The inverse of the function as it has been written is f(x) = (x - 32) 5/9.
What is the inverse of the function?We know that the inverse of a function can easily be obtained as long as we have the function as we do in the question here. The function has been given to us as; f(x)=9/5 x + 32.
Let y = f(x)
Hence;
y=9/5 x + 32
y - 32 + 5/9 = x
We would then have the inverse of the function as;
f(x) = (x - 32) 5/9
This is the procedure that would help us to obtain the inverse of the function that have been given here.
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Missing parts;
Given f(x)=9/5 x + 32, find the following;
Inverse of the function
A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of 8 dollars.
What proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars?
The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars are 0.0099.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the datas are arranged in a symmetrical bell shaped graph.
Given that,
Mean, μ = 87
Standard deviation, σ = 8
We have to calculate P (104.60 < x < 108.20).
For that find z score.
z = (x - μ) / σ
At x = 104.60, z = (104.60 - 87) / 8 = 2.2
At x = 108.20, z = (108.20 - 87) / 8 = 2.65
From the z table,
P(z < 2.65) = 0.9960 and P(z < 2.2) = 0.9861
P (104.60 < x < 108.20) = 0.9960 - 0.9861 = 0.0099
Hence the proportion is 0.0099.
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Select 2 fractions that are equivalent to 1
Step-by-step explanation:
2/2
23/23
749876/749876
...
you did not show us any fractions to select.
a fraction is always 1, when the value on the top is the same value as on the bottom.
There are 4 boys and 4 girls. In how many ways they can sit in a row
(i) there is no restriction.
(ii) not all girls sit together.
(iii) no two girls sit together.
If there are 4 boys and 4 girls , then the number of ways in which
(i) there is no restriction is 40320 ways ,
(ii) not all girls sit together is 37440 ways ,
(iii) no two girls sit together is 2880 ways .
the number of boys in the class is = 4 boys ;
the number of girls in the class is = 4 girls ;
Part(i) ,
we have to find number of ways in which they can sit in a row where there is no restriction .
there are total of 8 persons ,
So ,the number of ways in which 8 persons can be arranged without any restrictions is = 8! ways.
= 40320 ways
Part(ii) ,
we have to find number of ways in which they can sit in a row where not all girls sit together.
the cases where all gets sit together is written as :
= B₁ , B₂ , B₃ , B₄ , G ⇒ 5! ways ;
= B: G₁ , G₂ , G₃ , G₄ ⇒ 4! ways ;
the number of ways all girls are together is = 5! × 4! ;
So , the number of ways not all girls are together is = 8! - 5!×4! ;
= 37440 ways
Part(iii) ,
we have to find number of ways in which they can sit in a row where no two girls sit together.
this case can be denoted as : G , B₁ , G , B₂ , G , B₃ , G , B₄ .
So , the boys can be arranged in 4! ways ;
and there will be 5 places for 4 girls , which can be arranged in ⁵P₄ ways ;
total number of ways is = 5!×4! = 2880 ways .
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15 cm
5 cm
4 cm
3 cm
Find the lateral surface area of the solid above.
Answer here
The answer for lateral surface area of the Triangular prism is 180 cm²
What is Lateral Surface Area?Any solid object's lateral area can be calculated using the lateral area formula. Any figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as the cuboid, cube, cylinder, cone, and sphere, is made easier using lateral area formulas.
The lateral area for a triangular prism
A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Additionally called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.
The total of the three regions is the triangular prism's lateral area. Consequently, the triangular prism's lateral area formula is
Triangular prism lateral surface area (LSA) = ah + bh + ch (or) (a + b + c) h.
We are aware that the perimeter of the base is (a + b + c) (triangle). Hence,
Triangular prism's lateral surface area (LSA) is equal to the product of the base's perimeter and the prism's height.
base perimeter × height
Explanation
The Given Image of the solid is Matching to a prism.so we are calculating the lateral surface area of the prism
The dimensions of each base are:
a = 5cm
b = 4 cm
c = 3 cm
The height of the triangular prism = 15cm.
Thus, the lateral area of triangular prism = (a + b + c ) h
= (5 + 4 + 3) 15
= (12) 15
= 180 cm²
Answer: The lateral area of the given triangular prism = 180 cm²
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a random sample of n people selected from a large population will be asked whether they have read a novel in the past year. let the random variable r represent the number of people from the sample who answer yes. the variance of random variable r is 6. assume the responses are independent of each other. if the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable r ?
If the proportion of people from the population who read a novel in the past year is 0.40, then a binomial variable with 25 independent trials is the best interpretation of random variable R. So the option 2 is correct.
If the proportion of people from the population who read a novel in the past year is 0.40, then we have define which of the following is the best interpretation of random variable R.
The variance of random variable R is 6.
The variance of binomial distribution is:
var = np(1-p)
n = number of trials
p = the probability
6 = n × 0.40 × (1-0.40)
6 = n × 0.40 × 0.60
6 = n × 0.24
Divide by 0.24 on both side, we get
n = 25
The number of binomial trails is 25.
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The complete question is:
A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ?
1. A binomial variable with 15 independent trials
2. A binomial variable with 25 independent trials
3. A variable that is not binomial with 25 independent trials
4. A binomial variable with 40 independent trials
5. A variable that is not binomial with 40 independent trials
I am a 3 digit number All of my digits are even numbers greater than 1 My hundreds digit is greater than my tens digit My tens plus mu hundreds digit is equal to my ones digit you can get my tens digit if you multiply a number by 3. What number am I
HE hundred digit less than the tens digit ,the tens digit is has to 9 .This is because of 9is the only positive integer less than 10 and only it also greater than 8 in one digit numbers. result when 8 is subtracted from it.
What is meant by positive?When you have an optimistic outlook on life, you have optimism and confidence and focus more on the positives than the negatives.
Be optimistic about the future and carry on with your normal life.
A positive person chooses to focus on the positive aspects of their life, finds delight in the little things, and adopts the mindset that while there are many things outside of their direct control, they can select what they choose to give their attention to.
According to one idea, having a positive outlook makes it easier for you to handle stressful situations, which lessens the negative consequences of stress on your body's health.
we already know that ones digit is 5 less than the tens digit, so it is 9-5=4,and the hundreds digital has to be 1, so the answer is 194.
so, let we can solve it as by the problem,
by the problem
units will be considered as a x
ok
x greater than or equal 9
tens digit digit is more than 5 units
we know that,
so, tens digit value is 9
hundreds digit value is 1
let we find ones digit value x+5<=9
x<=4
hundreds digit is less than
x+5
x+5-8>=0
x-3>=0
x>=3
>3=4
thus the x is 4
then the number is 194
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Evaluate this expression using order of operations when x=1.5 7.5 - 2 ÷ (4x - 2)
Please help I don’t get how to answer this !!
The length of sides in congruent triangles are MN=30, MP=18, PN=30
How to find MN, MP, PN, PS?QR=30, RS=30, SQ=18
In the diagram two congruent triangles are given ΔPMN ≅ ΔQSR.
So by CPCTC (corresponding parts of congruent triangles are congruent)
In ΔPMN and ΔQSR
PN=QR=30 in.
PM=SQ=18 in.
MN=RS= 30 in.
PN=QR=30 then PN=30
PM=SQ =18 then PM=18
MN=RS =30 then MN=30
Congruent triangles are the triangles of which all the sides and all the angles are congruent.
If two triangles are said to be congruent then its all corresponding parts must be equal.
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< Question 8 of 42
Macmillan Learning
>
Arrange the given numbers from largest to smallest.
Largest
0.51
7.6
10²
5.6
105
4.9
10-3
Smallest
Answer Bank
From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
What is Descending order?
Descending order can be defined in such a way that the order is from largest to smallest.
Given numbers are ,
0.51 , 7.6 , 10^2 , 5.6 , 105 , 4.9 , 10^-3
10^2 = 10*10 = 100 .
so a^m = a multiplied by m times .
a^-m = 1/ a^m.
10^-3 = 1/1000 = 0.001
So,
We have to write from largest to smallest
we get,
105,100,7.6,5.6,4.9,0.51,0.001
Hence, From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001
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solve this system of equations by using the elimination method.
2x+y=4 x+3y=2
Answer:x=1 y=5
Step-by-step explanation:
The question is in the image below
Answer:
y=4/3x-3
Step-by-step explanation:
By using rise/run, you can see the slope in the equation, as it goes 4 units up and 3 units to the right.
For the y-intercept, you can see that the line intercepts (0,-3), which makes it the y-intercept.
Answer: y=-3+4/3x
Step-by-step explanation:
You get -3 because that is the point on the y axis
You get 4/3x from rise every additional point after
-------
run
the owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. the following data with waiting times in minutes were collected over a one-month period. 9 11 3 12 11 4 3 3 4 24 13 22 5 18 6 9 12 23 15 2 (a) develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24.
Classes Frequency
0-4 7
5-9 5
10-14 2
15-19 4
20-24 1
The frequency of each class is determined by counting the number of waiting times that fall within each range. For example, the class 0-4 has a frequency of 7, meaning 7 customers waited between 0 to 4 minutes for their oil change.
The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.
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FOR WHICH INEQUALITY IS Z = 3 A SOLUTION??/
The inequality is z = 3 a solution. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (A), the inequality is given as follows:
z+5 ≥ 9
z ≥ 9 - 5
z ≥ 4
As per option (B), the inequality is given as follows:
z+5 > 9
z > 9 - 5
Apply the subtraction operation,
z > 4
As per option (C), the inequality is given as follows:
z + 5 ≤ 8
z ≤ 8 - 5
z ≤ 3
Since the solution is less than or equal to three,
Then, this inequality is z = 3 a solution.
Hence, the correct answer would be option (C).
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This question seems incomplete, the complete question would be as:
For which inequality below is z = 3 a solution?
A. z+5 ≥ 9
B. z+5 > 9
C. z+5 ≤ 8
D. z+5 <8
problem solving you go on a hayride to take photographs of landmarks. the map shows your path and two landmarks. each unit in the coordinate plane corresponds to 10 yards. approximate your minimum distance from the giant pumpkin. if necessary, round your answer to the nearest tenth.
The minimum distance from the giant pumpkin is 8.9 yards.
We will use the minimum distance formula between a line and a point to obtain the distance in this case.
A linear function is given according to the standard notation by:
Ax+By+C=0
A point with 'x' and 'y' coordinates are given by:
P(x*,y*)
The formula to find the shortest distance between a point and a line is denoted by the formula:
d=|Ax*+By*+C|/√(A²+B²)
In this issue, the path's line includes:
When x = 0, and y = 0, the intercept is 0.
0.5 slope means that when x rises by 4, y rises by 2.
Thus, y=1/2x
-1/2x+y=0
or, -x+2y=0
The coefficients of the line are:
A=-1 and B=2
Coordinates of the giant pumpkin is (x*,y*)=(-4,-3)
Therefore, the minimum distance is:
d=|(-1)(-4)+2(-3)|/√5
or,d=2/√5
or, d=0.89 units
We know, 1 unit=10 yards
or, 0.89 units=8.9 yards
Thus, the minimum distance between a point and a line is 8.9 yards.
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suppose that 22 inches of wire cost 66 cents. how much will 38 inches of wire cost in cents?
Answer:
114 cents
Step-by-step explanation:
1. 66÷22=3 cents per inch
2. 3×38=114
3. 114 cents ($1.14) for 38 inches
Consider the two triangles shown below. Which of the triangle congruence theorems could be used to prove the triangles are congruent?
The triangles are congruent by ASA theorem.
How to find congruent triangle?Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. In other words, congruent triangles are triangles that have the same size and shape.
Therefore, If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA(angle side angle).
Therefore, the triangle are congruent by ASA(angle side angle)
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the distribution of the time it takes for different people to solve a certain suduko puzzle is strongly skewed to the right, with a mean of 30 minutes and std of 15 minutes. the distribution of z-scores for those times is:
The distribution of z-scores would be a normal distribution centered at 0, with a standard deviation of 1.
The distribution of time it takes for people to solve a certain Sudoku puzzle is strongly skewed to the right. This means that most people take a shorter amount of time to solve the puzzle, but some take a longer amount of time. The mean (average) of this distribution is 30 minutes and the standard deviation is 15 minutes.
To find the distribution of z-scores, we need to convert the times into z-scores, which is done by subtracting the mean (30) from each time and then dividing by the standard deviation (15). This gives us a new distribution of z-scores, which is centered at 0 (since the mean of the times was subtracted from each time) and has a standard deviation of 1.
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In each figure for what values of x and y is the figure a parallelogram
The values of x and y that makes the figure a parallelogram are x = 17 and y = 26
How determine what values of x and y makes the figure a parallelogram?
A parallelogram is a four-sided geometric shape that has opposite sides that are parallel to each other.
The opposite sides of a parallelogram have the same length, and the opposite angles are also equal. The opposite sides of a parallelogram are also known as the bases, and the other two sides are known as the legs.
Since the opposite sides of a parallelogram are equal in length, we can say:
3x + 6 = 4 - x
3x + x = 4 - 6
4x = -2
x = -2/4
x = -1/2 = -0.5
y + 2 = 2y - 3
2 + 3 = 2y - y
5 = y
y = 5
Likewise, the opposite angles of a parallelogram are equal, so we can say:
(4x - 12)° = (3x + 5)°
4x - 12 = 3x + 5
4x - 3x = 5 + 12
x = 17
(3y + 46)° = (5y - 6)°
3y + 46 = 5y - 6
46 + 6 = 5y - 3y
52 = 2y
2y = 52
y = 52/2
y = 26
Thus, x = 17 and y = 26 makes the figure a parallelogram
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The Treasury Department auctioned $26. billion in 3-month bills in denominations of $10,000 at a discount rate of 5.250%. What would be the effective rate of interest? Note: Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent. Effective rate of interest %?
Answer:
5.35%
Step-by-step explanation:
3 month 5.25%
So 4 times a year
(1+5.25%/4)^4 = 1.0535
So effective rate is 5.35%
Geometry I don’t understand
The value of x is -20 and can be calculated using basic proportionality theorem.
What is Basic Proportionality Theorem?The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the well-known Greek mathematician Thales.
Basic Proportionality Theorem asserted that the ratio of any two related sides is always the same for any two equiangular triangles.
Thales provided the basic proportionality theorem based on this idea (BPT). Similar triangles have introduced this idea before. If two triangles resemble one another, then
The corresponding angles of both triangles are equal.
The corresponding sides of both triangles are proportional to one another.
Since the ratio of other side pair is 1:1, similarly 4x+20 = 3x
20 = 3x-4x
20 = -x
x = -20
Therefore, the value of x is -20
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Please help as soon as possible.
The translation of point A to point B is done by translation vector (- 3, - 6).
How to determine the translation vector
In this problem we find the a point that is part of a rectangle and that must be translated by means of a rigid transformation formula, that is, a translation formula that does not alter the features of the rectangle. We need to determine the translation vector by means of the following formula:
T(x, y) = B(x, y) - A(x, y)
Where:
A(x, y) - Initial pointB(x, y) - Final pointT(x, y) - Translation vectorIf we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:
T(x, y) = (3, 3) - (6, 9)
T(x, y) = (- 3, - 6)
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Evaluate the expression using the given value of the variable:[ z + (-1 (z - x)) ]; use [x = 4], and [z = 5] .
Answer:
[z+(-1( z-x))]
given,
z=5 X=4
[5+(-1(5-4))]
[5+(-1x(1))]
5+(-1)
5-1
4
Which of the following statements about quadrilaterals are true? Select each correct answer. Responses All squares are rhombuses, but not all rhombuses are squares. All, , squares, , are, , rhombuses,, , but, , not, , all, , rhombuses, , are, , squares., EndFragment, Opposite angles in a parallelogram are congruent. Opposite, , angles, , in, , a, , parallelogram, , are, , congruent., EndFragment, The diagonals of a rectangle are perpendicular.
All of the statements about quadrilaterals that are true include the following:
A. all squares are rhombuses, but not all rhombuses are squares.
B. opposite angles in a parallelogram are congruent.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumGenerally speaking, a typical characteristics of all squares are rhombuses is simply that all squares are classified as rhombuses, but it is not all rhombuses that are classified as squares.
Additionally, the opposite angles of any parallelogram are always congruent because they form parallel lines. However, the diagonals of a rectangle, parallelogram, and trapezium are not perpendicular.
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4. Trevor's science class is studying the rainfall
on the first day of each month for one
year. Explain why studying the rainfall on
the first day of September, October, and
November is not a random sample.
The reason studying the rainfall on the first day of September, October, and November is not a random sample is: These are three consecutive months.
What is random sample?Random sample can be defined as the type of sample in which some number of people or group of people are choose from a large population when conducting a test.
The reason why studying the rainfall on the first day of September, October, and November is not a random sample was because the September, October and November are three consecutive months.
Based on this the sample should be spread out to the entire year and should include more than three months.
Therefore these are three consecutive months.
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please help me with math i’ll give you brainlist
Answer:
1. Funnel cakes- 12
2. Oreos- 21
Step-by-step explanation:
1. x= 42/3.50
x=12
2. y= 42/2
y= 21
Four friends shared the cost of a pizza dinner. They ordered 1 large pizza for $17.50, 4 sodas for $1.25 each, and 4 salads. Salads normally cost $1.75 but were on sale: "Buy one, get one free." If the friends split the total cost of dinner equally, what was each person's share?
Answer:
$6.50
Step-by-step explanation:
So writing out everything
1 Pizza = $17.50
1 soda = $1.25
1 salad = $1.75
Exception; Salad is buy 1 get 1 free, so only 2 salads were paid for
Now we multiple
1 Pizza * 17.50 = 17.50
4 soda * 1.25 = 5
2 salad * 1.75 = 3.50
Now we add
17.50 + 5 = 22.50 + 3.50 = $26.00
Now lastly, we divide by 4 since there are 4 friends
26/4 = 6.5
Giving us a answer of $6.50
Vectors: Find the vector from the point (-4,8,7) to the point (6,5,5).Enter the coordinates (_, _, _)Equations of lines: Consider the vector equation of the line through the two points listed above. For each equation listed below, answer T if the equation represents the line, and F if it does not. Here is the list of questions:1. (x,y,z) = (-4,8,7) + t (-10,+3,+2)2. (x,y,z) = (6,5,5) + t (10,-3,-2)3. (x,y,z) = (-4,8,7) + t (6,5,5)4. (x,y,z) = (-4,8,7) + t (10,-3,-2)5. (x,y,z) = (6,5,5) + t (-4,8,7)
The direction vector from the point (-4,8,7) to the point (6,5,5) is (10, -3, -2). The equations which represent the line are: 1. True 2. True 3. False 4. True 5. False.
The direction vector for the line that passes through the two points A (-4,8,7) and B (6,5,5), the position vector of point A is subtracted from the position vector of point B, hence:
v = AB = (6 –(-4), 5 – 8, 5 – 7) = (10, -3, -2)
The vector equation of the line is given by:
r = r0 + tv
where r0 is position vector, t is a scalar parameter, and v is position vector.
Considering the vector equation, the equation which represents the line are:
1. (x,y,z) = (-4,8,7) + t (-10,+3,+2); True
2. (x,y,z) = (6,5,5) + t (10,-3,-2); True
3. (x,y,z) = (-4,8,7) + t (6,5,5); False
4. (x,y,z) = (-4,8,7) + t (10,-3,-2); True
5. (x,y,z) = (6,5,5) + t (-4,8,7); False
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jahdiel is waxing a hardwood floor that has an area of 4 3/8 square yards. He takes a break aftr waxing 8/9 of the total area of the floor. What is the area, in square yards,that jahdiel waxed? write your answer as a mixed fraction in simplest form.
The amount of hardwood floor that Jahidel waxed is 3 8/9 yards²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of hardwood floor that Jahidel waxed be A
Now , the equation will be
The total area of the hardwood floor is = 4 3/8 yards²
The total area of the hardwood floor is = 35/8 yards²
The amount of floor waxed by Jahidel A = ( 8/9 ) x total area of the hardwood floor
Substituting the values in the equation , we get
The amount of floor waxed by Jahidel A = ( 8/9 ) x ( 35/8 ) yards²
On simplifying the equation , we get
The amount of floor waxed by Jahidel A = ( 35/9 ) yards²
The amount of floor waxed by Jahidel A = 3 8/9 yards²
Hence , the amount of floor waxed is 3 8/9 yards²
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State if the two triangles are congruent. If they are, state how you know.
Correct the right choice
HL
LL
AAS
cannot be determined
According to the figure the two triangles congruency state cannot be determined
D. cannot be determinedWhat does triangular congruency mean?Triangles are considered congruent when their sides and angles match those specified by the triangle congruency rules.
The triangle congruency rules.
Side - Side - Side = SSS.
Angle - Side - Side = SAS
Side - Angle - Angle = ASA
Angle, Angle, and Side = AAS
Hypotenuse plus one leg = HL
To demonstrate that the triangles are congruent, the is need for three parameters to be known except for right triangle
In the problem, only two parameters can be deduced the side and the angle equal by vertical angle theorem
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Will mark Brainliest!! The table shows the city bus schedule for certain bus lines. Both buses are at the bus stop right now. In how many minutes will both busses be at the bus stop again?
Table is A=25 minutes
Table is B=15 minutes
Answer:
75 minutes
Step-by-step explanation:
You want to know when both buses will be at the stop again if bus A arrives every 25 minutes, and bus B arrives every 15 minutes.
Least common multipleThe number of minutes until both buses are at the stop again is the least common multiple (LCM) of their arrival times.
Factors of the times are ...
25 = 5·5
15 = 3·5
A common multiple must have all of these factors, so will have factors ...
LCM = 3·5·5 = 75
After 75 minutes, both buses will be at the stop again.
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Additional comment
You can see that 5 is a common factor of the two numbers. The LCM can also be found as the product of the two numbers, divided by their greatest common factor (GCF).
LCM(a, b) = a·b/GCF(a, b)
LCM(15, 25) = 15·25/5 = 75
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