The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
A(x₁,y₁) = (-8,4)
B(x₂,y₂) = (-1,3)
C(x, y ) = (x ,0)
equation of a line is given as:
y - y₁ = (y₂ - y₁)/ (x₂ - y₁) (x - x₁)
y - 4 = (3 - 4)/(-1 + 8)(x + 8)
y - 4 = -1/7(x + 8)
7(y - 4) = -1(x + 8)
7y - 28 = -x + 8
x + 7y - 36 = 0
when y = 0 then the value of x is given as:
x + 7y- 36 = 0
x + 7(0) - 36 = 0
x = 36
point C on the x-axis (x , 0) = (36,0)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
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The lengths of the three sides of a triangle (in feet) are consecutive even integers. If the perimeter is 60 feet, find the value of the shortest of the three side lengths.
Step-by-step explanation:
3 consecutive even integer numbers :
x
x + 2
x + 4
their sum is the perimeter : 60 ft.
x + x + 2 + x + 4 = 60
3x + 6 = 60
3x = 54
x = 18
the shortest of the 3 sides is 18 ft.
and then we have the other 2 sides with 20 and 22 ft.
Can anyone please help me I would really appreciate it a lot
Using the geometric mean theorem,
[tex]\frac{y}{14.4}=\frac{14.4}{19.2} \\ \\ y=10.8[/tex]
Using Pythagoras on triangle [tex]ABD[/tex],
[tex]x=\sqrt{14.4^2+10.8^2}=18[/tex]
Triangles [tex]ABD[/tex] and [ted]CBD[/tex] are similar because corresponding angles are congruent and pairs of corresponding sides have proportional lengths.
To determine this, use the complementary angles.
what is the equation of the line in point slope form that contains the point (-2,5) and has a slope of 1/3?
Have an answer I got already, wanting to check and see if its correct :) thank you in advance
An equation of the line in point-slope form that contains the point (-2, 5) and has a slope of 1/3 is y - 5 = 1/3(x + 2).
What is the point-slope form?In Mathematics, the point-slope form can be defined as a type of equation that is typically used when the slope of a straight line and one of the points on this line is given (known).
Mathematically, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 5 = 1/3(x - (-2))
y - 5 = 1/3(x + 2)
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Five thousand dollars is deposited into an ordinary annuity after each quarter for 3 years. The account pays 6
percent interest compounded quarterly. What is the future value of the account in 3 years?
The future value of the account in 3 years is $15,918.
What is a future value?
The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.
Here, we have
FV =C×[ ((1+i)ⁿ −1)/i]
where:
C = cash flow per period
i = interest rate
n = number of payments
By applying the future value formula, we get
= $5,000×[ ((1+0.06)³ −1)/0.06 ]
= $5,000×3.1836
= $15,918
Hence, the future value of the account in 3 years is $15,918.
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Based on problems 1-3, what can you conclude about
triangle ABC's orthocenter if x is less than 90°?
What happens to the orthocenter as x increases towards 90°?
What happens to the orthocenter as x reaches 90°?
What happens to the orthocenter as x increases to larger than 90°?
Answer:
Step-by-step explanation:
smaller
larger
bigger
larger
Prove that
cos 2A/cos A-sin A
= cos A + sin A
The value of cos 2A/cos A-sin A = cos A + sin A is proved
cos 2A = 2cos²A - 1
= 2cos²A - (sin²A + cos²A)
= 2cos²A - sin²A - cos²A
= cos²A - sin²A
We need to prove that
cos 2A/cos A-sin A = cos A + sin A
L.H.S
cos 2A/cos A-sin A
= cos²A - sin²A/ cos A-sin A
= (cos A + sin A)(cos A-sin A)/ cos A-sin A
= cos A + sin A
R.H.S
LHS = RHS proved
Therefore, cos 2A/cos A-sin A = cos A + sin A is proved
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what is -112 = -7(v + 4) ?
Answer:
Step-by-step explanation:
1.) -112*-7=784
784=v+4
2.)784-4=780
v=780
Answer:
v = 12
Step-by-step explanation:
-112 = -7v -28
7v = 112 - 28
7v = 84
7/7 v = 84/7
v = 12
Write a detailed equation in slope-intercept form for the line that passes through (3,1) and (1,2).
25 points
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}[/tex]
What is the slope of the points (19, -2), (-11, 10)?
Answer:
-2/5
Step-by-step explanation:
the slope is change in y over change in x
formula for slope is
(y2-y1)/(x2-x1), so if you input the coordinates, (10-(-2))/(-11-19) = 12/30 = 2/5
If you double a number and then add 32,you get 2/9of the original number. What is the original number?
Answer:
- 18
Step-by-step explanation:
let the number be n then double the number is 2n and
2n + 32 = [tex]\frac{2}{9}[/tex] n
multiply through by 9 to clear the fraction
18n + 288 = 2n ( subtract 2n from both sides )
16n + 288 = 0 ( subtract 188 from both sides )
16n = - 288 ( divide both sides by 16 )
n = - 18
the original number is - 18
Help! I’m so confused
The measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
First, let us understand the types of angles formed by parallel and transversal lines:
Corresponding Angles — Corresponding angles are angles on the same side of a transversal that are either above or below the lines.
Alternate Interior Angles - Alternate interior angles are the pairs of interior angles on opposing sides of the transversal.
Alternate Exterior Angles - Alternate exterior angles are the pairs of exterior angles on opposing sides of the transversal.
Consecutive interior angles - Internal angles on the same side of a transversal are also known as consecutive interior angles, related angles, or co-interior angles.
We are given:
∠2 is 48 degrees and ∠3 is 62 degrees.
We need to find the ∠5.
From the given figure we can see that;
∠3 and ∠5 are alternate interior angles.
So, ∠3 = ∠5 = 62 degrees.
So, the measure of ∠5 is 62 degrees.
Thus, the measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
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If India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate. What is her hourly overtime rate?
factorise fully 15x³ + 3x²y
Answer: 3x²(5x+y)
Step-by-step explanation:
15x³ + 3x²y
Apply exponent rule: 15x²x+3x²y
Rewrite 15 as 5*3: 5*3x²x+3x²y
Factor out common terms 3x²: 3x²(5x+y)
Hope this helps!!! :)
a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = -1.11.
b) The p-value is: 0.1342.
c) The conclusion is that the null hypothesis is not rejected.
d) The final conclusion is that there is not sufficient evidence to conclude that the population mean is of 6.
What is the test statistic?The standard deviation for the population is unknown, only the sample standard deviation is known, hence the t-distribution is obtain the test statistic.
The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the variables of the equation are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.For this problem, the values of these parameters are as follows:
[tex]\overline{x} = 5.83, \mu = 6, s = 2.11, n = 189[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{5.83 - 6}{\frac{2.11}{\sqrt{189}}}[/tex]
t = -1.11.
P-value and conclusionThe p-value is obtained using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less a value, with 189 - 1 = 188 df and t = -1.11, hence it is of 0.1342.
Since the p-value is greater than the significance level of 0.10, it is found that:
The null hypothesis is not rejected.There is not sufficient evidence to conclude that the population mean rating is less than 6.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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what is 20 x4 please i need a answer quickly
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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1. research institute reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 50 unemployed individuals for a follow-up study.
a. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean of less than 1 week?
b. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean?
The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:
X = N(17.5)
Where μ = 17.5 and σ = 4
Since the distribution for X is normal then, the distribution for the sample mean is given by:
X = N(17.5, σ/√n)
X =N(17.5.4/√50) = 0.566
We select a sample of n =50 people. And we want to find the following probability
P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )
And using the normal standard table or excel we find the probability:
P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92
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Solve for x.
giving 20 points for the right answer
Answer:
m∠D = 54°
Step-by-step explanation:
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the measures of an interior angle and its corresponding exterior angle is 180°.
With this knowledge, we can construct the equation:
50° + (3x + 18)° + (180 - (8 + 8x))° = 180°
and solve for x.
50° + (3x + 18)° + (180 - 8 - 8x)° = 180°
(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°
240° - 5x° = 180°
5x° = 240° - 180°
5x° = 60°
x° = 12°
Now, we can solve for m∠D by plugging in the x value that we solved for.
m∠D = (3x + 18)°
m∠D = 3(12)° + 18°
m∠D = 36° + 18°
m∠D = 54°
measure the diameter of 1 rupee coin 2 rupee coin and Rs 5 coin find their circumference
(not suppose)
A road has a speed limit sign at the beginning that is noticed by 84 % of people. 95 % of people who didn't notice the sign speed on the road. Of those who notice the sign, 75 % follow the speed limit.
How many percent of people speeding on this road noticed the sign? In other words, how many people on this road speed on purpose. Give your answer in percentage.
The percentage of people over speeding on this road on purpose is 9%
Find the percent of people speeding on this road who noticed the signPercentage of people who notice the speed limit at the beginning of the road = 84%Percentage of people who didn't notice the sign = 95%Percentage of people who notice the sign and follow the speed limit = 75%Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit
= 84% - 75%
= 9%
In conclusion, the percentage of people who intentionally speed on purpose is 9%
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What is the angle θ in the triangle below?
Answer:
θ = 64.98310506 degrees (65 degrees rounded to unit)
Step-by-step explanation:
4.2 * tanθ = 9
4.2 * tanθ/ 4.2 = 9/4.2
tanθ = 2.142857
θ = arctan 2.142857
θ = 64.98310506
Step-by-step explanation:
using the SOH CAH TOA Rule,
tan 0=opp÷adj
tan 0=9÷4.2
tan 0=2.14
0=tan inverse of 2.14
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The standard equation of a circle is:
[tex]x^{2} +y^{2} +2gx+2fy+c=0[/tex]
Given circle equation:
[tex]x^{2} +y^{2} -2x-8=0[/tex]
on comparing
2gx = -2x
g = -2
2fy = 0
f = 0
Center = (2,0)
radius r = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]
= [tex]\sqrt{9}[/tex]
r = 3 units.
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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The amount of Jerry's pay every week before taxes, J, is given below as a function of the number of overtime hours that he works (the number of hours over 40), h.
J = $493.60 + $18.51h
Assuming that Jerry is only paid for each whole hour that he works, how many total hours would Jerry have to work during a week to make at least $700.00?
A. 51
B. 52
C. 62
D. 11
The total number of hours that Jerry would work during a week to make at least $700.00 is 11 hours
How to determine number of hours that Jerry would workinformation given in the query
The amount of Jerry's pay every week before taxes, J,
a function of the number of overtime hours that he works (the number of hours over 40), h
J = $493.60 + $18.51h
The given equation is an equation of linear function
considering the equation J = $493.60 + $18.51h, the number of hours that Jerry would work is gotten by substituting the value of $700.00 and solving for number of hours
J = $493.60 + $18.51h
700 = 493.60 + 18.5h
18.5h = 700 - 493.60
18.5h = 206.4
h = 11.16
h = 11 hours
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Write a proof for the statement.
If a quadrilateral is a square, then the quadrilateral is a rectangle.
Proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.
Explain quadrilaterals.A quadrilateral is a closed shape created by uniting four points, any three of which cannot be collinear. Four sides, four angles, and four vertices make up a quadrilateral.
Quadrilaterals have a few characteristics. The list is as follows.
Each side has four sides.
Each of them has four vertices.
Two diagonals are present.
360 degrees is the sum of all interior angles.
Given, to prove if a quadrilateral is a square, then the quadrilateral is a rectangle.
The Square has four equal sides, and all four angles are right-angled.
Rectangle has equal opposite sides, and all four angles are the right angle.
Here, the two sides of the square can be increased to form a rectangle.
Hence, proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.
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Alton estimated that 260 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error.
The percent of error concerning Alton's estimated attendance and actual attendance at the band concert is 30%.
What is the percentage of error?The percent of error is a measure showing how big an error is between the estimate and actual results.
The smaller the percent of error the closer the estimate is to the actual observations, and vice versa.
Actual Observed Value = 200
Expected Value = 260
Percentage of error = (Expected Value - Observed Value) ÷ Actual Value
= (260 - 200)/200
= 60/200
= 0.3
= 30%
Thus, we can conclude that Alton made a 30% error in his estimate of attendance at the band concert.
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there are 121 boys and 116 girls signed up for a trip to an amusement park the leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students how many groups of 10 students will there be explained and how many groups of nine students will there be explained
By using addition, subtraction, multiplication and division of integers,
it can be calculated that
There are 3 groups of 9 and 21 groups of 10
What is addition, subtraction, multiplication and division of integers?
Addition of integers is used to find the sum total of two or more integers.
Subtraction of integers is used find the difference between two integers.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
Division is the process in which the value of single unit can be calculated from the value of multiple unit
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here, addition, subtraction, multiplication and division of integers will be used
Total number of boys = 121
Total number of girls = 116
Total number of students = 121 + 116 = 237
Now,
The leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students
So the group of 9 is to be made in such a way that on multiplying the number by 9, unit digit of 7 is obtained
So the number is 3 as 9 [tex]\times[/tex] 3 = 27
Remaining number of students = 237 - 21 = 210
They will enter into a group of 10
Number of group of 10 = 210[tex]\div[/tex] 10 = 21
There are 3 groups of 9 and 21 groups of 10
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5 lily pads are found in a pond. Thirty days later, there are 16 lily pads. Find the exponential growth
model, L(t) = Aekt for the lily pad colony. Enter your answers as expressions or numbers rounded to four
decimal places.
A =
k=
The exponential model for the lily pad colony is L(t) = A[tex](1+r)^{kt}[/tex] and the values of A=5 and k=1.2.
What is meant by exponential growth?Over time, anything grows in quantity through an exponential growth process. When a quantity's rate of change over time (or derivative) is proportional to the quantity itself, this phenomenon takes place. A number that is increasing exponentially is referred to as a function, and the exponent, which stands for time, is the variable that represents time (in contrast to other types of growth, such as quadratic growth).
When a quantity decrements with time, it is considered to be experiencing exponential decay rather than a positive constant of proportionality. It is also known as geometric growth or geometric decay when the definition's discrete domain has equal intervals since the values of the function form a geometric progression.
Given, there are 5 lily pads that are found in a pond
And after 30 days, there are 16 lily pads in that pond
Here, a=5
r=(11-5)/5=1.2
f(x)=a(1+r)ˣ
f(x)=5(1+1.2)³⁰
From the above equation, A=5, and k=1.2
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William plans on buying the new Callaway Rogue Max ST driver for at least $550 He already has $325 saved and earns $20 each time he details his parents car. Write and solve an inequality to determine the number of times he must detail his parents car to have enough money to buy the golf club.
William needs to detail his parents at least 12 times to buy the golf club.
What is Inequality:An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
The symbols we use in Inequality Expressions are
Not equal ' ≠ '
Greater than ' > '
Less than ' < '
Less than or equal ' ≤ '
Greater than or equal ' ≥'
Here we have
William plans to buy the new Callaway Rogue for at least $ 550
The amount that William saved = $ 325
The amount he earns each time he details his parents = $ 20
Here we don't know how many times he detailed his parents,
So represent it with a variable x
After detailing x times the amount he earned will equal $ 20x
The total amount that William will have = $ 325 + $ 20x
William wants at least $550
Therefore,
The inequality that will represent the above situation is
=> 325 + 20x ≥ 550 ------(1)
Now solve the above inequality to get the value of x
=> 65 + 4x ≥ 110
=> 4x ≥ 45
=> x ≥ 11.25
Here we can say 11.25 times so x = 12 times
Therefore,
William needs to detail his parents at least 12 times to buy the golf club.
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A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 1450 downloads of the song, for a total download size of 5629 MB. How many downloads of the standard version were there?
The number of downloads that were standard version were 560 songs.
How many downloads of the standard version were there?The first step is to form a system of equations:
2.9s + 4.5h = 5629 equation 1
s + h = 1450 equation 2
Where:
s = number of standard songs downloaded h = number of high quality songs downloadedMultiply equation 2 by 4.5:
4.5s + 4.5h = 6525 equation 3
Subtract equation 3 from equation 1:
896 = 1.6s
Divide both sides of the equation by 1.6:
s = 560
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Riley wants to find the smallest of the fractions One-sixth, Eleven-twelfths, Five-sixths, and Ten-twelfths. She uses 0 and 1 as benchmarks. Which fraction is closest to 0?
Answer: 1/6
Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.