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The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.

A =-1/3 [tex]\left[\begin{array}{cc}27&-9\\-15&24\\\end{array}\right][/tex]

A = [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

Hence the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

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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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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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Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.

A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.

given

substituting the value of x

7+x > 2x

so x = 1

x = 2

x = 3

x= 4

x= 5

Consequently, x = 1, 2, 3, 4, 5, 6,..., and no matter what x number we enter, 7 + x is always more than 2x.

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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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In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.

A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A set of numbers connected by a rule is referred to as a number sequence. You can determine the following numbers in the sequence if you figure out the rule. Therefore, adding 6 each time is the rule for this sequence.

given

In a table cell, enter a formula. Choose the table cell in which you wish the result to appear.

Delete the contents of the cell if it is not empty. Click Formula under the Data group on the Layout tab of the Table Tools.

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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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An object that appears to be identical but is really turned the opposite way in the plane perpendicular to the mirror surface is called a mirror image.

It appears as an optical phenomenon as a result of reflection from surfaces like water or mirrors. People might be able to see a reflection of themselves in the mirror behind the glass. The "mirror image" is produced when light rays strike the mirror-like surface and reflect back. One that is commonly misinterpreted is the notion that the reflection is reflected from left to right. Mirrors are turned from left to right rather than from front to back.

When looking at printed surfaces from the inside out, as well as in the reflections of mirrors and other reflecting surfaces, one may notice two-dimensional mirror images. After gazing at what is effectively a two-dimensional object when we first glance at a card, we notice a left-right reversal in the mirror when we turn the card such that the lettering is facing a mirror (like the text on a card).

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The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.

Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.

In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.

In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.

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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:

The number of multiple-choice question points plus the number of short-answer question points is 80. Therefore, the correct answer is option A.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points.

Let the number of 2 points questions be x and the number of 4 points questions be y.

A test is worth 80 points.

2x+4y=80 -------(I)

The test has 25 questions.

x+y=25 -------(II)

Therefore, option A is the correct answer.

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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 distance between Jasmine’s house and her grandmother’s house is 504 miles.

To find the distance, we can use this following formula:

X = V x T

Where: X = distance, V = Velocity, and T = Time

By using the following equations above, we can assume that

V x 45 = (V-4) x 70

45 V = 70 V – 280

25 V = 280

V = 11.2 mph

Now that we have the velocity, we can find the distance =

X = V x T

X = 11.2 mph x 45 minutes

X = 504 miles

Thus, the distance between Jasmine’s house and her grandmother’s house would be 504 miles

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Answer:

Step-by-Step answer:

8 2/5 miles

Given that ∠MPN is a right angle, we know that MP and NP are perpendicular to each other. Since NP is also a perpendicular bisector of MO, it bisects MO at a 90-degree angle.

Also given that NP is a perpendicular bisector of MO, we know that NP is equidistant from M and O. Therefore, NP is the midpoint of MO and so MN = NO.

Since MP and NP are perpendicular and MN = NO, it follows that △MNP is similar to △ONP.

Therefore, we can conclude that △MNP ≅ △ONP

Answer:

4 gal / day

Step-by-step explanation:

12 gallons / 3 days

12/3 = 4

4 gallons / 1 day

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 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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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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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:

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

Given system:

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

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

143x11

=1573 cherries

One bag holds 11 cherries and there are 143 bags. To find out how many cherries there are, we would need to multiply the amount of cherries by the number of bags.

[tex]11\times143[/tex]

[tex]=\fbox{1573 total cherries}[/tex]

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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It is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 11 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 5 and 7

5 + 7 > 11

12 > 11

Now we add 7 and 11

7 + 11 > 5

18 > 5

Now we add 5 and 11

5 + 11 > 7

16 > 7

It is possible to construct a triangle whose sides are 5 cm 6 cm and 11cm because the sum of two sides are greater than third sides.

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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:

Step-by-step explanation:

44/4= 11

44-24/2=12

20/2=10

The room is 10 x 12' long

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 area of the irregular figure is equal to 27.5 square units.

Irregular figures are the result of combining of two or more geometric figures. The irregular figure shown in the image is the result of seven figures, triangles and rectangles, whose area formulas are:

Triangle

A = 0.5 · w · l

Rectangle

A = w · l

Now we proceed to calculate the area of the irregular figure:

A = 0.5 · 1 · 5 + 2 · 5 + 0.5 · 2² + 2 · 3 + 0.5 · 1 · 2 + 3 · 1 + 0.5 · 3 · 2

A = 2.5 + 10 + 2 + 6 + 1 + 3 + 3

A = 27.5

The irregular figure has an area of 27.5 square units.

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