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The concept of zero was used by Indian mathematicians.

It was developed in India

1. History of the concept of zero:

a. The concept of zero was used by Indian mathematicians as early as the 5th century AD, including Aryabhata and Brahmagupta.

b. It was developed in India, and then spread to the Middle East and Europe.

c. The concept of zero was important during this time in history because it revolutionized mathematics by allowing for more complex calculations and the development of algebra. It also had implications for astronomy and navigation.

d. The use of zero changed the way people did math by allowing for the development of place value notation and the ability to represent numbers using a positional system. This made arithmetic and higher level mathematics much easier and more efficient.

2. Teaching of the concept of zero:

a. Teachers, family and friends typically teach the concept of zero in early elementary school through the use of counting, number lines and place value charts.

b. A tip for teaching the concept of zero is to use visual aids such as drawings, diagrams or objects to help illustrate the concept. It can also be helpful to use real-life examples to demonstrate the importance and usefulness of zero.

3. Everyday use of the concept of zero:

a. Adults use the concept of zero in everyday life when dealing with money, measurements, and other numerical calculations. For example, when making change, measuring ingredients for a recipe, or calculating interest on a loan.

b. Teenagers use the concept of zero in many of the same ways as adults, but also in areas such as computer programming, where zero is often used as a placeholder or to represent an absence of data. It is also used in video games, where scores often start at zero and increase as the player progresses.

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Answer:

Step-by-step explanation:

i have know idea #87;9

How we can find out the inequality graph for number line in the given chart, that shows by the specific values.

It is a solid line and a portion of area is shaded which satisfy the condition of the inequality of the values.

The graph inequality define as per rules, the <, ≤, >, or ≥ sign and as an = sign, and graph the equation. If the graph inequality is < or >, the graph equation as a dotted line. If the graph inequality is ≤ or ≥, graph the equation as a solid line. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not.

The graph inequality on each number lines are:

Values of x:  x = (-5, 4]  or we can also define as  -5 < x ≤ 4

Values of r:  r = [1, 3)  or we can also define as  1 ≤ r < 3

Values of y:  y = (-∞, -2) ∪ [2, ∞)

Values of z:  z = (-∞, -3] ∪ (0, ∞)

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The empty squares in the addition chain can be completed thus:

1. 3 + 0 + 11 = 14

2. -1 + 5 = 4

3. -9 + 1 + 2 = -6

For the middle part;

1. 14 + 4 = 18

2. 4 + (-6) = -2

For the last part;

18 + (-2) = 16

In order to complete the empty squares, a knowledge of the additive inverse will be required. This states that + x - x = 0. In that vein, we can calculate the negative and positive figures aright.

For instance, in the third square, we have an equation of this sort:

-9 + 1 + x = -6

Now, we know that -9 + 1 is equal to -8

The expression becomes;

-8 + x = -6

Make x the subject of the formula:

x = -6 + 8

x = 2.

Now we can fill in the missing box with the figure 2.

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Answer:

80

Step-by-step explanation:

Simplifying the expression  (3ab/4xy) ÷ (-21a²b/10x²y) = -5x/14a

A mathematical expression is a relationship that does not contain an equality sign.

Since we have the expression (3ab/4xy)/(-21a^2b/10x^2y), we desire to simplify it.

We proceed as follows

(3ab/4xy) ÷ (-21a²b/10x²y) = 3ab/4xy × 10x²y/-21a²b

Expanding out the factors, we have

(3ab/4xy) ÷ (-21a²b/10x²y) = 3ab/4xy × 10x²y/-21a²b

= 3 × a × b/(4 × x × y) × 10 × x × x × y/(-21 × a × a × b)

=  3 × a × b/(2 × 2 × x × y) × 2 × 5 × x × x × y/(-3 × 7 × a × a × b)

Canelling out the common factors, we have that

= 3 × 2 × a × b × x × 5 × y × x/(3 × 2 × 2  × a × b × x × y × -7 × a)

Cancelling out 3 × 2 × a × b × x × y, we have that

= 5 × x/(2 × -7 × a)

= 5x/-14a

= -5x/14a

So,  (3ab/4xy) ÷ (-21a²b/10x²y) = -5x/14a

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A relationship have the same constant of proportionality between y and x as the equation 3y = 27x include the following: A, B, and C.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the required equation as follows:

3y = 27x

y = 27x/3

y = 9x

By multiplying both sides of the equation by 2, we have:

y = 9x

2y = 18x

Constant of proportionality, k = 9/1 = 9.

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The probability of getting at most 329 miles on a tank of gas is indeed 0.841345 or 84.1345%.

This means that there is a high likelihood that you will be able to drive at least 329 miles on a tank of gas. However, it is important to note that probability is not a guarantee, and there is still a small chance that you may not be able to drive the full 329 miles on a single tank of gas. It is always a good idea to keep an eye on your gas gauge and plan your trip accordingly to ensure that you do not run out of gas.

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To prove that triangle ABC is congruent to triangle ADC, we need to show that all three pairs of corresponding sides and all three pairs of corresponding angles are congruent.

We can begin by observing that both triangles share the common side AC. Therefore, we can start by showing that the two triangles share the same length of AC.

Next, we can show that both triangles have a right angle at C. This means that angle BCA and angle DCA are complementary and add up to 90 degrees.

Finally, we need to show that the length of sides AB and AD are equal. We can do this by using the Pythagorean Theorem.

Let x be the length of AB and y be the length of AD. Then we have:

AC^2 + x^2 = BC^2 (from the Pythagorean Theorem in triangle ABC)

AC^2 + y^2 = DC^2 (from the Pythagorean Theorem in triangle ADC)

Since both triangles share the common side AC, we can subtract the two equations to eliminate AC^2, which gives us:

x^2 - y^2 = BC^2 - DC^2

But we know that BC = DC, since both triangles share the common side AC. Therefore, we can simplify the equation to:

x^2 - y^2 = 0

This implies that x = y, since both x and y are positive lengths. Therefore, we have shown that the length of sides AB and AD are equal.

In summary, we have shown that:

Corresponding side AC is shared by both triangles and has the same length.

Corresponding angles BCA and DCA are both right angles.

Corresponding side AB and AD have the same length.

Therefore, by the Side-Angle-Side (SAS) congruence criterion, triangle ABC is congruent to triangle ADC.

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The expression of a in terms of b is given as (b + 2)/[3absin150° - (b + 2)] using the areas for triangles A and B,

area of triangle A = (absin150°)/2

area of triangle B = (a + 1)(b + 2)/2

Given that the area of triangle B is 3 times the area of triangle A, then;

(a + 1)(b + 2)/2 = 3(absin150°)/2

we shall make a the subject as follows:

(a + 1)(b + 2) = 3absin150° {denominators will cancel out}

(a + 1)/a = (3absin150°)/(b + 2) {cross multiplication}

divide all terms by a at the left hand side

1 + 1/a = (3absin150°)/(b + 2)

subtract 1 from both sides

1/a = (3absin150°)/(b + 2) - 1

1/a = [3absin150° - (b + 2)]/(b + 2) {simplify to a single fraction}

by cross multiplication

a = (b + 2)/[3absin150° - (b + 2)]

Therefore, using the areas for triangles A and B, the expression of a in terms of b is given as (b + 2)/[3absin150° - (b + 2)].

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The segment length indicated is given as follows:

? = 8 units.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Applying the Pythagorean Theroem, the diameter of the circle is given as follows:

12² + d² = 20²

d = sqrt(20² - 12²)

d = 16 units.

The radius is half the diameter, hence it is given as follows:

r = ? = 0.5 x 16 = 8 units.

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Answer:
5/13= sinΘ
since tanΘ = 5/12 and tanΘ= Perp/base
perp = 5
base= 12
use pythagorean theorem

H2= P2 + B2
H=13 by putting values.
now sinΘ= Perp/hypo
so sinΘ= 5/13

Step-by-step explanation:

i) There are the following combinations in all:

    9 × 9 × 9 × 9 × 9 = 59,049

ii) There are the following combinations in all:

    9 × 8 × 7 × 6 × 5 = 15,120

iii) There are the following combinations in all:

    8 × 8 × 8 × 8 × 5 = 16,640

(i) If repetition of digits is allowed and the number 6 is not used, there are 9 possible digits that can be used for each of the 5 positions. Hence, there are the following combinations in all:

9 × 9 × 9 × 9 × 9 = 59,049

(ii) If repetition of digits is not allowed and the number 6 is not used, there are 9 possible digits for the first position, 8 possible digits for the second position (since one digit has already been used), 7 possible digits for the third position, 6 possible digits for the fourth position, and 5 possible digits for the fifth position. Hence, there are the following combinations in all:

9 × 8 × 7 × 6 × 5 = 15,120

(iii) If repetition is allowed and Mike wants his combination to be an even number, then the last digit must be either 0, 2, 4, 6, or 8. There are 8 possible digits (0, 1, 2, 3, 4, 5, 7, 8) that can be used for each of the first four positions, since the digit 6 cannot be used. Hence, there are the following combinations in all:

8 × 8 × 8 × 8 × 5 = 16,640

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The approximate solutions are x ≈ 1.225 and x ≈ -1.225.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To solve this equation, we need to isolate the variable x on one side of the equation.

2x² - 9 = -6

Add 9 to both sides:

2x² = 3

Divide both sides by 2:

x² = 3/2

Take the square root of both sides:

x = ±√(3/2)

We can approximate this value using a calculator or by expressing 3/2 as a decimal:

x ≈ ±1.225

Therefore, the approximate solutions are x ≈ 1.225 and x ≈ -1.225.

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Answer:

1/3

Step-by-step explanation:

[tex]\frac{1}{6} * 2 = \frac{1}{6} * \frac{2}{1}[/tex]

multiply across to get: [tex]\frac{2}{6}[/tex]

reduce to get 1/3

For a normal distribution with mean of 100 and standard deviation of 20, we can use the z-score formula to find the requested values. The z-score formula is z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation.

a)   Using a z-table, we find that the z-score for the 20th percentile is -0.84. So, solving for x, we get:

-0.84 = (x - 100) / 20
x - 100 = -16.8
x = 83.2

b)  For x = 110, the z-score is (110 - 100) / 20 = 0.5. For x = 120, the z-score is (120 - 100) / 20 = 1. Using the z-table, we find that the percentile for z = 0.5 is 69.15% and the percentile for z = 1 is 84.13%. The difference between these percentiles is the proportion of cases that fall between these values, so:

84.13% - 69.15% = 14.98%

c) For x = 90, the z-score is (90 - 100) / 20 = -0.5. Using the z-table, we find that the percentile for z = -0.5 is 30.85%. The percentile for z = 1 (corresponding to x = 120) is still 84.13%, so the difference between these percentiles is:

84.13% - 30.85% = 53.28%

d) For x = 80, the z-score is (80 - 100) / 20 = -1. Using the z-table, we find that the percentile for z = -1 is 15.87%. Since we want to find the number of cases that fall above this score, we need to subtract this percentile from 100%:

100% - 15.87% = 84.13%

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Answer: To determine the number of different ways a new car can be ordered with regard to these options, we need to use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

In this case, we have 5 options to consider: color, air conditioning, automatic transmission, power windows, and CD player. Let's assume that there are k different options for each of these features. For example, there may be 5 different color options, 2 options for air conditioning, 2 options for automatic transmission, 2 options for power windows, and 2 options for a CD player.

Using the multiplication principle, we can determine the total number of ways a new car can be ordered by multiplying the number of options for each feature together:

Total number of ways = k x k x k x k x k = k^5

Therefore, the total number of different ways a new car can be ordered with regard to these options is equal to k raised to the power of 5. The actual value of k will depend on the number of options available for each feature, but we can use this formula to calculate the total number of possible order combinations.

Step-by-step explanation:

The rate of change of the function is -4, as the change in y (from 15 to 11 and then to 7) is -4 for each unit change in x (from 1 to 2 and then to 3).

A unit is a standard measure of a quantity. It is a normalized quantity used as a reference to compare other measurements. Units are used in mathematics, science, engineering, and many other disciplines. The most common units of measure are length, mass, volume, time, and temperature. Other quantities, such as electric current and light intensity, also have their own units. Units are important because they provide an easy way to express the size and type of a measurement.

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Answer:

Step-by-step explanation:

The formula for the area of a trapezoid is:

A = ((b1 + b2) / 2) * h

where A is the area, b1 and b2 are the lengths of the parallel sides, and h is the height.

Rearranging this formula to solve for h, we get:

h = 2A / (b1 + b2)

Plugging in the given values, we get:

h = 2(35mm²) / (b1 + b2)

Since we don't have enough information to find the lengths of the parallel sides or the value of their sum, we cannot determine the height of the trapezoid with just this information.

The area of the polygon = 21 square units

To calculate the area of an object, we need to identify the shapes that are embedded in the image.

From the image, I can get 2 triangles. Using the formula for finding the area of a triangle, we can find the area of the given polygon.

A = 1/2 x b x h

where b = base

h = height

triangle A has base of 6 units and height of 4units

triangle B has base of 6 units and height of 3 units

Area of A = 1/2 x 6 x 4 = 12 square unit

Area of B = 1/2 x 6 x 3 = 9 square unit

Total area will be area of triangle A + area of triangle B

= 12 + 9 = 21 square unit.

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Teddy used the perfect square trinomial pattern, but the difference of squares pattern is the proper method to factor x² - 49.

Teddy made an error in factoring x² - 49 by assuming that both terms in the binomial are perfect squares. This is not true, as only the second term (-49) is a perfect square.

To factor this expression correctly, we can use the difference of squares pattern, which states that a² - b² = (a+b)(a-b).

In this case, a² is x² and b² is 49, which is the perfect square of 7. Thus, we can write:

x² - 49 = (x+7)(x-7)

So, the correct factored form of x² - 49 is (x+7)(x-7). This is because when we expand the product of (x+7)(x-7), we get:

(x+7)(x-7) = x² - 7x + 7x - 49 = x² - 49

So, the correct way to factor x² - 49 is to use the difference of squares pattern, not the perfect square trinomial pattern that Teddy used.

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The geometric mean of the numbers are 9.8 and 10.3

Question 1

From the question, we have the following parameters that can be used in our computation:

8 and 12

The geometric mean is calculated as

Mean = √8 * 12

Evaluate the expression

Mean = 9.8

Question 2

From the question, we have the following parameters that can be used in our computation:

8.5 and 12.4

The geometric mean is calculated as

Mean = √8.5 * 12.4

Evaluate the expression

Mean = 10.3

Hence, the geometric means are 9.8 and 10.3

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Answer:

x = 68°

Step-by-step explanation:

here it is of surely we're finding for x

Answer:

  15 V

Step-by-step explanation:

You want the voltage across parallel resistor R2 when the current through 30 Ω parallel resistor R1 is 0.5 A.

The voltage across resistor R1 is the product of its resistance and the current through it:

  E = IR

  E = (0.5A)(30Ω) = 15 V

All of the branches of a parallel circuit have the same voltage across them. The voltage across R2 is 15 V.

To determine which expressions have a positive value based on the positions of a and b, we need to consider the signs of a and b and then evaluate each expression:

(-b) is positive if b is negative

(a+b) is positive if both a and b are positive or if a is negative and b is greater than the absolute value of a

(a-b) is positive if a is greater than b

(ab) is positive if both a and b have the same sign (either both positive or both negative)

(-b) is negative if b is positive

(a) is positive if a is positive

So, based on the positions of a and b, the expressions that have a positive value are:

(a+b), if both a and b are positive or if a is negative and b is greater than the absolute value of a

(a), if a is positive

Therefore, the correct answers are:

a+b

a

The length of the arc of the given circle will be equal to:

B. 3.05 cm

The length of the arc of a circle is calculated with the formula:

Length of arc = θ/360 × 2πr

Where the angle is given as 25°

Pie = 22/7 (another way to express this is 3.14) and

Radius = 7 cm

The 2 is a standard for the calculation of the circumference of a circle.

Substituting the values in the equation will yield:

25/360  × 2  × 22/7  × 7cm

= 3.05 cm

So, the length of the arc in the given circle is 3.05 cm.

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The value of x is 10.

Triangle is a plane figure with three angles and three straight sides.

Given information: In ΔABC, AD is the angle bisector, AB = 8, BD =( x+4),

DC = (2x+1), and AC = 12

The angle bisector theorem states that an angle bisector divides the opposing side of the triangle into two segments that are proportional to the other two sides.

In ΔABC, AD is an angle bisector, By using the angle bisector theorem, we get

BD/DC = AB/BC

(x+4) / (2x+1) = 8/12

By Cross Multiplying, we get

12(x+4) = 8(2x+1)

12x + 48 = 16 x + 8

After solving the above equation we get,

4x = 40

x = 10 (By Dividing 40 by 4 )

Therefore the value of x is 10.

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Answer: The answer is B

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

[tex]-6 - (-4)[/tex]

Expand the parenthesis using the Distributive Law:

[tex]-6+4[/tex]

[tex]-6[/tex] is written first, therefore it is represented by the first arrow. This arrow is the one drawn at the bottom. The starting point is [tex]0[/tex] and extends six units to the left. The left direction is because [tex]6[/tex] has a negative sign.

[tex]+4[/tex] is to be represented by the second arrow, which is drawn at the top. This extends four units to the right from [tex]-6[/tex] . This arrow is pointing in the right direction because [tex]4[/tex] has a positive sign

∴Option B

The standard normal distribution is a normal distribution addressed in z scores. It generally has a mean of nothing and a standard deviation of one.

P[Z>z] = 0.350

Subsequently, z=0.385......................by utilizing Z table or Succeed order =NORMSINV(1-0.35)

P[Z<z]=0.950

Subsequently, z=1.645.......................by utilizing Z table or Succeed order =NORMSINV(0.950)

The standard deviation of the z-scores is generally 1. The diagram of the z-score distribution generally has a similar shape as the first distribution of test values. The sum of the squared z-scores is dependably equivalent to the quantity of z-score values.

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Answer: 6 1/2 in

Step-by-step explanation:

6 3/4 - 1/4 = 6 2/4 = 6 1/2