The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.
What are quadratic functions?A polynomial function with one or more variables, where the greatest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the highest degree term in a quadratic function is of the second degree. The formula for a quadratic equation is ax² + bx + c = 0, where a and b are referred to as the coefficients of x² and x, respectively. The function's constant is the c term.Given quadratic function f(x) = x² - 5x + 6.
The values of the coefficients and constant in the function are
a = 1
b = -5
c = 6
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What equation is graphed in this figure?
A y+2=−32(x−2)
B y−4=−23(x+2)
C y+1=−23(x−3)
D y−3=32(x+1)
The equation of the line that passes through the graph is y + 2 = -3/2(x - 2)
How to determine the equation of the line?The graph represents the given parameter
From the graph, the points are given as
(0, 1) and (2, -2)
Calculate the slope of the points using
Slope = (y₂ - y₁)/(x₂ - x₁)
Rewrite as
m = (y₂ - y₁)/(x₂ - x₁)
This means that
Slope = m
So, we have the following representation
m = (-2 - 1)/(2 - 0)
Evaluate
m = -3/2
The equation of the line is then calculated as
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (2, -2)
m = -3/2
So, we have
y = -3/2(x - 2) - 2
Add 2 to both sides
y + 2 = -3/2(x - 2)
Hence, the equation of the line is y + 2 = -3/2(x - 2)
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What’s the answer to this question
The recursive formula of the arithmetic sequence is:
xₙ = n*4 + 13
With that we can see that x₁₁ = 57
How to write the arithmetic sequence?Here we know that the first elements of the sequence are:
17, 21, 25, 29, ...
To find the common difference, d, we take the difference between any two consecutive elements, so we have:
c = 21 - 17 = 4
Then the recursive formula for the n-th term is:
xₙ = n*4 + d
The first element x₁ is 17, so we will have:
17 = 1*4 + d
17 - 4 = d = 13
The recursive formula is:
xₙ = n*4 + 13
b) the eleventh term of the sequence is given by replacing n in the above formula by 11.
x₁₁ = 4*11 + 13 = 44 + 13 = 57
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What is the product of 8300 and 7.7x 10^2 expressed in scientific notation
Answer: 6391000 or 6.391 x 10^6
Step-by-step explanation:
**First, convert 7.7 x 10^2 to a number**
770
**Then multiply 8300 and 770**
6391000
**Convert to scientific notation**
6.391 x 10^6
Hope this helps <3
HELP PLEASE!!
Use the point and the slope to graph each line. Write the equation of the line
Answer:
y = x in the slope intercept form
y - 2 = 1(x -2) in the point-slope form of a line
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals of each other. So the perpendicular slope would be 1.
We could write this in the point slope form of a line and the answer would be:
y - 2 = 1(x -2) This would be the point slope form of a line.
If you want your answer in the slope intercept form
y -2 = 1(x-2)
y - 2 = x - 2 Add two to both sides
y = x
WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?
IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.
TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY
[tex]m1 \times m2 = - 1 \\ - 1 \times m2 = - 1 \\ m2 = 1[/tex]
THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1
the general equation of the straight line is y=mx+c
[tex] - 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4[/tex]
This means that
[tex]y = 1x - 4 \\ simply \\ y = x - 4[/tex]
HELP FAST! Write an inequality for each of the phrases or word problems. Solve for the missing variable and
graph the solution set on the number line.
a. The value of number plus 17 is less than 12.
b. A number times negative three is at least 12.
c. The difference between a number and three is more than 10.
d. There were at most b bananas on your banana bunch. You have eaten at least one and have 8
left. How many were on the bunch?
e. Susanna purchased a shirt for $5, pants for $10, and a jacket for $25. She wants to buy at least
one purse for the outfit, but she wants to have something left of her original $65. How much
money might she spend on the purse?
f. An lift holds no more than 1200 pounds. If you are rolling a cart that weighs 760 pounds, how
much more can the elevator hold?
Question 7A: Keisha has $585.43 in her checking account. She must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today. Write an inequality, using x for the variable, that would be used for the least amount of money she needs to deposit to avoid a fee.
585.43x - 302.05 ≥ 300
585.43 - 302.05 + x ≥ 300
585.43 - 302.05 + x ≤ 300
585.43x - 302.05 ≤ 300
The inequality that shows the least amount of money she needs to deposit to avoid a fee is 585.43 - 302.05 + x ≥ 300
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let x represent the least amount of money Keisha needs to deposit to avoid a fee. Keisha has $585.43 in her checking account and must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today, Hence:
585.43 - 302.05 + x ≥ 300
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Please help me on this. I really need this done.
The area hexagon using Lin's and Andre's method is:
By Lin's method = 93.48inch^2
By Andre's method = 93.53 inch^2
What is Mensuration ?
The field of mathematics known as mensuration explores how to measure geometric objects and their attributes, such as length, volume, shape, surface area, lateral surface area, etc.
By Lin's method
He parted the hexagon into six equilateral triangle
So, area of equilateral triangle = √3/4 × (side)^2
Since the given side = 6inch
Therefore,
area of equilateral triangle = √3/4 × (6)^2
=√3/4 × 36
= √3 x 9
= 1.732 x 9
= 15.58inch^2
The area of hexagon will be = 15.58 x 6
= 93.48inch^2
Now, By Andre's method
he parted two triangle and one rectangle
The triangle has two equal side that means its an isosceles triangle
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
given,
base = 10.4 inch
side = 6 inch
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
= ½[√(6^2 - 10.4^2/4) × 10.4]
= ½[√(36 - 108.16 /4) ×10.4]
= ½[√(36 - 27.04) × 10.4]
= ½[√(8.96) × 10.4]
= ½[2.99 × 10.4]
= 15.56inch^2
for two triangles the area will be = 15.56 x 2
= 31.13 inch^2
Now, area of rectangle = length x width
where,
Length = 10.4 inch
Width = 6 inch
So,
area of rectangle = 10.4 x 6
= 62.4 inch^2
Then, The area of hexagon will be = area of rectangle + area of two triangle
= 62.4 inch^2 + 31.13 inch^2
= 93.53 inch^2
Hence, by both methods the area from Lin's method = 93.49 inch^2
and by Andre's method = 93.53 inch^2
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Use the given information to prove that DE=FD
The condition for the figure to be similar is that; DE = FD
What are similar figures?Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
In the problem, the ratio should be CD/DE = GD/DF
We can also write the ratios of the corresponding sides as:
CD/DE = GD/DF
Therefore, CE and GF are similar
Thus, the condition for the figure to be similar is that;
DE = FD
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Suppose that 14 inches of wire costs 56 cents.
At the same rate, how many inches of wire can be bought for 44 cents?
by using the unitary method, 11 inches of wire can be bought for 44 cents.
We are given that:
14 inches of wire costs 56 cents.
14 inches = 56 cents
Now, by using the unitary method, we get that:
1 cent = 14 / 56 inches.
1 cent = 1 / 4 inches.
Now, for 44 cents, by using the multiplication, we get that:
44 cents = 1 / 4 inches × 44
44 cents = 11 inches.
Therefore, we get that, by using the unitary method, 11 inches of wire can be bought for 44 cents.
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Cedar just graduated from college. he accepted a position with a firm at an annual salary of 45,000. using the department of housing and urban development guidelines, what is the maximum amount cedar should pay for rent on a monthly basis?
The maximum amount Cedar should pay for monthly rent is 13,500.
We need to know the maximum amount of monthly rent cost to solve this problem. In this country, the department of housing and urban development has ruled that the maximum monthly rent cost is 30% of gross profit.
Max cost = 30% Gross
From the question above, the given parameter is
Gross profit = 45,000
By substituting the given parameter, the maximum monthly rent cost is
Max cost = 30% Gross
Max cost = 30% x 45,000
Max cost = 13,500
Hence, the monthly rent cost should have a maximum amount of 13,500.
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What is the expression in radical form?
(5ab) =
○ √√25a²b²
O√√5a²b²
O √5a³b3
O √125a³b3
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
What does radical form mean?Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
What in mathematics is radical form?The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions.
According to the given data:Radical equation = b[tex]\frac{m}{n}[/tex]
= [tex]\sqrt[n]{b^m}[/tex]
So,
(5ab)[tex]^\frac{3}{2}[/tex] = [tex]\sqrt[2]{5^3}[/tex]
[tex]\sqrt[2]{5^3}[/tex] a³ b³
5³ = 125
√(125 a³b³)
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
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quick question thx!!
What is the slope of the line that passes through the points (7, -4) and (11,−4)?
The slope of the linear equation is 0, so this is a horizontal line.
What is the slope of the line?
A linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we have the points (7, -4) and (11,−4), then the slope is:
a = (-4 + 4)/(11 - 7) = 0
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is 89.396668... a rational number
Answer: yes it is rational
Step-by-step explanation:
Answer: 89.396668... is a rational number
Step-by-step explanation:
Please help what is the answer???
is w a subspace of v? if not, state why. assume that v has the standard operations. (select all that apply.) w is the set of all 2 × 2 matrices of the form 0 v u 0 v = m2,2
A) W is a sub space of V
given that V =R^4 and W= [(x1, x2, x3, 0)|x1 ,x2, x3 E..R]
W is a subspace of V because of the following.
let (x1, x2, x3, 0), (y1, y2, y3, 0) ∈ W and a, b ∈ V
now
a(x1, x2, x3, 0)+b (y1, y2, y3, 0)= (a x1, a x2, a x3, 0)+(b y1, b y2,b y3, 0)
= (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)=
(a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)
LHS =RHS
∈W
since (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ) are all elements of R
W is closed under vector addition and scalar multiplication.
Hence W is a sub space of V.
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write the equation of the line that is parallel to the given line and goes through the point (-8 2)
The equation for the line that is parallel to the given line and goes through the point (-8 2), is y = 3x + 26. See the explanation below.
What is the explanation for the above?Recall that the equation for the line is always given as:
y = mx + b
Where m is the slope.
Assuming that you have a line y = 3x + 2
The line parallel to this line but intersecting the point (-8,2) is found by using y = mx + b and solving for b
m = 3; x = -8; and y = 2
b = y - mx
b = (2) - (3) (-8)
b = 26
Hence the equation for the line that is parallel to the given line going through point (-8, 2) is
y = 3x + 26
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Full Question:
Find the equation in slope-intercept form of the line y= 3x + 2 that passes through the point (-8,2) and is parallel to the line.
O skaters are racing toward the finish
race. The first skater has a 40 meter
d and is traveling at a rate of 12 meters
second. The second skater is travelin
ate of 14 meters
per
second. How long
it take for the second skater to pass
st skater?
The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.
What is the definition of time?Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.
Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.
12x+40=14x
40=2x
x=20
it will take 20 seconds for second skater to pass the first skater.
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Which is a counterexample of: The difference of two numbers is less than the greater
number.
(5)-(2) = 3
(-5)-(4) = -9
(3)-(3)=0
(2)-0 =2
The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"
How to determine the counterexample?"The difference of two numbers less than the greater number," is how the claim is expressed.
Give us x and y, where x is greater than y.
Thus, the statement can be interpreted as follows:
x - y < x
To both sides, add x.
-y < 2x
Replace with: y > -2x
This indicates that only when the smaller number is higher than twice the additive inverse of the larger number is the assertion true.
The smaller number must be bigger than twice the additive inverse of the larger number in order for the statement "the difference of two numbers is greater than the greater number" to be false.
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David is a nurse, he wants to buy an apartment near his sister. Apartments in her neighborhood cost around $120,000. The bank has approved him for a loan with an interest rate of 3.95%. David is a recent graduate and needs his monthly payment to be low, he can afford to pay about $550 a month. David plans to sell the apartment or refinance the loan within five years when he knows he will be earning more money. PLEASE HELP
Answer:
Describe how anthropology challenges more commonly held notions of progress
Step-by-step explanation:
Jasim works in a restaurant.
The table shown gives his rates of pay.
Day
Mon to Fri
Weekend
Jasim worked for a total of 30 hours last week.
He worked 12 of these hours at the weekend.
Work out Jasim's pay for last week.
Rate of pay
£8.70 per hour
£10.80 per hour
Answer:
Step-by-step explanation:
The option that is most suitable for tabular data will be provided by-
Jasim's last week's total pay was £286.2.
Describe tabular data.Tabular data is data presented in the form of rows and columns.
Here,
Total time for which Jasim works last week = 30 hours
Time for which Jasim works at the weekend = 12 hours
Time for which Jasim works at the weekdays = (30 - 12) hours
= 18 hours
Jasim's pay during weekdays = £8.70
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £8.70 [tex]\times[/tex] 18
= £156.6
Jasim's pay during weekends = £10.80
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £10.80 [tex]\times[/tex] 12
= £129.6
Total pay of Jasim for last week = £(156.6 + 129.6)
= £286.2
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A trapezium of area 140cm square has parallel sides 10cm apart and one of these 16m long. Find the length of the other parallel side
The length of the other parallel side = 7.5 cm
what is trapezium?
Trapezium is the quadrilateral whose only one pair of side is parallel.
as we know ;
AREA OF TRAPEZIUM=1/2*(sum of parallel side)*(height)
given:- one parallel side = 10 cm
height = 16 cm
Area= 140 cm
Assume:-
other parallel side =x cm
so,
140=1/2*(10+x)*16
140*2/16=10+x
280/16=10+x
35/2=10+x
17.5-10=x
x= 7.5cm
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Expand and simplify (y + 3)(y + 7)
⇒[tex]=(y+3)(y+7)\\=y(y+7)+3(y+7)\\=y^{2} +7y+3y+21\\=y^{2} +10y+21[/tex]
Attached is the solution in detail
Walt is mixing fruit punch for a party. He combines 1 gallon 2 quarts 3 pints of orange juice, 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. What's the total liquid measure of the punch? New answers Rating 3 emdjay23 1 gallon = 8 pints. 1 quart = 2 pints.
When Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.
As given in the question,
Conversion factor as follows:
1 gallon = 8 pints.
1 quart = 2 pints.
Walt is mixing fruit punch for a party
Convert all the units to pints we get,
Walt combines 1 gallon 2 quarts 3 pints of orange juice, which is equivalent to 15 pints
He also combines 1 gallon 3 quarts 7 pints of pineapple juice, which is equivalent to 21 pints
He then combines 1 gallon 3 quarts 3 pints of ginger ale, which is equivalent to 17 pints.
Total measure of the punch = 15 + 21 + 17 = 53 pints.
Therefore, when Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.
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please answer number 5 by finding the length indicated
Estimate the answer to 783 + 329 by rounding each number to the nearest hundred
Answer:
1100
Step-by-step explanation:
783 rounded to the nearest hundred is 800
329 rounded to the nearest hundred is 300
800+300=1100
The estimation of 783 + 329 = 1100.
What is Rounding off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
783 + 329
Now rounding off nearest hundred
783 rounded off to 800
and, 329 rounded off to 300.
So, 800+ 300 = 1100
Hence, the estimation is 1100.
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Domain and range, HELP!
The function is decreasing because it is going down.
The domain is the set of x-values, which is [tex]x \leq 4[/tex] or [tex](-\infty, 4][/tex].
The range is the set of y-values, which is [tex]-6 \leq y < -1[/tex] or [tex][-6, -1)[/tex].
3) Two rooms in a house need to be painted.
Each room can be painted either white or
yellow.
Answer:
Paint them white as it looks better
Step-by-step explanation:
Yellow is a very bad choice to paint a room
A landscape architect accrued $7,834.54 in credit card debt. If the architect makes a monthly payment of $500 (and makes no additional charges on the account), how many months will it take to repay the debt if the annual interest rate on the credit card is 18.6%? (Round your answer up to the nearest month.)
The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months
What is a monthly payment?Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]
Where;
M = The amount the landscape architect paid monthly = $500
P = The amount loaned or borrowed = $7,834.54
r = The interest per annum = 18.6%
n = The number of monthly payment made
Therefore;
[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]
Evaluating the above equation gives;
[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]
[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]
[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]
Which by taking natural logarithms of both sides gives;
n•ln(1.0155) = ln(1.32077843609)
n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09
Rounding up to the nearest month gives;
The number of months it will take the architect to pay the debt is approximately 19 months
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Esimate the value of 13 squared, between which two whole numbers
Answer:
168 and 170
Step-by-step explanation:
A scale drawing of a car is presented in the following three scales. Order thescale drawings from smallest to largest. Explain your reasoning. (There areabout 1.1 yards in a meter, and 2.54 cm in an inch.)A. 1 in to 1 ftB. 1 in to 1 mC. 1 in to 1 yd?
The smallest drawing will be the one that has the smallest drawing unit with respect to the the actual unit.
We have:
A. 1 in to 1 ft
B. 1 in to 1 m
C. 1 in to 1 yd
If we put them all in meters, we have:
A. 1 in to 0.3048 m
B. 1 in to 1 m
C. 1 in to 1/1.1 = 0.90... meters
Then, the small drawing will be B, as 1 meter is the largest actual unit.
Second, will be B, that has 1 in by approximately 0.9 meters.
Third and last, option A, which drawing has an scale of 1 in in 0.3048 meters.
We can calculate the scale as a ratio between the drawing units and actual units, expressed in the same units.
For example, for A, we have:
[tex]\frac{1\text{ in}}{1\text{ ft}}\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{12}[/tex]So the scale is 1:12.
NOTE: look that we have cancelled all the units with this operation.
For B, we have:
[tex]\frac{1\text{ in}}{1\text{ m}}\cdot(\frac{2.54\text{ cm}}{1\text{ in}})\cdot(\frac{1\text{ m}}{100\text{ cm}})=\frac{2.54}{100}=\frac{254}{10000}[/tex]For C, we have:
[tex]\frac{1\text{ in}}{1\text{ yd}}\cdot(\frac{1\text{ yd}}{3\text{ ft}})\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{36}[/tex]You can verify that B has the smallest scale (0.0254)