‘Basic exponent rules’ simplifying to a single power .

If the Set A is denoted by the set of elements  {1,2,3}  , then the number of ordered pairs that it can have is 9  .

The Ordered Pair is defined as a pair formed by two elements which are separated by comma and written inside the parentheses .

For Example : the (x,y) represents a ordered pair .

The Ordered Pairs can be obtained by developing a function or by performing the operation which is called as Cartesian product.

The set A is given as : {1,2,3} ;

the ordered pair can be written as : [tex](1,1) , (2,2), (3,3) , (1,2) , (1,3) , (2,1) , (2,3) , (3,1) , (3,2) .[/tex]

Therefore , The number of ordered pairs formed of Set A are 9 .

The given question is incomplete , the complete question is

How many ordered pairs can be formed from the set A = {1,2,3} ?

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A triangle's exterior angle is the product of its interior opposing angles.

Exterior angles are those that run parallel to a polygon's exterior angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.

At each vertex, there are two equivalent exterior angles.

Each vertex often only shows one external angle, though.

A triangle's exterior angles have these three essential qualities:

(1) A triangle's corresponding and exterior angles pair together to form a linear pair of angles. The inner and exterior angles therefore total up to 180 degrees.

(2) The size of a triangle's external angle is equal to the sum of its two diametrically opposed internal angles. The exterior angle theorem is another name for this property.

(3) A triangle's outside angles add up to a total of 360.

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Answer: 3

Step-by-step explanation:

Maximum number of bracelets Tara can make is 6.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Tara has a plastic string that is 3 3/4 feet.

And, She will cut the string to make bracelets that are each 5/8 feet long.

Now,

To find maximum number of bracelets Tara can make, we can draw the point at equal distance 5/8 feet to reach 15/4 feet.

Then, Calculate the number of points to draw which is equal to the maximum number of bracelets Tara can make.

That is,

Maximum number of bracelets Tara can make = 15/4 ÷ 5/8

                                                                        = 15/4 × 8/5

                                                                        = 6

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His monthly payment, to the nearest dollar, if the loan is taken over 25 years is $1,978.54

Mortgage is a loan taken out to purchase a property. It is usually secured against the value of the property with the lender having the right to repossess the property if the loan is not repaid.

The fixed monthly payment for a mortgage can be calculated using the following formula:

Monthly Payment = [P x R(1+R)^N]/[(1+R)^N-1]

P = Principal Amount

R = Monthly Interest Rate

N = Total Number of Payments

Where Interest Rate is the interest rate per annum, Principal Loan Amount is the amount of money borrowed, and Term in Months is the duration of the mortgage loan in months.

Solution:

Monthly Payment = [$420,000 x (0.03/12)(1 + 0.03/12)^300]/[(1 + 0.03/12)^300 - 1]

Monthly Payment = $1,978.54

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Therefore , the solution of the given problem of triangle comes out to be  angle is 58°  is third angle.

Since a triangle has four or even more sections, it is a polygon. It has an easy geometric form. Triangle ABC refers to a square with edges A, B, and C. A single plane or square are produced by Euclidean geometry when the edges are not collinear. A triangle is a polygon if it has three sides & three corners. Where a triangle's three sides come together are known as the corners. A triangle's angles add up to 180 degrees.

Here,

Given :

A triangle has given angles ,

To find the angle :

=> x + 98° + 24° = 180°

=> x = 180° - 122°

=> x = 58°

Thus , angle is 58° .

Therefore , the solution of the given problem of triangle comes out to be  angle is 58°  is third angle.

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The variable for the number of wraps and the number of gift bags are x and y.

A linear function can be used to depict a straight line on the coordinate plane. The equation y = 3x - 2 serves as an illustration of a linear function since it represents a straight line in the coordinate plane.

Nonlinear functions are those whose graphs do not follow a straight line. A graph of it can be any curve other than a straight line.

A quadratic function is an illustration of a non-linear function.

Let, The number of wraps be 'x' and the number of gift bags be 'y'.

Therefore, From the given information x + y = 25 and 6x + 2y = 110.

Solving this linear system graphically we have an intersection (x, y)

at (15, 10).

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Answer:

------------------------

Given system:

Plot each line and find the intersection, this is the solution.

The solution is (-4, - 4) as per attached graph.

On solving the provided question, we can say that by addition new total cost  = 36    52    76   92

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

here,

Number of portrait sheet = 1        3         6          8                                                                    

Total cost =                           33      49       73        89

A, This year the price of the basic package increased by $3.

so new total cost              =    36    52            76          92

here,

we use addition                      

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The point of intersection is (1, 0, -2)

To find the point where the line through (-1, 1, -8) and (5, -2, 10) crosses the ZX plane, we need to find the point on the line that has a y-coordinate of 0.

We know that the equation of a line in 3D space is given by:

P = P0 + t(P1 - P0)

where P0 is a point on the line, P1 is another point on the line, t is a scalar parameter, and P is a variable point on the line.

We can substitute in the coordinates of the two given points for P0 and P1:

P = (-1, 1, -8) + t((5, -2, 10) - (-1, 1, -8))

and set the y-coordinate to 0:

1 + t(-3) = 0

t = 1/3

so the point of intersection is:

P = (-1, 1, -8) + (1/3)((5, -2, 10) - (-1, 1, -8))

P = (-1, 1, -8) + (1/3)((6, -3, 18))

P = (-1, 1, -8) + (2, -1, 6)

P = (1, 0, -2)

So the point of intersection is (1, 0, -2)

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The correct answer is B.

Given that the hypotenuse of the right triangle is as given then;

i. α = 56^o

ii. Adjacent = 2.80

iii. Opposite = 4.15

A right triangle is a type of triangle which has only one of its internal angles equal to 90^o. Thus the hypotenuse is opposite to the greatest angle, while the second long side is opposite to the greater angle, and the shortest side opposite to the measure of the least angle.

Applying the Pythagorean theorem to the triangle, we have;

i. The sum of angles in a triangle is 180^o. So that;

α + 34 + 90 = 180

α + 124 = 180

α = 56^o

ii. Let the length of the opposite side be represented by y;

   Sin θ = opposite/ hypotenuse

   Sin 34 = y/ 5

y = 5 * Sin 34

 = 2.796

The length of its opposite side is 2.80.

iii. Let the length of the adjacent side be represented by x;

Cos θ = adjacent/ hypotenuse

Cos 34 = x/ hypotenuse

            = x/ 5

x = 5 * Cos 34

  = 4.145

The length of its adjacent side is 4.15.

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Answer:

How many prime numbers are there in 2020?

There are 12 factors of 2020, of which the following are its prime factors 2, 5, and 101. The Prime Factorization of 2020 is 2^2 × 5^1 × 101^1.

...

Sum of Factors of 2020: 4284.

Step-by-step explanation:

So, the sequence is 10, 100, 1000, 10000, 100000

A pattern that multiplies each number by 10 to get the next number in the sequence would be as follows:

Start with 10.

Multiply 10 by 10 to get 100.

Multiply 100 by 10 to get 1000.

Multiply 1000 by 10 to get 10000.

Multiply 10000 by 10 to get 100000.

This pattern creates a sequence of numbers that increases exponentially, with each number being 10 times larger than the previous one. The pattern can be represented by the following rule: "Each number in the sequence is the previous number multiplied by 10."

So, the sequence is:

10, 1010 = 100, 10010 = 1000, 100010 = 10000, 1000010 = 100000

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The value of x is 0.

The value of y is 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

2y = 6x + 4 _____(1)

y = -2x + 2 ______(2)

Substituting (2) in (1).

2 (-2x + 2) = 6x + 4

-4x + 4 = 6x + 4

4 - 4 = 6x + 4x

10x = 0

x = 0

Now,

x = 0 in (2)

y = -2 x 0 + 2

y = 0 + 2

y = 2

Thus,

The value of x and y is 0 and 2.

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Answer:

Step-by-step explanation:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on.

Answer:

3x - 5y = - 18

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x - 5y = 10 ( subtract 3x from both sides )

- 5y = - 3x + 10 ( divide through by - 5 )

y = [tex]\frac{3}{5}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{3}{5}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{5}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (- 1, 3 ) into the partial equation

3 = - [tex]\frac{3}{5}[/tex] + c ⇒ c = 3 + [tex]\frac{3}{5}[/tex] = [tex]\frac{18}{5}[/tex]

y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{18}{5}[/tex] ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fractions

5y = 3x + 18 ( subtract 5y from both sides )

0 = 3x - 5y + 18 ( subtract 18 from both sides )

- 18 = 3x - 5y , that is

3x - 5y = - 18 ← in standard form

According to the concept of time difference, the resulting situation is explained below.

The term time difference refers the difference between one measurement of time and another; the length of a time interval and the difference in clock time between two or more different time zones.

Here we have given that  Waimarama goes on a flight from Buenos Aires to Auckland and misses all 24 hours of her birthday.

Here we want to know that we need to consider that the cities are in different time zones is Buenos Aires is 16 hours behind of Auckland.

Here we also know that Airlines require travelers to check in 2 or three hours before the flight. Check with the Airlines for their regulations. Accordingly ensure you reach the Airport at least 2 or 3 hours before the scheduled departure of the Aeroplan.

Through the given details, we have identified that following values,

Aeroplan Travelling time = 16

Check in time = 3

Departure time = 3

Home town travel time = 2

when we sum up all these we can get the total time as,

=> 16 + 3 + 3 + 2

=> 24 hours.

Based on these we have concluded that she misses her whole birthday for travelling.

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Therefore , the solution of the given problem of table comes out to be we can create a table in form by following below steps.

A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.

Here,

Import the layout table by moving the pointer to the desired location on the form template.

Click Insert, followed by Layout Table, in the Tables toolbar.

The number of rows and rows to be included in the table should be entered with in Insert Table dialog box.

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The two types of longitude are the Prime Meridian and the International Date Line.

The Prime Meridian is the imaginary line of 0° longitude that divides the earth into the Eastern and Western hemispheres. It passes through Greenwich, England and is the reference point for all other longitudes on the Earth’s surface.

The International Date Line is an imaginary line located on the opposite side of the Earth from the Prime Meridian at 180° longitude. It is the reference point from which we measure the date change when traveling from one side of the world to the other.

The calculation for longitude is fairly simple. Longitude is measured in degrees, with a full circle being 360°. Each degree can be divided into 60 minutes and each minute into 60 seconds. To calculate the longitude, the degree and minutes are added together and converted into decimal form. For example, if a point has a longitude of 15° 22’ 30”, the calculation would be 15 + (22/60) + (30/3600) = 15.375°.

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Answer:

An exponent refers to how many times a number is multiplied by itself.

Step-by-step explanation:

For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

Answer:

4 gal / day

Step-by-step explanation:

12 gallons / 3 days

12/3 = 4

4 gallons / 1 day

The box will start at 72 and end at 86. At 78.5, a vertical line will be drawn through the box. Arrows will appear at both ends of the box. The one on the left will come to a halt at 65 miles per hour, while the one on the right will come to a halt at 98 miles per hour.

A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles. A box plot is a graphical representation of statistical data that uses the lowest, first quartile, median, third quartile, and maximum values. The name "box plot" refers to how the graph resembles a rectangle with lines extending from the top and bottom. Box and whisker plots, often known as box plots, are an excellent graphic for displaying the distribution of data points over a specified metric. These graphs show ranges within variables that have been measured. Outliers, the median, the mean, and where the majority of the data points fall inside the "box" are all included.

Here,

65, 66, 72, 76, 78, 79, 85, 86, 90, 98

Q1 = 72

(78 + 79) / 2 = 78.5 Q2 (median)

Q3 = 86

min = 65

max = 98

So the box plot will look like this:

The box will begin at 72 and conclude at 86. At 78.5, a line will be drawn vertically through the box. Arrows will emerge from both ends of the box. The one on the left will come to a stop at 65, while the one on the right will come to a rest at 98.

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The answers are as follows:

1 Angle Bisector Theorem

2 Sum of Adjacent Angles

3 Co-interior angle property

4 Additive law

Given:

Note: Diagram for Question is attached

1. Angle Bisector Theorem

The angle bisector is BD. Bisection entails splitting into two equal pieces. Angles 3 and 4 are therefore equal.

2. Sum of Adjacent Angles

To determine the greater angle that is created by the two adjacent angles, add the two angles together.

3. Co-interior angle property

According to the co-interior property, the sum of interior angles (on the same side) formed when a single line crosses two parallel lines is equal to 180.

4. Additive law

By applying the additive law, we can take a value away from both sides of the equation without throwing the equation out of balance. Therefore, we may take 110 out of both sides of the equation to get the final result of 70.

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The value of the given equation with a fractional index is 15.

What are fractional indices?

We can determine how many times a term has been multiplied by itself using an index, which is a small number. Powers of a term that are fractions are known as fractional indices.

The fractional power's two components both have significance. The number's or letter's root serves as the fraction's denominator. The power to raise the answer is contained in the fraction's numerator.

For example,

A value raised to the power of ½ means we have to find the square root.

A value raised to the power of ⅓ means we have to find the cube root

Some of the rules of fractional indices are

[tex]a^{1/m} * a^{1/n} = a^{1/m + 1/n} \\\a^{1/m} / a^{1/n} = a^{1/m - 1/n} \\\a^{1/m} * b^{1/m} =( ab)^{1/m}\\\a^{1/m} / b^{1/m} =( a/b)^{1/m}[/tex]

[tex](a^\frac{1}{m}) ^\frac{1}{n} = a^\frac{1}{mn}[/tex]

For the given question,

    [tex](15^\frac{1}{5} )^5[/tex] = [tex]15^\frac{5}{5} =15^1 =15[/tex]

Therefore the value of the given equation with a fractional index is 15.

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Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.

The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.

With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.

The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

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Answer:

23.9

Step-by-step explanation:

The five steps to solving inequalities are:

To solve an inequality, one must isolate the inequality symbol, simplify the inequality, graph the inequality on a number line, make a sign analysis of the inequality, and find the solution set of the inequality.

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