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No, two equilateral triangles need not to be always congruent with one another .

Justification of answer:

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

1. All 3 side of an equilateral triangles have same length .

2. All 3 angles of an equilateral triangles have same measure.

3. Each angles of an equilateral triangles is 60 degree .

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

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The factor form of 3x² 10x 3 is 3x(x+3)(x-3). This is because 3x² 10x 3 can be factored into three linear terms: 3x(x+3)(x-3).

Factor is a quantity or an expression that is multiplied to another quantity or expression to obtain a product. Factors are used in mathematics to solve problems involving multiplication, division, and equations. Factors can also be used in financial analysis to calculate interest payments, loan repayments, and other financial transactions. Factors can also be used to analyze supply and demand, market trends, and other economic indicators.
This is achieved by using the 'FOIL' method, which stands for First, Outer, Inner, Last. The first two terms, 3x and x+3, are multiplied together to give 3x². The outer two terms, 3x and x-3, are multiplied together to give 3x-9. The inner two terms, x+3 and x-3, are multiplied together to give x²-3. The last two terms, 3x² and x²-3, are added together to give 3x² + x²-3 = 3x² + 10x - 3.
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The coefficient of variation is 200%.

The coefficient of variation is the ratio of the standard deviation to the mean. One form of measure of dispersion is the coefficient of variation. A number called a measure of dispersion is used to assess the degree of data variability. As a result, the coefficient of variation is used to assess how much data deviate from the mean or average value. The acronym CV stands for coefficient of variation.

Given that,

Arithmetic mean = 10
Standard deviation = 20

Therefore of coefficient of variation is SD/AM*100 = 20/10*100 = 200%

Hence, the coefficient of variation is 200%.

Correct question: If the arithmetic mean is 10 and the standard deviation is 20 then what is the coefficient of variation?

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Answer: 6.3 hours

Step-by-step explanation:

I have attached an image of how I solved it!

Answer:

Step-by-step explanation:

(6t - 3ax)(t+ ax)

use FOIL

6[tex]t^{2}[/tex] +6tax - 3tax -3[tex](ax)^{2}[/tex]

6[tex]t^{2}[/tex] + 3tax - 3[tex](ax)^{2}[/tex]

If any two angles and 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 the two triangles are said to be congruent.

There are 5 main rules of congruency for triangles:

Three Ways To Prove Triangles Congruent:

SSS (Side-Side-Side) Postulate: If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.

SAS (Side-Angle-Side) Postulate: If there exists a correspondence between the vertices of two triangles such that the two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

ASA (Angle-Angle-Side)Postulate: If there exits a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

By using these rules, If two angles and one side of a triangle are respectively equal to two angles and the matching side of another triangle, then the two triangles are congruent.

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Linear equations are easy to solve .They are a type of mathematical equation that involve one or more variables, in which all terms are of the first degree.

The general form of a linear equation is Ax + B = C, where A, B and C are numerical coefficients and x is a variable. Linear equations can be solved by first rewriting the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Then, the y-intercept can be determined by substituting in a value for x and solving for y. To find the slope, two points on the line must be chosen, and the formula            m = (y2 - y1)/(x2 - x1) is used to calculate the slope. Once the slope and y-intercept are known, the equation can be written in its slope-intercept form and solved for x.

Linear equations can also be solved using the substitution method, where one of the variables is substituted with a numerical value. This method can be used when the equation is already written in its standard form, Ax + B = C. By solving for x, the value of x can be found and substituted back into the equation to find the value of C.

Finally, linear equations can also be solved using the elimination method, which is used when there are two linear equations with two unknowns. The two equations are added together, and the coefficients of one of the variables are eliminated. This method is useful for solving systems of linear equations.

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Answer: 22.5 gallons of gas

Step-by-step explanation:

1 1/2 = 3/2 or 1.5

Take 1.5 divided by 10 = 0.15 gallon per mile

Then take 0.15 times 150 miles = 22.5 gallons of gas

To find the zeros and poles of a function, you can use the following steps:

Generally, It's also important to note that a function can have multiple zeros and poles, and they can be complex numbers as well as real numbers. In that case, you can use the same steps above to find all of the zeros and poles.

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CQ

How do you find the zeros and poles of a function?

continuous function can be represented by a graph without holes. A function whose graph has holes is a discontinuous function

Hole is a point on the graph where the value of the function is not defined. If the numerator and denominator of a rational function have a common factor they will cancel when simplifying.

Therefore to find the hole of a function is to consider numerator and denominator. If there is the same factor in the numerator and denominator there is a hole.

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Answer:

222222222222222222222%

Answer: A = 67%

Step-by-step explanation:

Answer: w = 4

Step-by-step explanation:

To solve the equation 10(w+3) = 70, we will work to get w by itself:

1. Divide by 10. This will get us closer to w.

(10( w + 3))/10 = 70/10

w + 3 = 7

2. We now have the equation w + 3 = 7. All we need to do now to get w by itself (or isolate it) is to subtract 3.

(w + 3) - 3 = 7 - 3

w = 7 - 3

w = 4

3. We can check our solution by inputting our found value, w = 4, into the equation.

10( 4 + 3 ) = 70

10(7) = 70

70=70

Because both sides of the equation are true, our solution of w = 4 is correct.

Answer: w = 4

Step-by-step explanation:

10(w+3)=70

10w + 30 = 70

10w = 40

w = 4

Answer:

∠ 6 = 38°

Step-by-step explanation:

∠ 6 and 38° are vertically opposite angles and are congruent , then

∠ 6 = 38°

The slope of the line is  [tex]m = \frac{4}{5}[/tex]

slope using standard form:

[tex]m = \frac{4}{5}[/tex]

slope m of a line of the form Ax + By = C, equals -[tex]\frac{A}{B}[/tex]

A = 4 , B = -5

[tex]m = - \frac{4}{-5}[/tex]

Therefore;

[tex]m = \frac{4}{5}[/tex]

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A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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Answer: 3.6

Step-by-step explanation:

20/100= 1/5

1/5*18=18/5 or 3.6

Answer:

Twenty percent of 18 is 3.6. To find 20% of a number, simply multiply the number by 0.20. For example, 20% of 18 can be calculated by multiplying 18 by 0.20, which gives us 3.6.

Step-by-step explanation:

[tex]{\huge{G = \frac{P-2M}{2} }}[/tex]

The solutions of the given quadratic equation are -1/2 and 4

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is a quadratic equation, 2x²-7x-4 = 0

Factoring,

2x²-8x+x-4 = 0

2x(x-4)+1(x-4) = 0

(2x+1)(x-4) = 0

x = -1/2

x = 4

Hence, The solutions of the given quadratic equation are -1/2 and 4

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Yes, a function can have no holes when it has no common factor at both numerator and denominator.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).

In Mathematics, a hole can be defined as a point on the graph wherein the input value of a given function is undefined or not defined. This ultimately implies that, a hole is a point on the graph of a rational function where the input value causes both its numerator and denominator to be equal to zero (0).

In conclusion, we can reasonably infer and logically deduce that it is very possible for a function to have no holes.

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1. Always (by definition)

2. Always (triangle inequality)

3. Always (Pythagorean theorem)

4. Sometimes (take x=y=1 and x=4, y=3)

5. Never (by definition)

6. Sometimes (Only if area = circumference)

7. Sometimes (Consider when scale factor = 1)

8. Never (Lines extend infinitely)

9. Sometimes (Only if both angles are right angles)

10. Always (Angle-angle similarity)

Information can not be determined by histogram.

What is histogram?

A histogram is an approximation of the distribution of numerical data. This term was first introduced by Karl Pearson. The first step in creating a histogram is to "bin" (or "bucket") the range of values. That is, divide the entire range of values ​​into a series of intervals and count the number of values. At each interval fall. Bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be contiguous and often (but not necessarily) the same size.

If the bins are the same size, bars are drawn across the bins, with heights proportional to frequencies (number of cases in each bin). Histograms can also be normalized to display "relative" counts, which indicate the proportion of cases falling into each of multiple categories with sum of heights equal to 1.

Information can not be determined by histogram.

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Answer:

Step-by-step explanation:

84848093

Answer:

  22098

Step-by-step explanation:

You want the difference between the largest and smallest 5-digit numbers whose digits are from the set {1, 2, 3} and include each of these at least once. The numbers cannot be divisible by 2 or 3.

The number will be divisible by 3 when its sum of digits is a multiple of 3. Since 1, 2, and 3 are prescribed digits, the remaining two digits must not have a total of 3 or 6. The largest possible remaining digits are {2, 3}, and the smallest remaining digits are {1, 1}. (Using {3, 3} for the largest digits would give a number divisible by 3.)

The number will be divisible by 2 if the least significant digit is 2. The largest and smallest digits are not 2, so that will not be an issue.

The largest number will place the largest available digit in the place with the highest place value: 33221.

The smallest number will place the smallest available digit in the place with the highest place value: 11123.

The desired difference is the difference of these numbers:

  33221 -11123 = 22098 . . . . difference of largest and smallest

The difference between the two numbers will be 1998.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

Given that Consider five-digit integers that have the following properties. Each of the digits is 1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not divisible by 2 nor divisible by 3.

The largest number will be 3211.

The smallest number will be 1213.

The difference between the largest and the smallest number will be calculated as,

D = 3211 - 1213

D = 1998

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Answer:

[tex]y=\frac{1}{2}x+4[/tex]

Step-by-step explanation:

[tex]y-3=\frac{1}{2}(x+2) \\ \\ y-3=\frac{1}{2}x+1 \\ \\ y=\frac{1}{2}x+4[/tex]

Answer: y = 1/2 x + 4

Step-by-step explanation:

1) They gave you the slope so: y= 1/2x + b

2) Goes through point (-2,3) so: 3 = 1/2(-2) + b

3) 3 = -1 + b

4) b = 4

5) answer: y = 1/2x + 4

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Answer:

Step-by-step explanation:

If you're wondering about what percent of 212 is 400, the answer is 189.3%. This means that 400 is 89.3% higher than 212. It’s easy to see that, when compared side by side, 400 is a much bigger number, almost twice as great as 212. Put another way, if you divide 400 by 212, you get 1.89—that’s your answer! Clearly, 400 is a great deal larger than 212 and this difference in size can be expressed as a percentage increase of 189.3%.

Approximately 19.05% of 212 is 400.

Answer:

Step-by-step explanation:

Solution for 212 is what percent of 400:

212:400*100 =

(212*100):400 =

21200:400 = 53

Now we have: 212 is what percent of 400 = 53

Question: 212 is what percent of 400?

Percentage solution with steps:

Step 1: We make the assumption that 400 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=400$.

Step 4: In the same vein, $x\%=212$.

Step 5: This gives us a pair of simple equations:

$100\%=400(1)$.

$x\%=212(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{400}{212}$

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{212}{400}$

$\Rightarrow x=53\%$

Therefore, $212$ is $53\%$ of $400$.  

the answer is 53 or 188.68%

A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.

A continuous function in mathematics is a function without discontinuities, or any sudden changes in value. If we can guarantee arbitrarily small changes in the input of a function by limiting small enough changes, then the function is continuous.

There is no function that is always discontinuous. A function is either continuous or discontinuous at a particular point, but it is not necessarily either one at all points.

For example, the function f(x) = x^2 is continuous at all points, but the function g(x) = |x| is discontinuous at x=0.

On the other hand, there are functions that are discontinuous at an infinite number of points, such as the Dirichlet function, which is defined as follows:

f(x) = { 1 if x is irrational

{ 0 if x is rational

This function is discontinuous at all rational points, but it is continuous at all irrational points

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The function f(x) = x^2 is continuous at all points, but the function g(x) = |x| is discontinuous at x=0.

On the other hand, there are functions that are discontinuous at an infinite number of points, such as the Dirichlet function, which is defined as follows:

f(x) = { 1 if x is irrational

{ 0 if x is rational

This function is discontinuous at all rational points, but it is continuous at all irrational points

Answer:

See explanation

Step-by-step explanation:

Answer:

Thus there are 3150 ways to select the 2 faculty members and 4 students for the committee.

Step-by-step explanation:

In math set refers the collection of unique objects that is no two objects can be the same.

In a set, the objects that belong in a set are called members or elements. And the elements of set can be anything that is numbers, animals, sport teams.

In order to represent the Sets either we have to List out the elements that are separated by commas and enclosed by curly brackets

For example,

W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Otherwise, we have to specify in words that objects in the set must have certain characteristics/properties by describing elements using words proves useful when we are describing sets of large sizes.

For example,

N = {Even numbers between 1 and 25}

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