tex]Extra\text{ }carpet=200ft^2[/tex]That means John would be paying the sum of $1500 to buy 1,200 square feet of carpet.
ANSWER:
[tex]\begin{gathered} Part\text{ }A: \\ p=1.30c \end{gathered}[/tex][tex]\begin{gathered} Part\text{ }B: \\ 1200ft^2 \end{gathered}[/tex]Consider the following loan. Complete parts (a)-(c) below.An individual borrowed $67,000 at an APR of 3%, which will be paid off with monthly payments of 347$ for 22 years.a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.The amount borrowed is $____ the annual interest rate is ____, the number of payments per year is _____, the loan term is _____ years, and the payment amount is _____$ b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?There are ____ payments toward the loan and the total amount paid is ____$ c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?The percentage paid toward the principal is _____% and the percentage paid for interest is ____%.(Round to the nearest tenth as needed.)
b) There are 12 payments per year for 22 years; multiply 12 by 22 to get the total number of payments:
[tex]12\times22=264[/tex]To find the total amount paid, multiply the number of payments by the payment amount:
[tex]264\times347=91,608[/tex]There are 264 payments toward the loan and the total amount paid is $91,608c) Toward principal: $67,000
Toward interest: subtract the principal from the payment amount:
[tex]91,608-67,000=24,608[/tex]Let 91,608 be the 100%, use a rule of three to find the % corresponding to the principal and interest:
[tex]\begin{gathered} Principal: \\ x=\frac{67,000\times100}{91,608}=73.1 \\ \\ Interest: \\ x=\frac{24,608\times100}{91,608}=26.9 \end{gathered}[/tex]The percentage paid toward the principal is 73.1% and the percentage paid for interest is 26.9%How do you solve this?
Answer: I thought you already asked this question.
Step-by-step explanation:
What is the largestNumber of these wooden Els that can be packed in a box that is 2 cm x 4 cm x 6 cm
The largest number of the wooden Els with it's total surface area that can be packed in the 2cm×4cm×6cm box is 2 wooden Els.
Total Surface Area of Solid ShapesIn finding the total surface area of a solid cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) and use the formula, SA=2(lw+lh+hw), to find the surface area.
For the box, l=2cm, w=4cm and h=6cm
total surface area of box=2(2×6+2×4+6×4) cm square units
total surface area of box=2(44) cm square units
total surface area of box=88cm square units
For the top cuboid of the wooden El, l=3cm, w=1cm and h=2cm
total surface area of top El cuboid=22cm square units
For the bottom cuboid of the wooden El, l=1cm, w=1cm and h=2cm
total surface area of bottom El cuboid=10cm square units
total surface area of the El=32cm square units
(88cm²/32cm²)=2.75
This implies that only two(2) whole Els with total surface area of 32cm² can be packed in the box.
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Please help i need the answers for a test and how to work em out for the future
Given: The angles as shown in the image
[tex]\begin{gathered} m\angle DEY=105^0 \\ m\angle DEF=27x+3 \\ m\angle YEF=6x+3 \end{gathered}[/tex]To Determine: The measure of angle DEF
Solution
It can be observed that
[tex]\begin{gathered} m\angle DEY+m\angle YEF=m\angle DEF \\ Therefore \end{gathered}[/tex][tex]\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=\frac{105}{21} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} m\angle DEF=21x+3 \\ =21(5)+3 \\ =105+3 \\ =108 \end{gathered}[/tex]Question 12
Given:
[tex]\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}[/tex]To Determine: The measure of angle HIU
Solution:
It can be observed that
[tex]m\angle UIJ+m\angle HIU=m\angle HIJ[/tex][tex]\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-\frac{14^0}{2} \\ x=-7^0 \end{gathered}[/tex]Therefore, the measure of angle HIU would be
[tex]\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}[/tex]Hence, the measure of angle HIU is 30⁰
An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?
Step 1
Given;
Step 2
When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).
[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]checking properly, the sample proportion =0.30, because
[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]Answer; Option D
[tex]0.30[/tex]A math teacher said that 18 out of 25 students passed the test. What percent of thestudents did NOT pass the test?C.72%A.18%D.28%B.82%
Let's begin by listing out the given information:
18 students passed
Total students = 25
Number of people who did not pass = 25 - 18 = 7
7 out of 25 students did not pass. This has its percentage as:
[tex]\begin{gathered} \frac{7}{25}\cdot100\text{\%}=28\text{\%} \\ \Rightarrow28\text{\%} \end{gathered}[/tex]Therefore, 28% of the students did not pass
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 7.25x − 36.25, where x is the number of bracelets he sells. What is the value of Q(5), and what is its interpretation?
Q(5) = 0; If Quincy sells 0 bracelets, he will earn $5.
Q(5) = 0; If Quincy sells 5 bracelets, he will earn $0.
Q(5) = 5.69; If Quincy sells 5.69 bracelets, he will earn $5.
Q(5) = 5.69; If Quincy sells 5 bracelets, he will earn $5.69.
The value of Q(5) is zero and represents the zero profit on selling 5 bracelets thus option (B) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
Daily profit function Q(x) = 7.25x − 36.25 where x is the number of bracelets he sells.
At x = 5 ( selling 5 bracelets)
Q(5) = 7.25(5) - 36.25
Q(5) = 36.25 - 36.25 = 0
It means selling 5 bracelets doesn't give any profit.
Hence "The value of Q(5) is zero and represents the zero profit on selling 5 bracelets".
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Help I’m stuck ‼️‼️‼️ Hw due in a couple minutes
The lines AD and BC cross at a point where we have two pairs of vertically opposite angles.
The angles labelled (2x +50) and 100 are vertically opposite angles.
Vertically opposite angles are equal. Therefore;
[tex]\begin{gathered} 2x+50=100 \\ \text{Subtract 50 from both sides} \\ 2x+50-50=100-50 \\ 2x=50 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{50}{2} \\ x=25 \end{gathered}[/tex]ANSWER:
The value of x is 25. The correct answer is option A
A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate in still water and what is the rate of the current?Rate of the boat in still water: mi/hRate of the current: mi/hmi/h= miles per hour
Given:
It takes the boat 3 hours to travel 108 miles going upstream
Return trip = 2hours going downstream
Distance, d = 108 miles
Time going upstream = 3 hours
Time going downstream = 2 hours
Let's find the rate in still water and the current rate.
Let s represent the still rate
Let c represent the current rate.
Apply the distance formula:
Distance = Rate x Time
We have the set of equations:
(s - c) x 3 = 108.................................Equation 1
(s + c) x 2 = 108.................................Equation 2
Apply distributive property:
3s - 3c = 108
2s + 2c = 108
Let's solve both equations simultaneously using substitution method.
Rewrite the first equation for s:
3s - 3c = 108
Add 3c to both sides:
3s - 3c + 3c = 108 + 3c
3s = 108 + 3c
Divide all terms by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{108}{3}+\frac{3c}{3} \\ \\ s=36+c \end{gathered}[/tex]Substitute s for (36 + c) in equation 2:
2s + 2c = 108
2(36 + c) + 2c = 108
72 + 2c + 2c = 108
72 + 4c = 108
Subtract 72 from both sides:
72 - 72 + 4c = 108 - 72
4c = 36
Divide both sides by 4:
[tex]\begin{gathered} \frac{4c}{4}=\frac{36}{4} \\ \\ c=9 \end{gathered}[/tex]Substitute c for 9 in either of thee equation.
Take the first equation:
3s - 3c = 108
3s - 3(9) = 108
3s - 27 = 108
Add 27 to both sides:
3s - 27 + 27 = 108 + 27
3s = 135
Divide both sides by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{135}{3} \\ \\ s=45 \end{gathered}[/tex]Thus, we have the solutions:
c = 9
s = 45
The rate of boat in still water is 45 miles per hour
The rate of the current is 9 miles per hour
Therefore, we have:
Rate of boat in still water: 45 mi/h
Rate of current: 9 mi/h
Take the firs
ANSWER:
Rate of boat in still water: 45 mi/h
Rae of the current: 9 mi/h
What is the exact surface area of the right rectangular pyramid below? Leave your answer in simplified radical form.
Usually, to calculate the area of a solid we need to calculate the area of every face. Here we have a rectangle down, and four triangles. Our desired area (TA) will be the sum of those areas. Let's calculate those areas:
Area of the rectangle) The area of the rectangle (R) is
[tex]R=(leng\ldots)(wid\ldots)=(10cm)\cdot(4cm)=40\operatorname{cm}^2[/tex]Area of the front triangle and the back tringle) Note that the front triangle and the back triangle are the "same". So the area of each of them is equal (this simplifies our work...). The area of each of them (FB) is
[tex]FB=\frac{(base)\cdot(high)}{2}[/tex]What is their high?
The triangle with red, blue, and green edges is a right triangle... Its hypotenuse is the blue edge. We know the red edge, its length is 6cm, but what is the length of the green edge? Because our solid is a rectangular pyramid, we can say that the green edge is half of the length of the rectangle. that is, 5cm (10cm/2). Now, we know the red and green edges; so we can apply The Pythagoras theorem to get
[tex](blue)^2=(red)^2+(green)^2[/tex][tex](blue)^2=(6cm)^2+(5cm)2=36\operatorname{cm}+25\operatorname{cm}=61\operatorname{cm}^2[/tex][tex]undefined[/tex]What the answer to this to solve the problem
Answer:
25
Step-by-step explanation:
180-88=92
92+61=123
123+30+x=180
153+x=180
x=25
Miles east of 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 Time (hours) Where were the two cars in relation to each other when they began traveling? O A. Car B was 5 miles east of car A. O B. Car B was 20 miles east of car A. O C. Car Awas 15 miles east of car B. D. Car A was 5 miles east of car B. < PREVIOUS
Car B was 5 miles east of car A, Option A
The diagram shows two similar polygonsN51P224048MR3016.5SFigures not drawn to scale.What is the length of CS?
Notice the correspondence between the vertices of the polygons:
[tex]VQRGX\approx CNPMS[/tex]Corresponding segments of similar polygons are proportional. Then:
[tex]\frac{CS}{VX}=\frac{PM}{RG}[/tex]Substitute VX=48, PM=22 and RG=16.5 and solve for CS:
[tex]\begin{gathered} \Rightarrow\frac{CS}{48}=\frac{22}{16.5} \\ \Rightarrow CS=\frac{22}{16.5}\times48 \\ \Rightarrow CS=64 \end{gathered}[/tex]Therefore, the length of CS is 64.
Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
The line plot below shows the number of minutes dog owners in a certain neighborhood spent walking their dogs last month.Which statement describes the data shown?The data has a range of 150 to 40, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 20, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.The data has a range of 150 to 20, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 40, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.
Looking at the graph, the minimum value is 40 and the maximum value is 150, therefore the range is between 150 and 40.
Also, we have a total of 27 points on the graph, which means the median is the 14th value of the data set in crescent order.
Counting the points from the left to the right, the 14th point has a value of 100, therefore the median is equal to 100.
So the correct option is
You cut a piece of wood that is 69 inches long. The wood is cut into 3 pieces. The second piece is 8 inches
longer than the first. The third piece is 8 inches longer than the second piece. Find the length of each of
the three pieces.
The length of piece one will be 15 inch, the length of piece two will be 23 inch and the length of third piece will be 31 inch as per the given conditions of "You cut a piece of wood that is 69 inches long. The wood is cut into 3 pieces. The second piece is 8 inches longer than the first. The third piece is 8 inches longer than the second piece."
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
What is equation?In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated statement that has been mathematically quantified.
Here,
according to the question,
x+y+z=69
y=x+8
z=y+8
z=x+16
3x+24=69
3x=45
x=15
y=23
z=31
According to the conditions specified, piece one will be 15 inches long, piece two will be 23 inches long, and piece three will be 31 inches long. "You chop a 69-inch-long piece of wood. Three pieces of the wood are cut out. Eight inches longer than the first piece is the second one. Eight inches longer than the second piece is the third one."
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