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We can find the image of point C reflected across line n by finding the distance d (perpendicular) from point C to line n, and then placing point C', the image, at an equal and perpendicular distance d on the other side of the line.
We can graph this as:
Related Questions
question 13Consider the following data: 12, 15, 13, 10, 15, 10. Answer the following questicwrite final answers only. [T/I - 4]#1) What is the mean of the data?#2) What is the median of the data?#3) What is the mode of the data?#4) What is the range of the data?
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Solution:
Given:
The data;
[tex]12,15,13,10,15,10[/tex]Question 1:
To get the mean:
The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.
[tex]\begin{gathered} \text{Mean}=\frac{\text{ sum of data}}{n\text{ umber of data}} \\ \text{Mean}=\frac{12+15+13+10+15+10}{6} \\ \text{Mean}=\frac{75}{6} \\ \text{Mean}=12.5 \end{gathered}[/tex]Therefore, the mean is 12.5
Question 2:
To get the median:
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest)
If there is an even number of data, the median is the average of the middle two numbers.
[tex]\begin{gathered} R\text{ earranging the data given in rank order,} \\ 10,10,12,13,15,15 \end{gathered}[/tex]
The data indicates an even number of data. There are 6 numbers in the set.
Hence, the median is the mean of the middle two numbers.
[tex]\begin{gathered} \text{The middle two numbers are;} \\ 12\text{ and 13} \\ \text{Hence, the median is the mean of 12 and 13} \\ \text{Median}=\frac{12+13}{2} \\ \text{Median}=\frac{25}{2} \\ \text{Median}=12.5 \end{gathered}[/tex]Therefore, the median is 12.5
Question 3:
To find the mode:
The mode of a set of numbers is the number that occurs the most. Hence, the mode of a set of numbers is the number with the highest frequency.
If a set of data has two modes, the data is said to be bimodal.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \\ \text{From the above, 10 appears twice} \\ 15\text{ also appears twice} \\ \\ \text{Hence, the mode is 10 and 15. The data has two modes, it is a bimodal data.} \end{gathered}[/tex]
Therefore, the modes are 10 and 15.
Question 4:
The range is the difference between the highest and lowest values in a set of numbers.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \text{Lowest number=10} \\ \text{Highest number=15} \\ \\ \text{Hence, range=highest number-lowest number} \\ \text{Range}=15-10 \\ \text{Range}=5 \end{gathered}[/tex]Therefore, the range is 5.
The slope of the line below is 2 Write the point-slope equation of the line using the coordinates of the labeled point.
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As per given by the question,
there are given that,
The slope of the line is 2, and the point is (3, 10).
Now,
For finding the point slope equation;
From the formula for point slope equation of the line,
[tex]y-y_1=m(x-x_1)[/tex]Here,
[tex]x_1=3,y_1=10,\text{ and m=2}[/tex]Then put the value in above formula,
[tex]undefined[/tex]From the waiting area, they walked another 0.1 miles to board the plane. The plane left the gate 45 min after they arrived at the waiting area. Part C: what was the length from the waiting area to the airplanes takeoff?
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C) We have to calculate the distance from the waiting area to the plane.
From the waiting area they walked 0.1 miles to board the plane.
Answer: from the waiting area to the plane there is a distance of 0.1 miles.
The Quadratic f(x)=x^2-2x-15Using the functions of your graphing calculator calculate the coordinates of the following points (as shown in the calculator videos in this lesson). If the parabola doesn't intersect the x-axis then write "none." If necessary, round to the nearest hundredths place (2 decimal places).a. The vertex using the min/max calculate function.b. X-intercept(s) using the zero calculate function.c. Y-intercept using the value calculate function (w/ a value of x=0).d. Now, copy down the t-table generated by your calculator for integer input values from-3≤x≤3.
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Given: The function below
[tex]f(x)=x^2-2x-15[/tex]To Determine: The vertex, the x-intercept, the y-intercept, and the table for -3≤x≤3
Solution
The graph of the given function is as shown below
Hence:
The vertex is a minimum value at y = -16 and coordinate (1, -16)
(b) The X-intercepets is x = -3, x = 5, coordinates: (-3, 0) and (5, 0)
(c) The Y-intercept is at y = -15, coordinate: (0, - 15)
(d) The table showing the values of f(x) for -3≤x≤3 is as shown below
Can you pls help me with this question thank you
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The Solution:
The difference of c and 7 is either:
[tex]\begin{gathered} c-7\text{ } \\ \text{ or} \\ 7-c \end{gathered}[/tex]Multiplying the result by 10, we get
[tex]\begin{gathered} 10(c-7) \\ \text{ or} \\ 10(7-c) \end{gathered}[/tex]We are asked not to simplify any part of the expression.
So, the correct answer is:
[tex]\begin{gathered} 10(c-7) \\ or \\ 10(7-c) \end{gathered}[/tex]
help me havig a hard time .
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What is the conversion factor?
It is a number used to change one unit to another when it is multiplied.
Jenna wants to know how many pounds correspond to 50 tons, she does know that 1 ton = 2,000lb. Then she has the following equivalence:
50 tons ⇄ ??
1 ton ⇄ 2,000 lb
We know that if we divide both sides of the equivalence we will have the same result:
[tex]\frac{50\text{tons}}{1\text{ton}}=\frac{?\text{?}}{2000lb}[/tex]Multiplying both sides by 2000lb we have that
[tex]undefined[/tex]what is the quotient of {24a^4 b^2 + 36a^2 b-36ab^2 +48 ab}÷(12ab)?
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To divide this polynomial, we will follow steps below:
Step 1
Arrange
step 2
Divide 24a⁴b² by by 12ab
The result will be 2a³b
Write the result at the top of the root sign
Step 3
Mutiply 12ab by 2a³b, the result will be 24a⁴b²
Write the result in the root sign under 24a⁴b²
step 4
subtract, the result is zero
step 5
Take down 36a²b
Step 6
divide 36a²b by 12ab
The result is 3a
write the result at the top of the root sign
step 7
Multiply 12ab by 3a
The result is 36a²b
Write the result in the root sign under 36a²b
Step8
subtract, the result is 0
step 9
Take down -36ab²
step10
Divide -36ab² by 12ab
The result is -3b
Write the result at the top of the root sign
step11
Multiply 12ab by -3b
The result is -36ab²
Write the result in the root sign under -36ab²
step12
subtract, the result is zero
step 13
Take down 48ab
step 14
divide 48ab by 12 ab
The result is 4
write the result at the top root sign
step 15
Mulltiply 12ab by 4
The result is 48ab
Write the result in the root sign under 48 ab and then subtract
The result is zero
Hence the quotient is : 2a³b + 3a -3b + 4
Question 8 of 10Which of these is a geometric sequence?O A. 2, 3, 5, 9, 17,...O B. 5, 2, 3, 4, ...O C. 2, 4, 6, 8, 10, ...
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We have that in a geometric sequence, the common ratio are equal in geometric sequence, this is:
[tex]\frac{second\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{second\text{ term}}[/tex]Next, check options:
A. 2, 3, 5, 9, 17
Common ratio
[tex]undefined[/tex]X = y - 4-2x + 3y= 6Solve each system by equation
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Answer: x=-6 and y=-2
Given:
[tex]\begin{gathered} x=y-4 \\ -2x+3y=6 \end{gathered}[/tex]Having these two equations, we can substitute the first equation with the second equation to solve for y:
[tex]\begin{gathered} -2x+3y=6 \\ \end{gathered}[/tex]Since the first equation says that x = y - 4,
[tex]\begin{gathered} -2x+3y=6 \\ -2(y-4)+3y=6 \\ -2y+8+3y=6 \\ -2y+3y=6-8 \\ y=-2 \end{gathered}[/tex]Then, we will substitute this y-value to the first equation to solve for x.
[tex]\begin{gathered} x=y-4 \\ x=-2-4 \\ x=-6 \end{gathered}[/tex]We now have the values x=-6 and y=-2. To check, let us substitute both values to the second equation
[tex]\begin{gathered} -2x+3y=6 \\ -2(-6)+3(-2)=6 \\ 12-6=6 \\ 6=6 \end{gathered}[/tex]Therefore, the answer is correct, and the answer is x=-6 and y=-2
Please Help! Functions and Relations The graph shows the absolute value parent function. which statement best describes the function?
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The function is increasing when, if xa > xb, then f(xa) > f(b).
Let's choose values for x < 0 and for x > 0.
First, let's compare x = -2 and x = -1
-1 > -2
f(-1) < f(-2)
Then, the function is decreasing for x < 0.
Second, let's compare x = 1 and x = 2.
2 > 1
f(2) > f(1)
Then, the function is increasing for x > 0.
Answer: c. The function is increasing when x >0.
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 3 and 8? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
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The two dice have 6 numbers each.
Look at the image to find the outcomes:
First, we need to find the total of outcomes with the sum of 3:
T. outcomes with the sum of 3 = 2
Now, find the total of outcomes with the sum of 8 = 5
When we ave in probability the expression "or" we add the probabilities:
In this case,
T. outcomes with the sum of 3 + T. outcomes with the sum of 8.
Replace the values and sum:
P = 2 +5
P = 7
Now, to find the probability divide it by the total of outcomes
Total outcomes= 36. because 6 * 6 = 36
P( sum being 3 or 8) = 7/36
To find the length of JK you’d set up and solve:
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According to the statement, to find x, it is necessary to use the following expression:
[tex]7x=3x+14[/tex]This expression is set up thanks to the definition of a parallelogram. To solve it isolate x to one of the sides of the equation.
[tex]\begin{gathered} 7x=3x+14 \\ 7x-3x=14 \\ 4x=14 \\ x=\frac{14}{4} \\ x=3.5 \end{gathered}[/tex]x has a value of 14/4 or 3.5.
According to the figure JK measures 7 times x. Use this information to find JK:
[tex]\begin{gathered} JK=7x \\ JK=7(3.5) \\ JK=24.5 \end{gathered}[/tex]JK measures 24.5.
[tex](3x^{2} -x+1)-(6x^{2} -x+2)[/tex]
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Answer:
−3x2−1
Step-by-step explanation:
−3x2−1 Is the answer to this equatiom
What number is 75% of 96?
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Answer
The number is 72
Explanation
75% of 96 is
[tex]\begin{gathered} =\frac{75}{100}\times\frac{96}{1} \\ =\frac{7200}{100} \\ =72 \end{gathered}[/tex]Find 3 ratios that are equivalent to the given ratio. 3 6 Find 3 ratios that are equivalent to the given ratio. g B. 18 9 DA. 24 6 D. 18 C. 6 24 1 F. 2 12 O E. 18 OH. 6 12 g G. 12
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Determine the coordinates of the midpoint of the segment with given endpoints. J(-3, 2), K(7,10) Midpoint:
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what are the similarities between rate and ratio
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A rate is a specific type of ratio. A rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a bowl, there are 12 fruits: 8 oranges and 4 apples. This means the ratio of oranges to apples is 8:4.
If we simplify the ratio, we can see that the ratio of oranges to apples is 2:1, because:
[tex]\frac{8}{4}=\frac{4\cdot2}{4\cdot1}=\frac{2}{1}=\frac{2}{1}[/tex]Then, there are 2 oranges in the bowl for every apple.
On the other hand, suppose we want to distribute the fruits to 3 people. We can use a rate to find out how many fruits correspond to each person because we have 2 different units:
[tex]\begin{gathered} \frac{12\text{ fruits}}{3\text{ people}}=\frac{x}{1\text{ person}} \\ \text{ Apply cross product} \\ 12\text{ fruits}\cdot1\text{ person}=x\cdot3\text{ people} \\ \text{ Divide by 3 people from both sides} \\ \frac{12\text{ fruits}\cdot1\text{ person}}{3\text{ people}}=\frac{x\cdot3\text{ people}}{3\text{ people}} \\ \frac{12\text{ fruits}}{3}=x \\ 4\text{ fruits }=x \end{gathered}[/tex]Now, we know that each person corresponds to 4 fruits, in other words, the rate is 4 fruits/person.
Therefore, we can see the similarities between rate and ratio are:
• Both are a comparison of two numbers.
,• Both can be written as fractions.
,• Both reduce to the lowest form.
Find the area of the triangle below. Be sure to include the correct unit in your answer. bu
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The area of the triangle = 0.5 x base x height
For the given triangle:
Base = 25 ft
The corresponding height to the base = 7 ft
So, the area =
[tex]0.5\cdot25\cdot7=87.5[/tex]So, the area of the triangle = 87.5 ft^2
19. Which of the following is equal to V-24 ?O-2iV64i 166i-1/2O21 V6
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The given value is,
[tex]\sqrt[]{-24}[/tex]We can write this as,
[tex]\sqrt[]{-24}=\sqrt[]{24\times-1}[/tex]As we know, 24 = 4 x 6 and,
[tex]\sqrt[]{-1}=i[/tex]the above expression can again be rewritten as,
[tex]\sqrt[]{-24\times-1}=\sqrt[]{4\times6}\times i=2i\sqrt[]{6}[/tex]Thus, the last option is correct.
The set consisting of all integers between -2 and -1 will be empty
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It is true that the set consisting of all integers between -2 and -1 is empty.
Integers are numbers that are not fraction. They are simply the whole numbers on the number line.
There are positive and negative integers.
Positive Integers are: 1, 2, 3, 4, 5, and so on
Negative Integers are: -1, -2, -3, -4, -5, and so on.
Between -2 and -1, there are no integers. Therefore, the set consisting of all the integers between them is empty.
the radius of a circle is 9 feet. what is the diameter? give the exact answer in simplest form.
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The diameter of a circle equals twice the radius of that circle.
Then:
[tex]\begin{gathered} D=2\times r \\ =2\times9ft \\ =18ft \end{gathered}[/tex]Therefore, the diameter of the circle is:
[tex]18\text{ feet}[/tex]Answer:
18 feetStep-by-step explanation:
The radius is always 2 times the diameter. Since the radius is [tex]9 ~feet[/tex], the diameter is [tex]9\cdot2=\boxed{18}~feet[/tex]
Katie rents a car when spending her vacation in Argentina while she returns the car she has driven 900 miles and used about 36 gallons of gas if you guess cost an average of $4.139 Per gallon estimate how much she spent on fuel
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Given that Katie had driven 900 miles and used about 36 gallons of gas.
The average cost of gas per gallon = $4.139
The amount she spent on gas would be:
[tex]\text{ The average cost of gas per gallon x gallons of gas used}[/tex]Hence, the amount Katie spent on gas would be:
[tex]\begin{gathered} \text{ }\frac{\text{\$4.139}}{\text{gallon}}\times\text{ 36 gallons} \\ =\text{ \$149.004} \end{gathered}[/tex]She spent $149.004
drawing and explanation for areaof triangle where h=137 and base = 203
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The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
Given that,
There is a triangle with height 137 cm and base 203 cm.
We have to find the area of triangle.
We know,
The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. A straightforward formula can be used to get the area of a triangle by multiplying the sum of the base and height by two.
Area of triangle =1/2×b×h
Area of triangle =1/2×137×203
Area of triangle =1/2×27811
Area of triangle =13905.5
Therefore, The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
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Can you please help me with this question thank youu.The first one.
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Given that:
- Tara has 18 pairs of white socks.
- She has 12 pairs of colored socks.
You can state the proportion of those types of socks using ratios.
By definition, a ratio can be written in this form:
[tex]a\colon b[/tex]And it is read "a to b".
In this case, you need to find the ratio of white socks to colored socks, then you have to set up this ratio:
[tex]18\colon12[/tex]You can simplify the ratio dividing both sides by 6:
[tex]\begin{gathered} 18\div6\colon12\div6 \\ \\ 3\colon2 \end{gathered}[/tex]Hence, the answer is: Option B.
Please help me solve the following problem:A conic kettle has a cover which height is 30% of its total height. The height is 2 cm less than the diameter of the base, which has an area of 380 squared cm. Which is the volume capacity of the kettle?
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If a conical kettles has a solid cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm², then the volume of the kettle is 798.6cm³.
As per the question statement, a conical kettles has a cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm²,
And we are required to calculate the volume capacity of the kettle.
To solve this question, first we need to know the formula to calculate the volume of a cone, which goes as, [Volume (V) = {π * r² * (h/3)}],
Where, "r" is the radius of the base of the cone,
And, "h" is the height of the cone.
Now, the height of our concerned cone is 2 cm less than the radius of it's base, and the area of the base is 380cm². Assuming that the height of the cone be "h" and the radius of it's base be "r", we get that,
[r = (h - 2)]...(i)
And, [(π * r²) = 380]
Or, [{(22/7) * r²} = 380]
Or, [(r²) = {(380 * 7)/22]
Or, [(r²) = 120.9090]
Or, (r = √120.91)
Or, (r = 10.9959)
Or, (r ≈ 11 cm)
Therefore, using the value for "r" in equation (i), we will get,
[h = (11 - 2)cm = 9cm]
And finally substituting these values of "h" and "r" in the above mentioned formula to calculate the volume of a cone,, we get,
[V = {π * (11)² * (9/3)}]
Or, [V = {(22/7) * 121 * 3}]
Or, [V = (7986/7)]
Or, (V = 1140.85714 cm³)
Or, (V ≈ 1140.86 cm³)
Since the cover of the kettle occupies 30% of the volume of the total structure of the conical kettle with it's cover, the volume capacity of the kettle is [(100 - 30)% = 70%] of the volume of the total structure of the conical kettle with it's cover, that is,
[1140.86 * (70/100)]cm³ = (1140.86 * 0.7)cm³ = 798.6cm³
Volume: The volume of any object is the three-dimensional space, occupied by the existence of that very object.To learn more about Volumes of Cones, click on the link below.
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How many red squares will there be if there are 60 squares?
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• There are 3 red squares.
,• There are 4 white squares.
To compare them and get the ratio, we can build the following relation:
[tex]\frac{3}{4}=\frac{x}{60}[/tex]where x is the number of red squares it will be when there are 60 white squares.
Solving for x:
[tex]x=\frac{3}{4}\cdot60[/tex][tex]x=45[/tex]Answer: C. 45
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Find the circumference in terms of . C = _
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Solution:
Given the circle with its radius, r;
[tex]r=11cm[/tex]Thus, the circumference, C, of a circle is;
[tex]C=2\pi r[/tex]Then;
[tex]\begin{gathered} C=2\pi(11)cm \\ \\ C=22\pi cm \end{gathered}[/tex]ANSWER:
[tex]C=22.0\pi cm[/tex]Also, the area, A, of the circle is;
[tex]A=\pi r^2[/tex]Then;
[tex]\begin{gathered} A=\pi(11)^2 \\ \\ A=121\pi cm^2 \end{gathered}[/tex]ANSWER:
[tex]A=121.0\pi cm^2[/tex]WILL GIVE BRAINLIST!!
a bakery. needs to pack 48 donuts, 12 pastries, and 24 cinnamon in identical quantities across all of the boxes. What is the maximum quantity of boxes she can utilize?
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It requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the Greatest comon factor.
What is Greatest common factor or GCF?The greatest common factor or GCF is the largest number that can be split into exactly two or more other numbers. It is the "best" thing for reducing the complexity of fractions. A factor is a number that, when multiplied by other numbers, produces the desired numbers in mathematics. Factors are another name for the total that results.
The largest factor that two or more numbers have in common is called the greatest common factor (GCF).
It is given that there are 48 donuts, 12 pastries and 24 cinnamon.
Find the greatest common factor of the given values.
Expand 48,12, and 24 in factors.
48= 2x2x2x2x3
12=2x2x3
24=2x2x2x3
Find the greatest common factors of the three factored-out numbers.
GCF=2x2x3=12
So, it requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the GCF.
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Find the answers to fill in blank 1. And blank 2.
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EXPLANATION:
We are given the linear equation;
[tex]y-4=3(x+1)[/tex]To graph this equation, we would begin by re-writing the equation in the slope-intercept form, which is;
[tex]y=mx+b[/tex]To do this, we first expand the parenthesis;
[tex]y-4=3x+3[/tex]Next we add 4 to both sides;
[tex]y-4+4=3x+3+4[/tex][tex]y=3x+7[/tex]We can now begin to plot the various points on the line. Starting from, x = -2 we would have;
[tex]\begin{gathered} x=-2: \\ y=3(-2)+7 \\ y=-6+7 \\ y=1 \end{gathered}[/tex]We can now go on and plot other points depending on the limit imposed by the graph page.
However, what we have here shows the coordinates from which we may begin;
ANSWER:
[tex]\begin{gathered} (-2,1) \\ That\text{ is;} \\ x=-2,y=1 \end{gathered}[/tex]A pair of shoes is on sale for 20% off. I paid $95. How much were the shoes originally? Write an equation and solve.
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118.75
0.80 * x = 95
x = 95/ 0.80
x = 118.75
With x being the original cost of the shoes.