As a result, we take the square root of the both sides since if two expressions are equal, then so are their square roots.
What is the definition of the square root?By multiplying the square root of a positive integer by oneself, the number is obtained. As an illustration, 5 is the square root of 25, since 5 × 5 equals 25. Since (5) (5) = 25, 5 is also the square root of 25 as you can see. The symbol, which is, is always used to indicate the square root of a number of a variable x.
Here,
In this case, we're using the square to solve a quadratic equation.
Never forget to use both the negative and positive roots of the equation and to square the values of both sides.
We can accomplish this because to the rule that states that if two expressions are comparable, then their square roots are also equivalent.
As a result, we take the square root of both sides since if two expressions are equal, then so are their square roots.
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Factor the expression using the GCF.
50+65h=
Greatest common factor (GCF) of 50 and 65 is 5.
How to find the GCF of 50 and 65?We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .
Step-1: Prime Factorization of 50
Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:
50 = 21 × 52
Step-2: Prime Factorization of 65
Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:
65 = 51 × 131
Step-3: Factors of 50
1, 2, 5, 10, 25
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 50 and 65 is 5.
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Zachary purchased a computer for $1,800 on a payment plan. Three months after he purchased the computer, his balance was 1,350. Five months after he purchased the computer , his balance was 1,050. What is an equation that models the balance B after m Months
Answer: y = -150x + 1800
Step-by-step explanation:
1. Find the linear slope of the line between two points.
(Change in Y)/(Change in X)
2. Write out an equation in point slope form.
(y-y1) = m(x-x1)
y-1800 = -150(x-0)
3. Simplify the equation and turn it into slope-intercept form.
y = -150x + 1800
A bag contains 27 balls. The ratio of red to blue to yellow balls is 6:1:2 find how many red, blue and yellow balls there are
Answer:
18 red balls, 3 blue balls, 6 yellow balls.
Step-by-step explanation:
Ratios:a ratio helps us understand the relationship between two or more values (in this case three values). More specifically it tells us how much of one item is present, for every amount another item is also present.
In this example, the ratio of red:blue:yellow is given to be: 6:1:2, which means, for every 6 red balls, there is one blue ball and two yellow balls.
In some cases, a ratio can be simplified, similar to a fraction, by dividing each number by some common factor, but in this case, the ratio cannot be simplified any further.
Solving the Problem:Instead of directly trying to find how many red, yellow, or blue balls there are first, we can instead try solving for how many group of sixes are there in the total number of red balls. It helps to think of it this way, since for every group of six red balls there are, there is one blue ball and two yellow balls, which means we can just multiply this number by one and two to find the number of blue and yellow balls in their respective orders. For simplicity, let's assign this to the unknown "G".
Using this logic, we can set up the following equation:
[tex]6G+1G+2G=27[/tex]
For every group of six red balls... there is 6 red balls, 1 blue ball, and 2 yellow balls, adding all these together should give us the total number of balls, which was given to be 27 balls. Now we can just combine the stuff on the left into one term, by adding the coefficients.
[tex]9G=27[/tex]
Now divide by 9
[tex]G=3[/tex]
Now that we know the number of group of six red balls there are, we can multiply six, one, and two to find the red, blue, and yellow balls.
[tex]\text{red balls} = 3 * 6 = 18\\\\\text{blue balls} = 3 * 1 = 3\\\\\text{yellow balls} = 3 * 2 = 6[/tex]
and you can all this together, to double check, which gives us 27.
Answer:
18,3,6
Step-by-step explanation:
Given ,
A bag contains 27 ballsThe ratio of red to blue to yellow balls is 6:1:2To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6x+x+2x = 27
9x = 27
x = [tex]\frac{27}{9}[/tex]
x = 3
Hence the number of,
Red Balls = 6x = 6 x 3 = 18
Blue Balls = x = 3
Yellow Balls = 2x = 2 x 3 = 6
x³ - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
the formula is written as x3 -10x = 100.
We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.
We've made multiple tries and have:
x = 5.4 (roughly) (approximately)
In x3 -10x = 100, replace x with 5.4.
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
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An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram. What is the area, in square units, of parallelogram ABCD? Enter your answer in the box.
In the new logo, what fraction of the parallelogram is shaded.
a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.
b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).
How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:
Area = base x height.
The base and the height for this problem are obtained counting the number of dots, hence:
Base: 4 units.Height: 6 units.Hence the area is given as follows:
Area = 4 x 6
Area = 24 units squared.
The shaded region is composed by a triangle with base 4 and height 3, hence:
Area shaded = 0.5 x 4 x 3 = 6 units squared.
(formula for the area of the triangle).
Meaning that the fraction is given as follows:
6/24 = 1/4.
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Find the product. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar. 4/3*5/3
The solution to the product expression 4/3 * 5/3 is 20/9
How to evaluate the product expression?From the question, we have the following parameters that can be used in our computation:
The product 4/3*5/3
To start with, we need to represent the statement as an expression
So, we have the following representation
4/3 * 5/3
Using a calculator, we multiply the numerator
So, we have the following representation
4/3 * 5/3 = 20/3 * 1/3
Using a calculator, we multiply the denominator
So, we have the following representation
4/3 * 5/3 = 20/9
Hence, the solution is 20/9
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In a equation is it true that when a variable is alone you have to add a number 1 to it?
I’m wondering since I have to add it to my notes.
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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What is the slope for y=-3/4x+7
Answer:
-3/4
Step-by-step explanation:
y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.
A raffle for 4 prizes is taking place. each person had to purchase a ticket to enter the raffle. If Lebron bought 4 tickets, Kobe 6 tickets, Jordan 7 and Diana Taurasi 7.
Round answer to the nearest thousandths (3 decimal places)
A). If the ticket gets put back into the raffle after each selections, what is the probability that Kobe wins the first prize and Dianna wins the second?
B) If each ticket can only be used once what is the probability that Kenton win first two prizes
C) What is the probability that Oberon wins first prize, Kobe the second, Jordan the 3rd and Diana the 4th, without replacement?
Raffles are chance-based contests in which participants compete to win exciting prizes.
How does a raffle work?To participate, all you need is a ticket with a number on it. Following the sale of all tickets, a drawing is conducted during which a random selection of tickets is made. If you chance to have the winning ticket, congratulations! a lot of engagement.
Raffles elicit a great deal of interest and support because people enjoy playing games of chance, especially when they have the possibility to win a significant prize.
high income. Your organisation has a strong possibility of making some big money from ticket sales if engagement is high!
low price. A virtual free raffle can be found online! A virtual raffle is the most cost-effective type of fundraising because you won't need to print actual tickets, reserve a location for the drawing, or buy refreshments.
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triangle has area 16 m ^2
. List all the possible positive integers that could
represent the lengths of its base and height.
Therefore , the solution of the given problem of triangle comes out to be base=4m,16 and height=8m,2m.
Defining a triangleIn a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.
Here,
Given :
Triangle area = 16[tex]m^{2}[/tex]
Thus,
To find the possible base and height of the triangle.
The base can be given by 4 m,16
and height be = 8m or 2m
vice-versa
height = 4m ,16mand base =8m,2m
Therefore , the solution of the given problem of triangle comes out to be base=4m,16 and height=8m,2m.
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Answer:
see below
Step-by-step explanation:
given that the area of the triangle is 16m² . We need to list all the possible lengths of its base and height. As we know that, the area of triangle is ,
ar(∆) = 1/2 * base* height
substitute the respective values,
16m² = 1/2* b * h
b*h = 32
now here we need to list out all the possible factors of 32 as ,
1 *32
2 *16
4*8
8*4
16 *2
32*1
therefore, all the possible lengths of heights and bases are ,
b = 1m , h = 32m b = 2m , h = 16mb = 4m , h = 8mb = 8m , h = 4mb = 16m , h = 2mb = 32m , h = 1mand we are done!
-Rishabh
On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. What is the ratio of the number of burgers without onions to the number of burgers with onions?
The ratio of number of burgers without onions to the number of burgers with onions is 4:1.
Ratio of numbers.The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.
Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;
ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)
= 12/ 3
= 4/ 1
The ratio of number of burgers without onions to burgers with onions = 4:1
Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.
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Given the number 254, 476, 951
What number is in the TEN THOUSAND's SPOT?
Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.
29) Which is a counterexample that shows the following conjecture is false: "If 21 and 22 are complementary, then one of the angles is obtuse" ? A. m/1 = 90° and m42 = 90° B. m/1 = 53° and m42 = 127° C. mz1 = 100° and m42 = 80° D. mz1 = 45° and mz2 = 45
D. mz1 = 45° and mz2 = 45 are complementary angles (mz1 + mz2 = 90°), but neither angle is obtuse (greater than 90°), so the guess is wrong. This is a counter-example to show.
What are supplementary angles?A supplementary angle is an angle where the sum of two angles is 90 degrees. That is, if angle A and angle B are complementary, angle A measurement + angle B measurement = 90 degrees. Supplementary angles may be adjacent (having a common vertex and edge) or non-adjacent (having no common vertex or edge), but they always complement each other.
There are various kinds of angles to study.
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Write a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8)
a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8) is: f(x) = - 2 (x + 3) (x - 1) (x - 4)
What is a cubic function?A cubic function is a function whose expression contains the cube of the x variable. A function is referred to as a cubic function if its formula is f(x) = ax³ + bx² + cx + d. a, b, c, and d can all be constants in this case, but make sure that a 0. The b, c, or d might all be zeros.
A cubic function has 3 roots.
Let, assume α, β and γ.
So, f(x) = K (x - α). (x - β). (x - γ)
f(x) is defined by values of x where f(x) = 0
0 = K (x - α). (x - β). (x - γ)
x = α, β, γ
The given cubic function graph is cutting x - axis at 3 points: (-3, 1 ,4)
Now, f(x) = K (x - (-3). (x - 1). (x - 4)
f(x) = K (x + 3) (x - 1) (x - 4)
Next, f(x) passes through point (0,8) which means:
f(0) = 8
so, 8 = K (0 + 3) (0 - 1) (0 - 4)
or, k = - 2
Now, f(x) = - 2 (x + 3) (x - 1) (x - 4)
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How many pairs of potential clients can be randomly chosen from pool or eight candidates
There are 34 ways by which pairs of potential clients can be randomly chosen from pool or eight candidates.
What is combination?We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.
As such we would have the use of the formula for combination as follows;
C = n!/r!( n - r)!
C = 8!/2!(8 - 2)!
C = 8 * 7 * 6!/2! 61
C = 8 * 7/ 2 * 1
C = 28
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help with explanation if possible
Answer: 448
Step-by-step explanation: Parallelogram formula base times height
find the values of the variable in the following, giving brief reasons:
Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.
Explain the trapezoid.A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.
Here,
Given : 110°
and 90°
To find the value of x ,
Thus,
The value of angle opposite to x :
=> 110° + y =180°
=>y =180°-110°
=>y = 70°
thus, x value is
=> x + 70° =180°
=> x =110°
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X+X+X+Y+Y=
im doing algebra and cant understand the above question
Answer:
3x + 2y
Step-by-step explanation:
X+X+X+Y+Y=
you simply count equal letters and add them x+x+x is 3x and y + y = 2y.
x + x + x + y + y =
3x + 2y
not knowing the value of x or y we stop hereFind the slope of the line in which x=-24
Answer:
it is undefined
Step-by-step explanation:
Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.
Answer:
undefined slope
Step-by-step explanation:
When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.
roxanne needs 134,000 three years from now. How much should she deposit at the beginning of each 3 months in order to accumulate the desired amount if money is worth 4% coumpounded quarterly?
what is the missing in the given question?
The amount that Roxanne should deposit at the beginning of each 3 months to accumulate $134,000 at 4% compounded quarterly for three years is $10,461.13.
How is the quarterly deposit determined?The quarterly deposit can be computed using an online finance calculator with the following parameters.
The quarterly deposit shows the periodic investment that must be made to accumulate a future value of $134,000.
N (# of periods) = 12 quarters (3 x 4)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $134,000
Results:
PMT (periodic deposits) = $10,461.13
Sum of all periodic deposits = $125,533.56
Total Interest = $8,466.44
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A maple tree grows 1.5 feet each year. The table shows the yearly growth for a pibe tree
Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.
How to find the tree that grow fasterA mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.
Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, b for maple is given as 1.5 and we calculate for pine using the data in the table. the equation is derived as follows
f(x) = a(b)ˣ
12 = a(b)¹
24 = a(b)²
dividing 24 = a(b)² by 12 = a(b)¹
b = 2
hence for pine tree the b is 2 which is greater than 1.5
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(tan A)/(sec(A) - 1) + (tan A)/(sec(A) + 1) = 2cos ecA
Answer:
Step-by-step explanation:
LHS = tanθ/secθ - 1 + tanθ/secθ + 1
Cross multiplication,
tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ
= tanθ(1 - secθ - 1 - secθ)/-tan^2θ
= -2secθ/-tanθ
= 2 x 1/cosθ / sinθ/cosθ
= 2cosecθ = RHS
Hence proved.
Ms. Lopez goal is to run 25 miles this week.
She runs 3 miles on Tuesday and 4 miles on Wednesday.
What percent of her goal has she accomplished?
Answer: 28%
Step-by-step explanation: First, we need to find how much she runs in total on Tuesday and Wednesday. So, we add 3 + 4 to get 7. With that, we need to determine how much 7 is from 25. So, it'd look like this:
7 * 100 / 25
700 / 25
=28
Therefore, she's done 28% of her goal (within the 2 days) I hope this helped!
Answer:
I think the other person who answered the question is right
Step-by-step explanation:
Write and solve a system of equations for each of the following problems. You must write two questions for each problem, thank you
1. Ella is a landscape photographer. She sells small prints for $50 each, and large prints for $75
each. One weekend she sold a total of 52 prints for a total of $2975. How many of each size print did
Ella sell?
2. At a hot air balloon festival, Georges's balloon is at an altitude of 40 meters and rises at a rate of
10 meters per minute. William's balloon is at an altitude of 165 meters and descends at a rate of 15
meters per minute. In how many minutes will both balloons be at the same altitude? What is that
altitude?
The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.
What is system of equations?A system of linear equations consists of two or more equations and looks for common answers.
1. Let us suppose small prints = x
Large prints = y
Total prints sold can be written as follows:
x + y = 52
The total cost of the prints can be written as follows:
50x + 75y = 2975
The system of equations is:
x + y = 52 . . . equation 1
50x + 75y = 2975 . . .equation 2
Using equation 1 we have:
x = 52 - y
Substituting the value of x in equation 2 we have:
50(52 - y) + 75y = 2975
2600 - 50y + 75y = 2975
25y = 2975 - 2600
25y = 375
y = 15
Now, substituting the value of y in equation 1 we have:
x + 15 = 52
x = 52 - 15
x = 37
Hence, the solution of the system of equations is y = 15 and x = 37.
2. Let us suppose the altitude = x.
The rising balloon can be thus written as:
40 +10x
The descending balloon can be written as:
165 - 15x
Solving the system of equations by substituting the value of x we get x= 5.
Hence, the altitude at which both the balloons are at the same height is 5m.
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guys please help its due today!
Answer:
Step-by-step explanation:
the answer is 6
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide.
an image
What is the length of the fence not including the gate?
m
Use π
= 3.14
Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.
What is the length of the fence?Let the circular pool has the radius (r ) = x cm.Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.Length of fence = Circumference of the pool – width of the gate.Length of fence = 2 π r – 150Length of fence = 2 × 3.14 × x – 150Length of fence = 6.28x – 150 cm.a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius.To learn more about length of the fence refers to:
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How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?
It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.
How to find the present value of bike?You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:
n = (1200 - 2550) ln / ln (1 - 0.05)
Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.
When we enter the values, we will get:
n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months
The motorcycle will take approximately 15.7 months to drop in value to less than £1200.
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The ratio of yellow houses to white houses on a street is 18 to 26.
Simplify the ratio.
Enter your answer by filling in the boxes.
to
Answer: The ratio 18:26 simplified is 9:13.
Step-by-step explanation:
To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.
The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13
Answer:9/13
explanation: k12