Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.
Series of transformation Matt can perform:
Reflection (Flip)
Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.
Rotations as a Transformation of Congruence
A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.
Congruence transformation through translation
When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.
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Related Questions
Please help me solve and show the steps so I could understand
Answers
Given polygon with sides 8 and radius 10yd.
Formula for area of ploygon
[tex]=n\times r^2\times tan\left(\frac{\pi}{n}\right)[/tex]So, solving further
[tex]\begin{gathered} =8\times10^2\times tan(\frac{\pi}{8}) \\ =800\times0.414 \\ =331.37 \end{gathered}[/tex]Hence, 331.37 yd square is the area of polygon.
The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:98.9 96.6 98.6 99.7 97 97.4 99.4Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidenceinterval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.98% C.I. -
Answers
Given the data temperatures to be;
[tex]98.9,96.6,98.6,99.7,97,97.4,99.4[/tex]We would require the following to get the 98% confidence interval of the mean body temperature.
Mean, Standard deviation, sample size, Probability of a confidence interval of 98%.
Using a calculator, we can get the mean to be
[tex]\text{(}\mu)=98.2285[/tex]The standard deviation would be derived to be;
[tex]\sigma=1.2230[/tex]The sample size can be gotten from the question to be;
[tex]n=7[/tex]The probability value of a 98% confidence interval is given to be 2.33
We can then derive the answer using the formula below;
[tex]\mu\pm z^x(\frac{\sigma}{\sqrt[]{n}})[/tex]We would substitute into the formula
[tex]\begin{gathered} \mu\pm z^x(\frac{\sigma}{\sqrt[]{n}}) \\ =98.2285+2.33(\frac{1.2230}{\sqrt[]{7}}) \\ =98.2285\pm1.0770 \\ =(97.152,99.306) \end{gathered}[/tex]ANSWER:
[tex](97.152,99.306)[/tex]What kind of transformation converts the graph of f(x) = -x - 10 into the graph of g(x)
-9x - 10?
horizontal stretch
vertical stretch
vertical shrink
horizontal shrink
=
Answers
Answer:
zeroay horizontal stretch vertical shrink
Step-by-step explanation:
1+1=2
Which equation is the correct translation of the following statement?Four less than a number is nine.9 - x = 49 - 4 = xx - 4 = 94 - x = 9
Answers
Given
The statement,
Four less than a number is nine.
To find:
Which equation is the correct translation of the following statement?
Explanation:
Let x be the number.
Since four less than a number is nine.
Then,
[tex]x-4=9[/tex]Hence, the correct statement is x-4=9.
2. Zandile invests her Christmas bonus for R 875.00 in a bank that offers
interest rates of 9% p.a. compounded half-yearly. How much interest will she
have earned after 6 years? I want the interest
Answers
After 6 years, Zandile earns an interest of rupees 608.9 after investing her Christmas bonus for R 875.00 in a bank that offers interest rates of 9% p.a. compounded half-yearly.
What is interest?The simplest way to calculate interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a friend with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5.
What is compound interest?Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The principal (original) sum and the interest that has already accrued over the course of previous periods are used to calculate compound interest.
Here,
Principal amount= 875
Rate of interest= 9% pa
Compounding= half-yearly (2/year)
Time= 6 years
A = P(1 + r/n)ⁿᵇ
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
b=number of time periods elapsed
A=875(1+9/6)⁶*²
A=₹1,483.90
Zandile invests her Christmas bonus of R 875.00 in a bank that offers interest rates of 9% per year compounded semi-annually, and after 6 years, she earns an interest of Rs 608.99.
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A table is on sale for 38% off. The sale price is $527.00.What is the regular price?
Answers
Given:
A table is on sale for 38% off, The sale price of table is $527.00.
To find:
The regular price of the table.
Step by step solution:
To solve this problem, we need to use the basic formula of sales price and discount:
Sale price = $527.00
Discount percentage= 38%
[tex]\begin{gathered} \text{sale price = cost price - discount }\times\text{ \lparen cost price \rparen} \\ \\ 527=cp-\frac{38}{100}(cp) \\ \\ 527=\frac{62}{100}(cp) \\ \\ cp=\frac{52,700}{62} \\ \\ cp=850 \end{gathered}[/tex]From here we can say that the Cost-price / Regular price of the table is equal to $850.
how to solve the problem “Compute 3'7 mod 7”
Answers
Given
[tex]3^7mod\text{ }7[/tex]Find
Compute the value of mod
Explanation
We have given
[tex]3^7mod\text{ }7[/tex]as we can rewrite it
[tex]\begin{gathered} 3^7mod\text{ 7} \\ 2187mod7 \\ \end{gathered}[/tex]here , we see dividend , a = 2187 and divisor , b = 7
we know ,
[tex]a\text{ mod b = a- \lparen int \lparen a/b\rparen}\times b\text{\rparen}[/tex]where int is a integer part of the value .
so ,
2187 mod 7 = 2187 -(Int (2187/7)*7)
2187 mod 7 = 2187 - 312 *7
2187 mod 7 = 2187 - 2184
2187 mod 7 = 3
Final Answer
Therefore , the value of 3^7 mod 7 = 3
you and three friends share a sushi boat at House of Kobe the cost of the boat is $50 you each also pay for a soft drink that is $2.39 what is the total cost of the meal after you pay 6% tax
Answers
ANSWER
$63.13
EXPLANATION
We have that the cost of the boat is $50.
Each of you and your friends (that is four of you) will pay for a soft drink that cost $2.39 each.
The cost of the soft drinks will therefore be:
4 * 2.39 = $9.56
Adding the cost of the boat, total cost will be:
$9.56 + $50 = $59.56
Now, we have to add a tax of 6%, so we find 6% of total cost:
[tex]\frac{6}{100}\cdot\text{ 59.56 = \$3.57}[/tex]Finally, add the tax to the cost:
$59.56 + $3.57
= $63.13
You pay a total of $63.13 (including tax)
Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
Answers
Answer: its not correct because the got different perenties or groupings and they mean different meaning
Step-by-step explanation:
3300 dollars is placed in an account with an annual interest rate of 6.75%. To
the nearest tenth of a year, how long will it take for the account value to reach
10700 dollars?
Answers
The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The simple interest formula is equal to
A = P(1+r t)
where, A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
P = $ 3300
A = $ 10700
r = 6.75 % = 6.75 / 100 = 0.0675
substitute in the formula above
$10700 = 3300(1+0.0675 t)
simplifying the above equation, we get
Divide both sides by 3300
[tex]$\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$[/tex]
Simplifying the above equation, we get
[tex]$1+0.0675 t=\frac{107}{33}$$[/tex]
Subtract 1 from both sides
[tex]$1+0.0675 t-1=\frac{107}{33}-1$$[/tex]
Simplifying the above equation, we get
[tex]$0.0675 t=\frac{74}{33}$$[/tex]
Divide both sides by 0.0675
[tex]$\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}[/tex]
[tex]$t=\frac{74}{2.2275}$[/tex]
t = 33.2210 years
Therefore, the value of t exists 33.2210 years.
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Factor: x^6-5x^4-5+x
Answers
The value of the expression x^6 -5x^4 - 5 + x when simplified is x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as
Factor: x^6 -5x^4 - 5 + x
From the above expression, we have
x^6 -5x^4 - 5 + x
Group the expression in two'2
So, we have
x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)
Factorize each group of the expression
So, we have
x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)
The above expression cannot be further simplified
Hence, the value of x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)
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I need help please 5. Find the distance between C (-5, 4) and Q (2,0). A. 22 B. 33 C. 53 D. 65
Answers
Given the two points:
C (-5, 4) and Q (2, 0)
To find the distance, use the distance formula below:
[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,
(x1, y1) = (-5, 4)
(x2, y2) = (2, 0)
Therefore, we have:
[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]Explain how you can use an array to find partial products for 4x36.
Answers
Answer:
(4 x 30) +(4 x6)
120 + 24
144
Step-by-step explanation:
Use a model to divide. 2/5÷4 Express the answer in simplest terms.
Answers
so the equation si:
[tex]\frac{\frac{2}{5}}{4}[/tex]This is equal to:
[tex]\frac{2}{20}=\frac{1}{10}[/tex]Finally:
[tex]\frac{1}{10}=0.1[/tex]Find the x-intercept and y- intercept of the function f(x) = (2x + 3)/(x ^ 2 + 3)can u draw the function of f(x) = (2x + 3)/(x ^ 2 + 3)?Need solution ^^
Answers
Answer:
• x-intercept: (-1.5, 0).
,• y-intercept: (0, 1).
Explanation:
Given the function:
[tex]f(x)=\frac{2x+3}{x^2+3}[/tex](a)x-intercept
The x-intercept is the value of x at which f(x)=0.
When f(x)=0
[tex]\begin{gathered} \frac{2x+3}{x^2+3}=0 \\ \text{ Cross multiply} \\ 2x+3=0 \\ \text{ Subtract 3 from both sides of the equation} \\ 2x+3-3=0-3 \\ 2x=-3 \\ \text{ Divide both sides of the equation by 2} \\ \frac{2x}{2}=-\frac{3}{2} \\ x=-1.5 \end{gathered}[/tex]The x-intercept is located at (-1.5, 0).
(b)y-intercept
The y-intercept is the value of f(x) at which x=0.
When x=0
[tex]\begin{gathered} f(x)=\frac{2x+3}{x^2+3} \\ f(x)=\frac{3}{3} \\ f(x)=1 \end{gathered}[/tex]The y-intercept is at (0, 1).
(c)Graph
The graph of f(x) is given below:
Please help me solve: Part CA sign in a freight elevator states that the maximum capacity of the elevator is 2,500 pounds. Use the average weight of a box as 75 pounds and the average weight of a crate as 160 pounds to complete the following parts.If there are 13 average-weight boxes on the elevator, what is the maximum number of average-weight crates that can also be on the elevator given its maximum capacity? Please explain.
Answers
Let
x ----> number of average-weight crates
so
we have that
[tex]75(13)+160x\leq2,500[/tex]solve for x
[tex]\begin{gathered} 975+160x\leq2,500 \\ 160x\leq2,500-975 \\ 160x\leq1,525 \\ x\leq9.53 \end{gathered}[/tex]therefore
the maximum number of average-weight crates is 9An item is regularly priced at $50. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?Amount discounted: sX5?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
regular price = $50
discount = 40% = 0.4
Step 02:
amount discounted:
amount discounted = regular price * discount
amount discounted = $50 * 0.4 = $20
The answer is:
$20
The sum is the measure of three angles of a triangle is 180 degrees. In a triangle, the measures of an angle are x,x+12 and x-48. What is the measure of each angle?
Answers
Answer:
24° , 72° , 84°
Step-by-step explanation:
sum the 3 angles and equate to 180 , that is
x + x + 12 + x - 48 = 180
3x - 36 = 180 ( add 36 to both sides )
3x = 216 ( divide both sides by 3 )
x = 72
Then the measure of the 3 angles are
x = 72°
x + 12 = 72 + 12 = 84°
x - 48 = 72 - 48 = 24°
A falling object travels a distance given by the formula d = 4t + 6t?, where d is measured in feet and t is measured in seconds.
How many seconds will it take for the object to travel 68 feet? Round the answer to 4 decimal places.
Answers
If a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
The formula of the object traveling a distance d = 4t + [tex]6t^{2}[/tex]
Where d is the distance traveled in feet
t is the time taken in seconds
Here
The distance traveled = 68 feet
Therefore the equation will be
68 = 4t + [tex]6t^{2}[/tex]
[tex]6t^{2} +4t-68=0[/tex]
We have to solve quadratic equation [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
a = 6
b = 4
c = -68
Substitute the values in the equation
= [tex]\frac{-4+/-\sqrt{4^2-(4)(6)(-68)} }{(2)(6)}[/tex]
= [tex]\frac{-4+/-\sqrt{1648} }{12}[/tex]
t = [tex]\frac{-1+/-\sqrt{103} }{3}[/tex]
We take only positive value
t = [tex]\frac{-1+\sqrt{103} }{3}[/tex]
t = 3.0496 seconds
Hence, if a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
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1. The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?
Answers
To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.
P = (8,533/68,811)* 100
P = 12.400, the nearest hundredth of a percent is 12.
11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus. so we need to find percentage 12 for 11690000.
(11690000* 12) / 100
1402800 is the number of people who would test positive for the virus
P(6, -3); y = x + 2
Write an equation for the line in point-slope form.
Answers
The equation of the line by using slope value is: y = x -9
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Equation of a line = x + 2 and the coordinate points = (6, -3): (x = 6; y = -3)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ -3 = (1)(6) + c
⇒ c = -3 - 6 = -9
Therefore, the value of the y-intercept is: c = (-9)
equation of the line by substituting the value of the y-intercept as well as slope value:
y = (1)x + (-9) = y = x -9
Hence, the equation of the line by using slope value is: y = x -9
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Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
Answers
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]Christina made 4 three-point shots and 5 two-point shots in her basketball game. How many points (p) did she score?
Answers
The total points Christina made is as follows:
[tex]T=4\cdot3+5\cdot2=12+10=22[/tex]Then, Christina scored 22 points.
If f(x) = 5x + 40, what is f(x) when x = -5?
Answers
we have the following:
[tex]f\mleft(x\mright)=5x+40[/tex]replacing, x = -5
[tex]\begin{gathered} f(-5)=5\cdot-5+40 \\ =-25+40 \\ =15 \end{gathered}[/tex]The answer is 15
The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle
Answers
The area of the triangle with base 12 units, and height of 3 units is: B. 18.
How to Determine the Area of a Triangle?To find the area of a triangle, find the height, which is the distance from its base to its highest point, and also find the length of the base of the triangle, then apply the formula below:
Area of triangle = 1/2 × base × height
From the information given, the following are the parameters we will need to work with:
Base of the triangle = QR = 12 units
Height of the triangle = PH = 3 units
Plug in the values
Area of triangle = 1/2 × 12 × 3
Area of triangle = 36/3
Area of triangle = 18 units
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Let p: The shape is a rhombus.
Let q: The diagonals are perpendicular.
Let r: The sides are congruent.
Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?
p ∧ (q ∧ r)
(p ∨ q) ∨ r
p ↔ (q ∧ r)
(p ∨ q) ↔ r
Answers
The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
What is Logic operators?
A symbol or words to use to connect two or more expressions are called Logic operators.
Given that;
The statement is,
''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent''
Now,
Since, The word ''if and only if'' is represent by using the biconditional logic operator (↔) and the word ''and'' is represented by using the logical conjunction operator (∧).
So, The logic representation of the statement;
"The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” will be;
⇒ p ↔ (q ∧ r).
Thus, The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
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Solve this inequality for the y variable: 6x-9y> 12 u y GON 4 3 2 4 O ya 3 2. 4 ys vs - 2 x + 2
Answers
We solve the inequality as follows:
[tex]6x-9y>12\Rightarrow-9y>-6x+12[/tex][tex]\Rightarrow y<\frac{2}{3}x-\frac{4}{3}[/tex]On the graph below, which dotted line represents a reflection across the x-axis of the red-solid-line graph?5 stars for quicknessplease look at png 1 is question 2 is answer
Answers
Hello!
The rule for a reflection across the x-axis is:
[tex](x,y)=(x,-y)[/tex]Knowing it, let's write some points that the red line passes through:
(-2, 0) and (0, 4).
Now, let's use this rule and change the sign of the y coordinate:
• (-2, 0) → (-2, 0) because +0 or -0 doesn't exist.
,• (0, 4) → (0, -4)
Let's analyze it and find a line that passes through these two points:
(-2, 0) and (0, -4)
It will be the blue line.
help meeeeeee pleaseee !!!!
Answers
The linear function that passes through the two points (-6, -2) and (-9, -1) is defined by the rule:
y = -(1/3)*x - 4
How to find the linear function with the given points?The general linear function in the slope-intercept form:
y = m*x + k
Where m is the slope (also called rate of change) and k is the intercept of the y-axis.
If we know that the line passes through two points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
So with only two points, we can find the slope.
In this case, the line passes through the points (-6, -2) and (-9, -1) , then the slope is:
m = (-1 +2)/(-9 + 6) = 1/-3 = -1/3
Then the slope is m = -1/3
So the linear function is something like:
y = (-1/3)*x + k
To find the value of k i will use the pint (-9, -1), replacing these values we get:
-1 = -(1/3)*-9 + k
-1 = 3 + k
-1 - 3 = k
-4 = k
So the linear function that passes through these points is:
y = -(1/3)*x - 4
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Which fraction is the smallest?8/9, 9/10, 11/12, 12/13
Answers
Given:
[tex]\frac{8}{9},\frac{9}{10},\frac{11}{12},\frac{12}{13}[/tex][tex]\frac{8}{9}=0.8889[/tex][tex]\frac{9}{10}=0.9[/tex][tex]\frac{11}{12}=0.9167[/tex][tex]\frac{12}{13}=0.9231[/tex][tex]\frac{8}{9}\text{ is the smallest fraction.}[/tex]