Answer:
The correct answer is A (x+1)(7x-10).
Step-by-step explanation:
To determine the dimensions of a rectangular poster that will cover an area represented by 7x² + 3x - 10, we need to find the factors of the expression 7x² + 3x - 10 that will give us the length and width of the poster.
One way to do this is to factor the expression 7x² + 3x - 10 using the difference of squares method. We can write the expression as follows:
7x² + 3x - 10 = (7x² + 3x) - 10
To factor (7x² + 3x) - 10, we can write the expression as the difference of squares:
(7x² + 3x) - 10 = (7x² + 3x + 10) - (10 + 10)
To simplify the expression, we can complete the square for the terms in parentheses:
(7x² + 3x + 10) - (10 + 10) = (7x² + 3x + 10) - 20
To complete the square, we need to add and subtract the square of half the coefficient of the x term, which is (3/2)² = 9/4. We can rewrite the expression as follows:
(7x² + 3x + 10) - 20 = (7x² + 3x + 10 + 9/4) - (20 - 9/4)
To simplify the expression, we can factor the terms in parentheses:
(7x² + 3x + 10 + 9/4) - (20 - 9/4) = [(7x² + 3x + 10 + 9/4) - (20 - 9/4)]
To simplify the expression further, we can factor out a common factor:
[(7x² + 3x + 10 + 9/4) - (20 - 9/4)] = (x + 1)(7x - 10)
From the given options, the expression that represents the area of the rectangular poster is (x+1)(7x-10), which is equivalent to 7x² + 3x - 10. We can verify this by multiplying (x+1)(7x-10) to get 7x² + 3x - 10. Therefore, the correct answer is A (x+1)(7x-10).
Q1)Here is a rectangle It is 8cm and (2b-5)cm
A)Find an expression for the perimeter of the rectangle, in terms of b.
Give your answer in its simplest form.
B) Find the value of b when the perimeter is 42 cm.
In terms of b, the perimeter expression is 6 + 4b and the value of b is 9
How to find an expression for the perimeter of the rectangle,From the question, we have the following parameters that can be used in our computation:
Dimensions = 8cm and 2b - 5 cm
The above parameters mean that
Length = 8
Width = 2b - 5
The perimeter is calculated as
Perimeter = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (8 + 2b - 5)
Evaluate the like terms
Perimeter = 2 * (3 + 2b)
Open the brackets
Perimeter = 6 + 4b
B) Find the value of b when the perimeter is 42 cm.Here, we have
Perimeter = 42
This means that
6 + 4b = 42
So, we have
4b = 36
Divide by 4
b = 9
Hence, the value is 9
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what is the probability that the number of systems sold is within 1 standard deviation of its mean value?
The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
Explain the term Discrete Variable?The term "discrete variable" refers to a variable that has a finite range of possible values. such as using only integer numbers. For instance, the total number of students in a class, the quantity of faulty goods in a batch, etc.The given data is
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
(a) calculate mean value of x:
μ = E(x)
= ∑(xi.P(xi))
= 4.13
(b) calculate variance of x:
σ² = ∑(xi - E(x))².P(xi)
= 1.81331
(c) calculate standard deviation of x:
σ = √σ²
σ = √1.831
σ = 1.3539
The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:
P(μ - σ < x < μ + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)
= P(2.7761 < x < 5.4839)
= P(x = 3) + P(x = 4) + P(x = 5)
= 0.13 + 0.30 + 0.31
= 0.74
Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
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The complete question is-
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
4. Choose all the equations that are true
if x = 8.
A. 0²/x = 6/²/
B. x +11.5 = 20.5
C. 23.42 - x = 15.42
D. 11x = 88
E. 40 ÷ x = 6
The equations that are true if x = 8 are:
B. x + 11.5 = 20.5
C. 23.42 - x = 15.42
D. 11x = 88
In equation B, x is equal to 8, so 8 + 11.5 = 20.5, which is a true statement. In equation C, x is also equal to 8, so 23.42 - 8 = 15.42, which is a true statement. In equation D, x is equal to 8, so 11*8 = 88, which is a true statement.
Equation A is not true because the expression 0^2/x is undefined, since division by zero is not allowed. Equation E is not true because 40 ÷ 8 is equal to 5, not 6.
Answer:
whats f
Step-by-step explanation:
4. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily. What is the annual percentage yield?
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
Define annual percentage.An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.
Given
Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily.
1.048353
The table on page A14 shows the cost per $1.00 (over the course of a year).
$35,000×1.048353=$36,692.36
The sum of the initial principle and the amount per $1.00 is the amount (for a year).
$36,692.36−$35,000=$1,692.36
The difference between the amount (for one year) and the initial principal is the interest (for one year).
$1,692.36÷$35,000
=0.04835
=4.835%
The interest (for a year) divided by the initial principle results in the annual percentage yield.
4.835%
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
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PLEASE HELP!!!
Ralph and Liza are both driving fro Los Angeles to Santa Fe. Ralph leaves at 7:00 and averages 60 mph (miles per hour) on the way. Liza leaves at 7:25 and averages 65 mph on the way. The situation is modeled by this system, where x is number of hours after Liza leaves and y is the distance each will travel:
y=60x+25
y=65x
How long after Liza leaves will she pass Ralph, and how far will they each have traveled?
A. Liza will not pass Ralph, because she will never catch up with him.
B. Liza will pass Ralph after 3 hours, and they each will have traveled 205 miles.
C. Liza will pass Ralph after 5 hours, and they each will have traveled 325 miles.
D. Liza will pass Ralph after 4 hours, and they each will have traveled 260 miles.
To find the time and distance at which Liza passes Ralph, we need to solve the system of equations.
Subtracting the first equation from the second, we get:
65x - 60x = y - 25
5x = y - 25
y = 5x + 25
Substituting this value of y into the first equation, we get:
60x + 25 = 5x + 25
55x = 0
x = 0
This means that Liza will pass Ralph 0 hours after she leaves, or at the same time as Ralph. At this time, they will have both traveled 0 miles.
Therefore, the answer is A: Liza will not pass Ralph, because she will never catch up with him.
Solve the system of equations using subtraction 4x − 4y = 4 4x + y =19
Answer:
4×-4y=4
-(4x+y=19)
0x -5y=-15
5y=15
y=3
4x-12=4
x=4
Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. If each set on sale contains 6 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Latanya should buy?
The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
What is the inequality equation?
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.
To determine the minimum number of sets of glasses that Latanya should buy, we can set up the following inequality:
x * 6 + 390 >= 739
This inequality states that the number of glasses Latanya has after buying x sets of glasses should be greater than or equal to the minimum number of glasses the restaurant needs.
To solve for x, we can subtract 390 from both sides of the inequality to get:
x * 6 >= 739 - 390
x * 6 >= 349
x >= 349/6
x >= 58.16
x >= 58
Hence, The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
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A manufacturing company produces 380 units per day currently. The company's goal is to increase the number of units manufactured per day by 30 each year. If the company meets its goal, how many units will it be producing per day 4 years from now?
Answer:
500
Step-by-step explanation:
You want to know the rate in 4 years if it is 380 units per day, and increasing by 30 units per day per year.
RateThe rate in 4 years will be the sum of the current rate and the amount of increase. The amount of increase is the rate of increase, multiplied by time:
amount of increase = (30 units/day)/year × (4 years) = 120 units/day
Then the rate in 4 years will be ...
new rate = current rate + increase
new rate = 380 units/day + 120 units/day = 500 units/day
The company will be producing 500 units per day in 4 years.
someone help me please
Answer:
Negative
Step-by-step explanation:
Knowledge Needed
The discriminant of a quadratic function is b^2-4ac.
If the discriminant is positive, there are 2 x-intercepts.
If the discriminant is 0, there is 1 x-intercept.
If the discriminant is negative, there are 0 x-intercepts.
Question
If the parabola does not intersect with the x-intercept, the discriminant is negative.
For the function defined by f (x) = startfraction 12 over x squared endfraction, what is the constant of proportionality? a. 120 c. 12 b. Undefined d. 1200.
The correct option c. 12, is the constant of proportionality.
Define the term constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that really are directly proportional to one another, the proportionality constant k is defined as k=y/x.For the stated question-
f (x) = startfraction 12 over x squared endfraction
Rewrite the function as;
f(x)=12/x^2,
Constant of proportionality = 12 (only fixed term in the function)
Thus, the constant of proportionality for the function f(x)=12/x^2, is found as 12.
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Select the graph for the solution of the open sentence. Click until the correct graph appears.
5|x| + 3 < 18
Answer:
graph D
Step-by-step explanation:
if x ≥ 0
5x + 3 < 18
5x < 18 - 3
5x < 15
x < 15/5
x < 3
0≤ x < 3
if x < 0
5(-x) < 18 - 3
- 5x < 15
x > 15/-5
x> -3
-3 < x < 0
final solution
-3 < x < 3
14. If AABC is similar to ADEF, what proportion would be used to solve for 2?
The proportionality used in the given diagram is 4/3=12/x if ΔABC and ΔDEF are similar. So, option 4 is correct.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.
We have to assume that ΔABC and ΔDEF are similar.
If the triangles are similar,
Then the proportionality is:
AB/BC=DE/EF
4/3=12/x
Therefore, the proportionality used in the given diagram is 4/3=12/x.
So, option 4 is correct.
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Rewrite -cot^2x/ 1+ cscx so its not in fraction form.
Rewriting the given trigonometric form using trigonometric identities by eliminating fraction form gives [tex]-cotx.cosx.(sinx+1)[/tex]
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Calculation:We know that,
[tex]cot^{2} x = \frac{cos^{2}x }{sin^{2}x }[/tex]
[tex]1+cscx = (1+\frac{1}{sinx} ) = \frac{sinx+1}{sinx}[/tex]
Rewriting the given trigonometric form using trigonometric identities by eliminating the fraction form gives[tex]-cotx.cosx.(sinx+1)[/tex]
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Please quick I’ll give brainliest
one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
What is called multiplication?
Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.
Given that :
One segment measures 161 cm
To find the multiple according to the number 3, divide 161 by 3.
161 ÷ 3 = 53.67
Nearest integer of 53.67 is 54
The multiple according to the number 3 = 54 × 3
= 162
To find the submultiple according to the number 7, divide 161 by 7.
161 ÷7 = 23
Nearest integer of 23 is 23
The submultiple according to the number 7 = 161 ÷ 23
= 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
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Mia' plant grow at an average rate of 5cm each month. When he bought it, it wa 18 cm tall. Select the function that model the relationhip between y, the height of the plant in cm, and x, the time in month that it grow. A. Y = 18x 5
B. Y = 18 5x
C. Y = x 18
D. Y = 23x
The function that models the relationship between plant height (y) and growth time (x) is y = 18 + 5x
The linear equation of two variables
The two-variable linear equation is a solving system for a mathematical problem in which there are two case variables.
In the problem, we get the info that the plant's initial height is 18 cm, meaning this value will not change.
We also get information that the height of the plants increases by 5 cm every month, meaning this value will change over time. If x is the growth time (in months), then the increase in height over time can be written mathematically as 5x.
Based on the two statements above, if y is the plant height (in cm) after x months, then mathematically it can be written as:
y = 18 + 5x
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What is the equation of the line that passes through the point (8, 6) and has a slope
of o?
Answer:
y=6
Step-by-step explanation:
The equation of a line in slope-intercept form is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis. In this case, we are given that the line passes through the point (8, 6) and has a slope of 0, so we can plug these values into the equation to find the equation of the line.
Since the slope of the line is 0, the equation of the line becomes:
y = 0x + b
To find the value of b, we need to plug in the coordinates of the point (8, 6) into the equation and solve for b. This gives us:
6 = 0 * 8 + b
b = 6
Therefore, the equation of the line is given by:
y = 0x + 6
This equation tells us that the y-coordinate of any point on the line is always 6, regardless of the x-coordinate of the point. This means that the line is horizontal and passes through the point (8, 6).
Hi can you please help me like rnn
js 1 & 2 for now
Step-by-step explanation:
1.
it is always the same.
the usual equation of a line is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
we see that the y-value is +3 when x = 0. that is "b".
for the slope we pick 2 points (with integer coordinates, if possible).
I see e.g. (0, 3) and (3, 0)
x changes by +3 (from 0 to 3).
y changes by -3 (from 3 to 0).
the slope "a" is -3/+3 = -1
the equation is
y = -x + 3
2.
and again the same
we see that the y-value is -3 when x = 0. that is "b".
I see e.g. (0, -3) and (3, 0) as points.
x changes by +3 (from 0 to 3).
y changes by +3 (from -3 to 0).
the slope "a" is +3/+3 = 1.
the equation is
y = x - 3
A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink receipts totaled $360, and 4 times as many cold beverages were sold as hot beverages.
Which system of linear equations represents the beverage sales on Saturday?
4c = h
1.5c + 2h = 360
c = 4h
1.5c + 2h = 360
c + h = 360
1.5c = 4(2h)
c + h = 360
4(1.5c) = 2h
Answer:4c=h
Step-by-step explanation:
The first linear equation, 4c=h
Julia decided to pend 5 1/4 hour exerciing over the weekend. She pent 3 1/3 hour exerciing on Saturday. How much longer doe he need to pend exerciing on Sunday in order to reach her goal?
Julia needs to spend 1.92 hours exercising on Sunday in order to reach her goal.
The number of hours Julia needs to spend exercising on Sunday can be calculated as follows;
Total number of hours to spend exercising = 5 1/4 = 21/4 = 5.25 hours
Total number of hours spent exercising on Saturday = 3 1/3 = 10/3 = 3.33 hours
Now the number of hours she needs to spend exercising on Sunday can be determined by subtraction as follows;
Hours on Sunday = Total hours - Hours on Saturday
Hours on Sunday = 5.25 hours - 3.33 hours
Hours on Sunday = 1.92 Hours
Thus the number of hours she needs to spend exercising on Sunday is calculated to be 1.92 hours.
Although a part of your question is incorrect, you might be referring to this question:
Julia decided to spend 5 1/4 hours exercising over the weekend. She spent 3 1/3 hours exercising on Saturday. How much longer doe he need to spend exercising on Sunday in order to reach her goal?
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Kane i training for a marathon. He tart running 3 mile during every training eion. Each week he plan to increae the ditance of hi run by 1/4 mile. Let w be the number of week. Write an expreion to how the ditance Kane run in a training eion after w week
The expression to which the distance Kane run in a training session after w week is {3+(1÷4)w}...
Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week.
Let w be the number of week.
So the expression is formed as that in 1st week if he sart running 3 miles and after every week 1/4 miles added ,it's mean 1 by forth part of one mile is added after every week so if;
we suppose that we have to calculate it for "w" weeks then these weeks will be multiply with 1/4 and then added to the starting miles which are 3 miles
So the expression will be:
{3+(1÷4)w}
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Your question is may be misspelled it will be...(Kane is training for a marathon. He start running 3 miles during every training session. Each week he plan to increase the distance of his running by 1/4 miles. Let 'w' be the number of week. Write an expression to how the distance Kane run in a training session after 'w' weeks?
how many of your 500 clients would you expect to have major depressive disorder (mdd)? if you used the phq-2 to screen for mdd, what number of those who are depressed would screen positive? among those who screened positive, what number would you expect to be confirmed for mdd at the follow-up visit?
As per the unitary method, the number would you expect to be confirmed for MDD at the follow-up visit is approximately 166.
The term unitary method in statistics refers a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Here we have to find how many of your 500 clients would you expect to have major depressive disorder and if you used the phq-2 to screen for MDD, what number of those who are depressed would screen positive.
In order to find the number of patients with MDD, we must know the process of PHQ - 2.
The process of PHQ - 2 involves the following steps:
Here the score ranges from 0-6.
And if the score is 3 or greater, then major depressive disorder is likely.
Based on these we have to test the 500 with PHQ test, let us consider that there is 2 person in every two person has MDD.
So, the number of MDD patient is approximately 166.
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what is the slop of this question
Answer:
slope = 6
Step-by-step explanation:
(0,6)
(1,12)
12-6
-------- = 6
1-0
Can You pls solve this problem
Write an equation of the line that passes through (-2, 4) and is perpendicular to y = -2x + 4
Answer:
y=-2x
Step-by-step explanation:
g. 390, 702 and 468 lcm of the following
Answer:
7020
Step-by-step explanation:
2÷390,702,468
2÷195,351,234
3÷
PLEASE HELP!!
Find c.
Round to the nearest tenth:
Answer:48
Step-by-step explanation:
The ratio of red marble to blue marble in a bag i 3:4. If there are 42 marble in the bag how many of the marble are red
The ratio of red marble to blue marble in a bag is 3:4. If there are 42 marble in the bag,There would be 30 red marbles in the bag.
Red and blue marbles are distributed in a 3:4 ratio.This means that for every 4 blue marbles, there are 3 red marbles.
If we divide 42 (the total number of marbles in the bag) by 4, we get 10.5. This tells us that if there are 4 blue marbles, there are 10.5 red marbles. We can't have a fraction of a marble, so we round down to 10.
Since for every 4 blue marbles there are 3 red marbles, if there are 10 blue marbles, there must be 10 x 3 = 30 red marbles.
Therefore, there are 30 red marbles in the bag.
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Here are the scores for two softball teams for seven innings. Each team's total score is the sum of the numbers in its row. Rosie's Riveters beat The Susan Bees by how many runs?
A baseball scoreboard with the points marked for Rosie's riveters versus The Susan bees.
The team of Rosie's Riveters beat the Susan Bees by 3 runs.
What is Addition?Addition is one of the four basic operations of arithmetic's. The other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.Given are the scores for two softball teams for seven innings.
The total score of Rosie's Riveters will be -
T{R} = 1 + 3 + 4 + 2 + 1 + 0 + 2 = 13
The total score of Susan Bees will be -
T{S} = 0 + 0 + 5 + 3 + 0 + 1 + 1 = 10
Now -
T{R} - T{S} = 13 - 10 = 3
T{R} - T{S} = 3
Therefore, the team of Rosie's Riveters beat the Susan Bees by 3 runs.
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A student takes an exam. The ratio of her right answers to her wrong answers is 11 to 3. Which of the following could describe this situation?
Answer:
She answered 9 wrong and 33 right.
Step-by-step explanation:
Choices:
She answered 9 wrong and 33 right.
She answered 33 wrong and 9 right.
She answers 14 wrong and 22 right.
She answered 22 wrong and 14 right.
11:3 = 22:6 = 33:9 = 44:12 = 55:15 = 66:18 = 77:21 = 88:24 = ...
33 right 9 wrong works.
Answer: She answered 9 wrong and 33 right.
Which statements proved that the two triangles are using the SSS similar theorem?a. its corresponding sides has a proportional ratio of 1/2
b. its corresponding sides has a proportional ration is 1/3
c. its corresponding sides has a proportional ration is 1/4
d. its corresponding sides has a proportional ration is 1/5
Option B is the correct answer. corresponding sides have a proportional ratio is 1/3 of the sss theorem.
If two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. This is called the SSS Similarity Theorem.
when the three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar, it is also called SSS Similarity Theorem.
SSS Theorem png
If ABYZ=BCZX=ACXY , then ΔABC∼ΔYZX .
Considering triangles have 3 sides, having each side has a 1/3 ratio will make it congruent to the other triangle.
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