Write the absolute value equations in the form |x-b|=c(where b is a number and c can be either number or an expression) that have the following solution sets:
One solution: x=15

No, All 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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Pure maths can be quite challenging. It requires the ability to think logically and to understand complex concepts.

What is pure math?

Pure mathematics is the branch of mathematics that deals with abstract concepts, such as numbers and equations, that are not related to any physical objects or phenomena. It is the study of abstract concepts and properties, including number theory, geometry, algebra, and analysis. Pure mathematics is used in many areas of mathematics, such as applied mathematics, which is the use of mathematical techniques for solving real world problems.

It also requires knowledge of calculus, geometry and trigonometry, as well as problem-solving and analytical skills. Pure maths is often used in physics, engineering and computing, making it a valuable tool for anyone in these disciplines. However, mastering pure math takes practice and dedication, as it can be difficult.

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AAS stands for Angle Angle Side

SSA stands for Side Side Angle

AAS Theorem (Angle-Angle-Side Theorem) states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent. This theorem is important because it allows us to determine if two triangles are congruent without having to know all three sides and all three angles.

SSA Theorem (Side-Side-Angle Theorem) states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. This theorem is important because it allows us to determine if two triangles are congruent without having to know all three sides and all three angles.

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The solution of the given system of equations 8x+3y=5 and 3x-2y=5 is x = 1 and y = -1

In this question we have been given a system of equations.

8x+3y=5                 ..........(1)

and 3x-2y=5           ..........(2)

We need to find the solution of the given system of equations.

As right hane side of both equations is equal, we equate LHS of both equations.

so, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - y                      .............(3)

By substituting x = - y in equation (1), we get,

8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 1

Substitute above value of y in equation (3)

⇒ x = - (- 1)

⇒ x = 1

Therefore, x = 1 and y = -1 is solution of given equations.

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Answer:

D. 16y – 20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

16y^2-16y-4(-4y+5+4y^2)

16y^2-16y+16y-20-16y^2

16y^2-20-16y^2

16y^2-16y^2-20

-20

Answer:

{x element R : x!=-sqrt(5) and x!=0 and x!=sqrt(5)}

(assuming a function from reals to reals)

So b:)

Step-by-step explanation:

Add all of the numbers together and then divide that by how many numbers there are.

Mean mode formula  - Mean = {Sum of Observation} ÷ {Total numbers of Observations}

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

              A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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The perimeter of the triangle is 35.0 inches

We should know that perimeter of an object is the distance round the very object.  the triangle has three sides, then the perimeter of the trianggle is the sum of the three sides.

Hence the altitude forms a right angled triangle, there are two right angled triangles.

Using  the Pythagoras theorem, let the two sides of the triangle be x and y

X²=13²+4²    (the altitude divided the base into 2)

x²=169+16

x²=185

Taking the square root of both sides

x=[tex]\sqrt{185}[/tex]

x=13.6 inches

For the length y

Use the same Pythagoras theorem

X²=13²+4²

x²=169+16

x²=185

x=13.6 inches

The perimeter is 8+13.6+13.6 = 35.2 inches

Therefore, the  perimeter of the triangle to the nearest tenth is 35.0 inches

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IQ scores follow a normal distribution, with a mean of 100 and a standard deviation of 15. Approximately 68% of people have IQ scores in the range [85,115].

In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.

Here,

In this example, the population mean is 100 and the standard deviation is 15. Based on the 68-95-99.7 Rule, approximately 68% of the individuals in the population have an IQ between 85 and 115. Values in this particular interval are the most frequent.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. About 68% of individuals have IQ scores in the interval [85,115] .

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Answer:

It's B, and the last one

Step-by-step explanation:

because 20% of omnivores like to exercise as opposed to the 14% of vegetarians.

Also about 16% of everybody LIKES to exercise, meaning more than 80% DON'T like to exercise

The equation 6p = 2(52p) getting no solution.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.

6p = 2(52p)

First, divide both sides by 2

6/2p = 2(52p)/2

3p= 52p

3= 52

No solution.

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As per the solenoid turn the measure of the current is written as 23.45

Here we have given that the inductor in is a 9.0-cm-long, 2.0-cm-diameter solenoid wrapped with 300 turns.

And we need to find the measure of the current flow.

While we looking into the given question, here we have given that  

Here the

R refers resistance of resistor = 30 Ω

V refers voltage of battery = 6.0 V

s refers length of solenoid = 9.0 cm = 0.09 m

d refers diameter of solenoid = 2.0 cm = 0.02 m

N refers number of turns of wire = 300

μ0 refers permeability of free space = 12.56 x 10⁻⁷ H/m

Then the flow of the current is calculated as,

=> [4π x 10⁻⁷ x 300  x 12.56 x 10⁻⁷] / 2 x 10⁻²

When we simplify this one then we get the result as,

=> 23.45

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The Factors of the given quadratic equation "3x² -x -4" is (3x - 4)(x + 1)  .

The Factors of a quadratic equations  is defined as the number which when multiplied together gives the original equation .

the equation is given as : 3x² -x -4 ;

writing it as equation ,

we get , 3x² -x -4 = 0 ;

To write the factors we use split the middle term method , we get ;

⇒ 3x² +3x -4x -4 = 0 ;

⇒ 3x(x [tex]+[/tex] 1) -4(x [tex]+[/tex] 1) = 0

⇒ (3x - 4)(x [tex]+[/tex] 1) = 0 ;

Therefore , the factors of the given equation will be (3x - 4)(x + 1) .

The given question is incomplete , the complete question is

What is the factor of the quadratic Equation 3x² -x -4 ?

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As per the concept of dot plot the team never scored exactly 2 goals in a single game.

In math the term dot plot which is also known as a strip plot or dot chart is referred as a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.

Here we have given that goals scored per game a dot plot going from 0 to 5. 0 has 3 dots, 1 has 2 dots, 2 has 0 dots, 3 has 5 dots, 4 has 3 dots, 5 has 8 dots.

And we need to find a true statement about the dot plot.

As we know that these types of charts are used to graphically depict certain data trends or groupings.

Here we know that the team never scored exactly 2 goals in a single game, based on this we can says the team never scored exactly 2 goals in a single game and the dot plot shows 0 dots in number 2.

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The range is { -5, -3, 7 }

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). A function's range is the set of possible values that it can accept. The values that the function outputs when we enter an x value are in this set.

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }

The complete question is : What is the range of the function y=2x-3 when the domain is {-1,0,5}

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Answer:

15/2

Step-by-step explanation: Have a nice day

Population of ants is 10,000 at the start of April. since then, it triples each month. Now, the calculated values become -

a) Table is complete below.

b) Notice that in every month there is an increase of 3 times population from month to month.

c) There are 8,10,000 ants in 4 months from April.

d) In the month of 6, there are 72,90,000 no. of ants.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population in statistics is the group of people from which a statistical sample is taken for a research.

Month since April                                   Number of Ants

         0                                                         10,000

         1                                                         30,000

         2                                                         90,000

         3                                                        270,000

         4                                                         810,000

Every month, the ant population triples so the multiply the previous population by 3 to find out the new population.

0 months from April = 10,000 × 1 = 10,000 ants

1 month from  April = 10,000 × 3 = 30,000 ants

2 months from April = 30,000 × 3 = 90,000 ants

3 months from April = 90,000 × 3 = 2,70,000 ants

4 months from April = 270,000 × 3 = 8,10,000 ants.

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The zeros of function f(x) = x2 - 5x + 6 are 3 and 2.

We can calculate the zeros of a polynomial using the quadratic equation.

The equation is:

x = [-b ± √(b2 - 4ac)] ÷ (2a)

In this case,

a = 1,

b = -5, and

c = 6.

Substituting these values into the equation, we get:

x = [-(-5) ± √((-5)2 - 4(1)(6))] ÷ (2(1))

Simplifying further, we get:

x = [5 ± √1] ÷ 2

Finally, we get:

x = 3 and 2

Therefore, the zeros of function f(x) = x2 - 5x + 6 are 3 and 2.

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A group of clearly defined objects or elements make up a set. A collection of numbers is known to as an element and forms up a set.

A collection of numbers is known to as an element and forms up a set. The set of numbers can either be an endless or a limited collection. Using "{" and "}" with the elements separated by commas is one way to represent a set in roster notation; for example, the set {5,29} has the elements 5 and 29.

A group of clearly defined objects or elements make up a set. The cardinal number of a set is shown in a curly bracket next to the capital letter symbol for a set, which denotes the number of elements in a finite set.

Sets of integers are among the most frequent types of sets in mathematics. Numbers come in a wide variety of forms. We have natural numbers, whole numbers, integer numbers, rational numbers and real numbers.

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Answer:

Answer Below

Step-by-step explanation:

A rhombus is a quadrilateral with 2 diagonals.

Answer:

A soultion is provided that makes assumptions about missing information.  

Step-by-step explanation:

The statement ". . . each goose gets 16 oz . . ." is missing some information about a time frame.  Is it 16 oz per day, week, month?  The question cannot be answered without this information.  

We also don't know the relationship between the number of seeds and ounces.  Is 16 oz 1 seed, 10 seeds, 1000 seeds?  Again, we cannot solve this without additional information.

To add some insight how to solve the problem, lets make two assumptions:

Assume 16 oz/week.  We can write this as a conversion factor:  (16 oz food)/(1 snow goose).

Assume 10 seeds/oz.

The Rescue Center has 1,656 seeds in total.  

(1,656 seeds)

Each snow goose gets 16 oz of seeds a week.  That is (16 oz)*(10 seeds/oz) = 160 seeds/week per goose.

There are 9 geese, so they consume (9 geese)*(160 seeds/week/goose) = 1440 seeds/week

There are 1,656 seeds.  At 1,440 seeds/week, they will last (1,656 seeds)/(1,440 seeds/week) = 1.15 weeks.

The snapshot of the graph of the function d(x, t=0s) of the wave is illustrated below.

The term function in math referred as a relation between a set of inputs having one output each.

Here we have given that d(x,t=0s) of this wave at t=0s.

And we need to find graph of the function

While we looking into the given question we have identified that the history graph of the wave is given at distance is written as,

=> x=2m

Then the velocity of the wave is given as v= 1 m/.sec

Here we have identified the wave is traveling to the right.

Then snapshot graph shows the displacement of the wave with respect to the position at a given time whereas a history graph shows the displacement of the wave with respect to the time at a given position.

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Answer:

Step-by-step explanation:

jjj

Children should be able to recite the letters and alphabets typically by the age of three.

An alphabet is a standardized system of fundamental written graphemes that correspond to the phonemes of certain spoken languages. a group of letters or other symbols used to write one or more languages, especially if they are organized in a regular sequence. a set of symbols or signals used to represent letters.

Children should be able to recite the letters typically by the age of three. All kids, nevertheless, are unique. While some toddlers may learn when they are two, others might not begin until they are late in the third year. The majority of the time, repetition is how kids pick up the alphabet.

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I.

The measure of the angle that is complementary to the angle 20° is 70°, 67° is 23°, 14° is 76°, 81° is 9° and 45° is 45°.

The sum of the complementary angles is 90°

Thus,

The complement of the angle 20° is 90°-20°=70°

The complement of the angle 67° is 90°-67°=23°

The complement of the angle 14° is 90°-14°=76°

The complement of the angle 81° is 90°-81°=9°

The complement of the angle 45° is 90°-45°=45°

II.

The measure of the angle that is supplementary to the angle 120° is 60°, 56° is 124°, 29° is 151°, 162° is 18° and 83° is 97°.

The sum of the supplementary angles is 180°

Thus,

The supplement of the angle 120° is 180°-120°=60°

The supplement of the angle 56° is 180°-56°=124°

The supplement of the angle 29° is 180°-29°=151°

The supplement of the angle 162° is 180°-162°=18°

The supplement of the angle 83° is 180°-83°=97°

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Answer:

x = 26

Step-by-step explanation:

Angles ABC and CBD are supplementary, so they add up to 180.

(2x - 10) + (5x +8) = 180

7x - 2 = 180

7x = 182

x = 182/7 = 26

Answer:

You could graph the points and recognize that it's a quadratic equation.

If you solve for the equation, it is clear that this table follows the relation:

[tex]f(x)=x^2-1[/tex].

Step-by-step explanation:

The picture attached shows the graph.