The two ways that sequences can be defined include the following: Arithmetic Sequences and Geometric Sequences.
What is a sequence in mathematics?A sequence is defined as the collection of items in such a way that repetitions can be observed.
There are two major ways the sequence can be defined in arithmetics and this includes the following:
Arithmetic Sequences: This is the type of sequence whereby every term is created by adding or subtracting a definite number to the preceding numberGeometric Sequences: This is the type of sequence whereby every term is obtained by multiplying or dividing a definite number with the preceding number.Learn more about sequence here:
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Sheila travels 65 miles per hours for 8 hours. Find the distance traveled in miles.
Answer: 520 miles per hour
Step-by-step explanation:
65 times 8 = 520 miles per hour
A copy machine makes 28 coples per minute. How long does it take to make 126 copies?
Answer: 4.5 minutes
Step-by-step explanation:
Take 126 divided by 28 = 4.5 minutes
Is AAA a postulate or theorem?
The AAA (angle-angle-angle) similarity theorem states that two triangles' corresponding angles are identical if and only if their corresponding sides are proportionate.
Knowing two angles, such as 32° and 64°, we may calculate the following angle, which is 84°, since 180-(32+64)=84. (This is commonly referred to as the AAA Postulate—which is valid in every way, although two angles are more than enough.) Working backwards will help you understand the proposition better.
The sides and angles of a set of triangles must be equal for them to be congruent. The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal.
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A system of equations is shown on the graph below.
How many solutions does this system have?
The system has no solution.
What is linear equations?
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y)
We know that
The solution of the system of two linear equations, is the intersection point both lines.
In this problem
The lines are parallel, the lines don't intersect
therefore
The system has no solution
Remember that, if two lines are parallel then their slope are equal
Verify that the slopes are the same
Blue line
take the points (0,2) and (-2,0)
[tex]m=(0-2) /(-2-0)=1[/tex]
Red line
take the points (0,-3) and (3,0)
[tex]m=(0+3) /(3-0)=1[/tex]
The slopes are equal
The lines are parallel
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Which of these numbers is closest to 1?
1.11
A
0.1
B
0.91
C
0.999
D
1.05
E
Answer:
C 0.91 D 0.999 E 1.05 and A 1.11 =1
Dave wrote a whole number greater than 0 and less than 11 on a piece of paper.
Find the probability that Dave's number is each of the following.
6. P(7)
7. P(less than 5)
9. P(less than 1)
10. P(greater than 10)
8. P(odd)
11. P(divisible by 2 or 3)
You draw a card from a deck that has 12 star cards, 8 yellow moon cards,
6 blue moon cards, 9 planet cards, and 1 sun card. Find each of the following.
12. P(moon)
13. P(star)
14. P(blue moon or planet) HOW DO U DO THIS I DONT GET IT
0.03, 0.04, 0.38, and 1 are the figures that could represent an event's likelihood .Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible
How does probability work exactly?Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.
How do probability and an example work?The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.
6. P(7) = 1/10
7. P(less than 5) = 4/10 = 2/5
8. P(greater than 10) = 5/10 = 1/2
11. P(divisible by 2 or 3) = 6/10 = 3/5
12. P(moon) = 8/36 = 2/9
13. P(star) = 12/36 = 1/3
14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9
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Answer:
Step-by-step explanation:
6. P(7) = 1/10
7. P(less than 5) = 4/10 = 2/5
8. P(greater than 10) = 5/10 = 1/2
11. P(divisible by 2 or 3) = 6/10 = 3/5
12. P(moon) = 8/36 = 2/9
13. P(star) = 12/36 = 1/3
14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9
What is expression example?
An example expression is the following:
$100 + $50n
What is an algebraic expression?An algebraic expression is a set of letters and numbers, in which the letters are called variables and take on an unknown value, the numbers are coefficients or independent terms while the variables are dependent terms.
We will write an algebraic expression to exemplify what has just been defined, with a verbal example.
A person has a business, and he adds $100 to the box (and his sales are on average $50 per hour, with this we build the expression of total income:
$100 + $50n
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In hopes of encouraging healthier snacks at school, Grace brought in a tray of carrot sticks and apple slices to share. She brought 20 snacks in all. 15 of the snacks were carrot sticks. What percentage of the snacks were carrot sticks?
Answer:
75%
Step-by-step explanation:
[tex]\frac{15}{20} \times 100=75\%[/tex]
How do you find the value of x and y in a triangle?
On solving the provided question, we can say that the value of x = 5√3
and value of y = 10.
How to find the value of x and y?
To find the values of x and y, you will need to use
the Pythagorean theorem,The trigonometric ratio: soh-cah-toa, andspecial values of trigonometric functions.According to the given question:
Using the table of trig values, we find that
sin30°=1/2
So, this gives us:
1/2 = sin 30° = 5/y
1/2 = 5/y
(1xy)/2 = 5
y= 2×5 =10
Next, using the Pythagorean Theorem, we find that
5²+x²=10²
x²=100−25=75
Solve for x:
x=√75=√3×25=5√3
Complete question:
How do you find the value of X and Y. Y is the hypotenuse, 5 is the adjacent side and X is the opposite side from Y, and in the triangle there is 30 degrees where X and Y lines meet?
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Is triangle ABC = triangle DEF by HL? Explain.
Answer:
If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.
The football team is selling gift cards in increments of $25 and $50. If they sold $6,000 worth of gift cards which equation could be used to determine how many $50 gift cards, g, were sold if 180 gift cards were sold in the $25 amount?
A 4,500 + 50g = 6,000
B 25 + 50g = 6,000
C 4,500 - 50g = 6,000
D 25g - 50(180) = 6,000
Answer:
A. 4,500 + 50g = 6,000
Step-by-step explanation:
25(18) + 50(g) = 6000
4500 + 50g = 6000
The correct option is A.
What is the parallel equation of Y 3X 1?
The parallel equation of y = 3x + 1 is y = 3x
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates.Given equation: y = 3x + 1
A point from which the parallel line will pass through is (0,0)
To find the slope using the slope-intercept form:
The slope-intercept form is: y = mx + b
Where, m = slope
b = y - intercept
Now comparing this equation with given equation, we find, slope (m) = 3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope 3 and a given point (0,0) to substitute for x₁ and y₁ in the point slope form: y - y₁ = m (x - x₁), which is derived from the slope-equation,
m = (y₂ - y₁)/ (x₂ - x₁)
so, putting the value we get,
y - 0 = 3 ( x - 0 )
or, y + 0 = 3 ( x +0 )
or, y = 3x + 0
or, y = 3x
The graph is shown below:
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The complete question is as follows:
What is the parallel equation of y = 3x + 1
What does 4 3 mean in math?
43 in arithmetic stands for multiplying 4 by three. Suppose x =43; then, x+4*4*4.
What is the power of numbers?If the power is positive, multiply the integer by itself that many times. If the power is negative, multiply the reciprocal of the integer by itself that many times. If the power is 0, the result is always 1.
Are 3 and 9 three the same?No, 3:9 and 9:3 are not equivalent. 3^9=19683 and 9^3=729.
4^3=4*4*4\s =16*4\s =64
Which one—math or maths—is correct?In the US and Canada, math is the word of choice. In the United Kingdom, Ireland, Australia, and other English-speaking countries, math is the preferred term. There isn't really a rational reason why math grew more popular in certain locations while maths was elsewhere.
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Find the total surface area of the right solid shown.
Dimensions are in m. Round to the nearest
whole number.
The volumes of the cone and cylinder are 1256m³ and 5652m³
What is the formula volume of a cone and a cylinder?For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.
Given here dimensions as the height of the cone = 12m and radius of its circular base = 10m and the height of the cylinder = 18m
thus Volume of the cone = 1⁄3πr²h
= 1/3×3.14×100×12
= 1256m³
And the volume of the cylinder = πr²h
= 3.14×100×18
= 5652m³
Therefore the volumes of the cone and cylinder are 1256m³ and 5652m³
Hence, the volume of the solid is 1256+5652 =6908m³
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At a football game, a vender sold a combined total of 191 sodas and hot dogs. The number of sodas sold was 43 more
than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Number of sodas sold:
Answer:
There were 74 hot dogs and 117 sodas sold.
Step-by-step explanation:
The following equation describes the conditions of the question:
[tex]191=x+(x+43)\\191=2x+43\\[/tex]
where x is the number of hot dogs sold.
Solve for x:
[tex]191=2x+43\\(191)-43=(2x+43)-43\\148=2x\\\frac{148}{2}=\frac{2x}{2}\\74=x[/tex]
There were 74 hot dogs sold and (74+43) or 117 sodas sold.
What kind of sequence is 3/6 12 24?
This is an arithmetic sequence. In this sequence, the common difference is 6 (12 - 3/6 = 6).
What is sequence?A sequence is an ordered arrangement of objects or events which follow one another in a specific order. This order can be based on a mathematical rule or pattern, such as a sequence of numbers, or it can be based on physical or temporal characteristics of the objects or events, such as the order in which they appear in a movie or story. Sequences are useful for representing and analyzing data, as well as for visualizing relationships between objects. They can also be used to model problems, such as predicting the future or solving a puzzle.
This is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant, called the common difference, to the preceding term. In this sequence, the common difference is 6 (12 - 3/6 = 6).
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How do you find the length of an altitude of an isosceles triangle?
The altitude of an isosceles triangle is sqrt (a^2 - b^2 / 4).
In the triangle ABC, sides AB and AC are equal (say a) and side BC = b. Let us consider the triangle ADC which is the right triangle in the isosceles triangle ABC, and by Pythagoras' theorem,
we get that the altitude AD of the isosceles triangle can be obtained:
AD ^ 2 = AC ^ 2 - (BC / 2) ^2
AD ^ 2 = (a ^ 2 - b ^ 2 / 4)
AD = sqrt (a ^ 2 - b ^ 2 / 4).
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Question Simplify. 13(5x−8)+23x
Answer:
8(11x-13)
Step-by-step explanation:
[tex]13(5x-8)+23x\\65x-104+23x\\88x-104\\8(11x-13)[/tex]
A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and Angle A. Round each answer to the appropriate number of significant digits
Answer:
x = 30.6 ft
A = 58.1°
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As the triangle is a right triangle, use Pythagoras Theorem to find length x.
[tex]\implies x^2+19^2=36^2[/tex]
[tex]\implies x^2+361=1296[/tex]
[tex]\implies x^2=935[/tex]
[tex]\implies x=\sqrt{935}[/tex]
[tex]\implies x=30.6\; \sf ft \;\; (3\;s.f.)[/tex]
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = AA = 19.0 ftH = 36.0 ftSubstitute the values into the formula and solve for A:
[tex]\implies \sf \cos A=\dfrac{19.0}{36.0}[/tex]
[tex]\implies \sf A= \cos^{-1}\left(\dfrac{19}{36}\right)[/tex]
[tex]\implies \sf A=58.1^{\circ}\;\;(3\;s.f.)[/tex]
What is the mean of the numbers 25 30 27 23 and 25?
The mean of the given data set is 26.
One of the most significant and often employed metrics of central tendency is the mean. In mathematics, there are various different kinds of means. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a particular set of observations.
To put it another way, calculating the mean of a data set only requires adding up all the values and dividing the result by the total number of values.
The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.
Mean = 25+30+27+23+25/5
Mean = 130/5 = 26
Thus, the mean of the given data set is 26.
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The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.
Mean = 25+30+27+23+25/5
Mean = 130/5 = 26
Thus, the mean of the given data set is 26.
A plumbing contractor obtains 60% of her boiler circulators from Company 1 whose defect rate is 0.005 and the rest from Company 2 whose defect rate is 0.01. If a circulator is defective, what is the probability that it came from the first company? Fill in the contingency table below in order to find the answer. Write your answer as a decimal using 4 significant digits, like for example 0.0247. Defective Non-Defective Total 600 Company 1 Company 2 Total 400 1000
The probability that it came from the first company is 1/2.88⁹.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, A plumbing contractor obtains 60% of her boiler circulators from Company 1 whose defect rate is 0.005 so 40% of her boiler circulators from Company 2 whose defect rate is 0.01.
Now, The probability of the defect rate of company 1 is P(D1) = 0.005/60.
And, The probability of the defect rate of company 1 is P(D1) = 0.01/40.
Therefore, The probability of that it came from the first company is,
= (0.005/60)×( 0.01/40)/60.
= (1/12000)×(1/4000)/50.
= 1/2.88⁹
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138 cm² = (x + 2) × ( 2x + 3) x 1/2
Answer:
Step-by-step explanation:
138 cm² = (x + 2) × ( 2x + 3) x 1/2
138 cm² = x + 2 × 2x + ) x 1/2
138 cm² = x + 4x + x * 0.5
0.5/138 cm² = 6x * 0.5 /0.5
6/69cm² = 6x/6
x = 11.5
This might be wrong so just take the square root of 138.
How do you write 3 more than 5?
“3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.
In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra. Similar to how a statement explains the link between certain words, algebraic equations describe the connection between unknown variables.
We are given a mathematical statement and have to convert it into an algebraic expression using the information above.
3 more than 5 is obtained after adding 5 to the given number which is 3.
So 3 more than 5 is equal to 3+5=8.
Hence “3 more than 5” written as an algebraic expression is “3+5” which is equal to 8.
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A women put $600 into a savings account for one year. The rate of interest on the account was 6%. How much was the interest for the year in dollars and cents.
Answer:
The interest is $36 or $3600 cent
Step-by-step explanation:
6% = 0.06
Take 600 times 0.06 = $36
$1 = 100 cent
$36 = $3600 cent
So, the interest is $36 or $3600 cent
Answer:
Let A = total amount principal + interest
P = principal amount , $600
R = interest rate, 0.06
T = time , 1
A = P(1 + r)^t
A = 600(1 + 0.06) we dont have to put 1 as exponent
A = 600(1.06)
A = 636
Interest = A - P
Interest = 636 - 600
Interest = 36
Therefore, the interest will be $36 dollars. The women will have a total amount of $636 on the accountStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-a 2 kg block is placed at the top of an incline and released from rest near earth’s surface and unknown distance h above the ground. the angle θ between the ground and the incline is also unknown. frictional forces between the block and the incline are considered to be negligible. the block eventually slides to the bottom of the incline after 0.75 s. the block’s velocity v as a function of time t is shown in the graph starting from the instant it is released. how could a student use the graph to determine the total energy of the block-earth system?
Therefore , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
What is force?It can push or pull. Acceleration is caused by unbalanced forces.
The Newton is the symbol for a force (abbreviation is N).The force required to cause a mass of one kilogramme to alter its velocity by one metre per second (m/s) per second is one Newton. The formula is: 1 N = 1 kg m/s2 (kilogram metre per second squared)
Here,
Let s represent the block's total distance travelled.
As a result, the block's work will be equal to the potential energy contained in the spring.
It is given as,
(mgsinθ)×s= 1/2 k[tex]x^{2}[/tex]
( √2 ×10×sin45 ∘ )×s= 1/2 ×100 x (0.75*0.75)
s=281 . 25m
Thus, the distance travelled by the block is 281 . 25m.
For energy :
=> 1/2 m v^2
=> 1/2 * 2* (3.75)^2
=> 14.0625 J
Therefore , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
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The distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
What is meant by work in physics?When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work in physics.
Define energy.The ability to exert a force that causes an item to move is what is meant by the definition of energy as the "power to accomplish work."
Let s= total distance travelled by block.
Therefore, the block's work will be equal to the spring's potential energy.
According to given information,
(mgsinθ)×s= 1/2 k
( √2 ×10×sin45 )×s= 1/2 ×100 x (0.75*0.75)
s=281 .25m
Therefore, the distance travelled by the block is 281 . 25m.
For energy we have:
=> E= 1/2 m v^2
=> E= 1/2 * 2* (3.75)^2
=>E= 14.0625 J
So , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J.
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What does power of 1 2 mean?
The square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.
What is Square root ?The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{x}[/tex] . Finding the square root of a number is the opposite of squaring a number.
In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.
For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16.
Thus , the square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.
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Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
If Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. The amount that is closest to how much she will earn in hourly wages and commission for those two weeks is A $592.
What is earnings?Earnings can be defined as the money a person earn as wages or as salary.
First step is to find the amount that Sandy earns per hours
Earnings per hour = 9+ (0.15×9)
Earnings = $10.35 per hour
Second step is to find her earnings
Earnings =73 × $10.35
Earnings = $755.55
Closest amount is $592.
Therefore the correct option is A.
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The complete question is:
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A $592
B $890
C $386
D $298
What is the arithmetic mean of the data set 11 12 13 14 15 16 17 18 19 and 20?
The arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.
The arithmetic mean, also known as the average, of a set of numbers is found by adding up all the numbers in the set and dividing by the total number of numbers in the set. In this case, the set of numbers is 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. When we add up all the numbers in the set, we get a total of 155. There are 10 numbers in the set, so the average is 155 / 10 = 15.5.
To find the arithmetic mean, we first need to add up all the numbers in the set. Then, we divide that sum by the total number of numbers in the set. This gives us the average value of the set.
In summary, the arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.
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State the area of the given triangle.
A: 28 Square Units
B: 24 Square Units
C: 60 Square Units
D: 36 Square Units
Answer:
24 Square Units (B)
Step-by-step explanation:
⭐ The formula for the area of any triangle is: 1/2(bh), where b = base, and h = height.
⭐ The height of a triangle is the triangle's altitude, which can be denoted by a straight line with a right angle. In this problem, the height is given to you.
Let's substitute what we are given to find the area.
area = 1/2(bh)base = 12 square unitsheight = 4 square unitsarea = 1/2(12*4)area = 1/2(48)∴ area = 24 square unitsHow do you know if ASA is congruent?
As per the value of angle of the triangle, we have identified that the ASA is congruent.
In math the term triangle refers the three sided triangle that contains the three angles, sides and edge.
Here we need to find the process to know if ASA is congruent.
According to the definition of triangle, here we must know the definition of congruent.
The term congruent is defined as if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In this theorem, we have to know that any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle then those two triangles are said to be congruent by ASA rule.
Based on this rule, we have identify that if the two triangle have the same angle, then it said to be congruent as per the ASA rule.
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