Ilya was using the properties to rewrite expressions. This time, his work is all correct. Fill in the blanks to explain the properties he used or to answer the questions.

The quadrilateral is a parallelogram because the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Given:- A quadrilateral ABCD in which AB=CD and AD=BC.

To prove:- AB∥CD and AD∥BC

Construction:- Joi A and C.

Proof:-

In △ABC and △CDA,

AB=CD(Given)

AD=BC(Given)

AC=AC(Common)

∴△ABC≅△CDA(By SSS)

Therefore, by CPCTC,

∠ACD=∠BAC

∠DAC=∠ACB

Since alternate angles are equal, thus the lines are parallel.

Therefore,

AB∥CD and AD∥BC

Since both the pairs of opposite sides of the quadrilateral are parallel, ABCD is a parallelogram.

Hence proved.

A quadrilateral in geometry may be a four-sided polygon with four sides and four corners (vertices). The Latin words Quadri, a variation of 4, and latus, meaning "side," are the source of the name. In regard to other polygons, it's also known as a tetragon, from the Greek "tetra" for "four" and "gon" for "corner" or "angle" (e.g. pentagon). Since "gon" is an anagram for "angle," it's also known as a quadrilaterals or 4-angle.

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Answer:  the distance is (4,2)

Step-by-step explanation: it takes from 3 to seven 4 1s. and 6 -4 will be 2

hope this helps

If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

In the given triangle below;

Line segment BC is intersecting at the midpoint of AD and AE.

Now,

Since ΔABC ≈ ΔADE by similarity property.

So,

AB/AD = BC/DE

AB/(AB + BD) = BC/DE

Since AB = BD = AB lets say,

AB/2AB = BC/DE

BC/DE = 1/2

Hence "If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved".

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The Measurement of  ∠6 i.e. m∠6 is 120°

The measurement of angle if the degree of that angle or we can also say that the angles are always measured in degrees. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360.  

In the question

as  ∠7 is an alternate angle to 60 degree,

thus ∠7 = 60°

According to sum of angle property :

∠7 +  ∠6 = 180

60 +  ∠6 = 180

∠6 = 180-60 = 120

Thus  m∠6 = 120°

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The complete question is :

Find measure m∠6

The value of a for the given equation is a=(r-q)/g.

The given equation is ga+q=r.

We need to find the value of a from the given equation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, ga+q=r can be solved for a as follows:

⇒ga=r-q

⇒a=(r-q)/g

Therefore, the value of a for the given equation is a=(r-q)/g.

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B

Step-by-step explanation:

just did this one and got a 100%

Graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

As given in the question,

Function: f(x)=(3.1)⁴

Here x  is independent variable and f(x) is dependent variable on x.

f(x)=(3.1)⁴ is a constant value and does not have any x variable.

It is shown in the drawn graph.

x =0 , f(x)=(3.1)⁴

x =1 , f(x)=(3.1)⁴

x = 2 , f(x)=(3.1)⁴

x = -1 , f(x)=(3.1)⁴

x = -2 , f(x)=(3.1)⁴ and so on.

Therefore, graph for the function f(x)=(3.1)⁴ is parallel to the x-axis and passing through coordinate (0, 92.3521 ).

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Answer: quadrant 4 (IV)

Step-by-step explanation:

Answer: h(-1) is equal to -2.

Step-by-step explanation:

We have to find , h(-1).

First you can plot the value of x = -1 in the graph.

Then you can draw a perpendicular line on the down ward direction and intersect to the parabola curve.

What is a parabola curve?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix. Parabola is an integral part of conic section topic and all its concepts parabola are covered here.

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )

Now you can see the point of (-1,-2) in the graph

Where,

                   h(-1) = -2

So, h(-1) is equal to -2.

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Using function concepts, it is found that:

3. Two ordered pairs are: (0, 0) and (130,260). The slope is of 2.

4. The equation of the line is of y = 2x.

5. The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.

6. a)

For Hill 1, we have that:

For Hill 2, we have that:

6. b) The rate of change down Hill 1 is of -5, while it is of -2 for Hill 2.

6. c) Due to the higher rate of change, Hill 1 is steeper.

7) The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.

Two ordered pairs are: (0, 0) and (130,260).

The slope is given by change in y divided by change in x, hence:

m = (260 - 0)/(130 - 0) = 2.

Considering the slope and the intercept(which is of 0, as when x = 0, y = 0), we have that:

The equation of the line is of y = 2x.

Hence:

The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.

For Hill 1, we have that:

For Hill 2, we have that:

The rates of change(change in height divided by change in length) are given as follows:

Due to the higher rate of change, Hill 1 is steeper.

A graph is a function if it has no vertically aligned points, that is, each value of the input is mapped to only one value of the output.

Hence:

The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.

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Software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.

What is a math conjecture?

A rotation of 75° (because 30 + 45 = 75) should map  △ABC to △A″B″C″. By using the

software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.

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Answer:

yes, it’s proportional

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

97 - 2 × (16 - 4) ← evaluate parenthesis

= 97 - 2 × 12 ← evaluate multiplication

= 97 - 24 ← evaluate subtraction

= 73

Answer:

73

Step-by-step explanation:

97 - 2 x (16-4) =

97 - 2 x (12) =

97 - 24 =

73

 The ratio of the height of the larger prism to the smaller prism is a/b = 5.

 To solve this problem we must know what a scale factor is.

  The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.

  If we have as reference the volumes of two hexagonal prisms, with the values of:

  If the reason or scale for the volume is given by

 Let's go for the reason of the length, for this we apply the cubic root.

a³/b³ ⇒ ∛(a³/b³)

∛250/2

a/b = 5

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Common difference = 3 , 32nd term = 100

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

The given series is

7, 10, 13, 16....

common difference = 10-7 = 13- 10= 16-13 = 3

Therefore there is a common difference between the two consecutive number.

In this series the common difference is 3.

Hence we get to know that the given series is an arithmetic series.

To identify the 32nd term we have a formula:

[tex]t_{n}[/tex] = a +(n-1)d

Here a = first number of the series

        n = number of series

        d = common difference

[tex]t_{32}[/tex] = 7 + (32-1)3

    = 7 + 31×3

    = 7 + 93

    = 100

Hence the 32nd term is 100.

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The table derive from the area formula of a triangle is summarized below:

     h (cm)                        A (cm²)

        6                                 24

        7                                 28

        8                                 32

        9                                 36

The area formula of a triangle (A), in square centimeters, is equal to the half of a product of the base (b), in centimeters, and the height (h), in centimeters. In this question we have the following triangle formula:

A = (1 / 2) · (8) · h

A = 4 · h

Where h is the height of the triangle.

Now we proceed to make a table with the given heights:

     h (cm)                        A (cm²)

        6                                 24

        7                                 28

        8                                 32

        9                                 36

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Answer:

Below in bold.

Step-by-step explanation:

3n + 4:

The common difference = 3,

First term = 3(1) + 4 = 7

First 4 terms

= 7, 10, 13, 16

10th term = 3(10) + 4 = 34.

4n - 5:

The common difference = 4,

First term = 4(1) - 5 = -1

First 4 terms

= -1, 3, 7, 11

10th term = 4(10) - 5 = 35.

The expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

The expression is given as:

3(−4.5b − 2.1) − (6b + 0.6)

Open the brackets

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b − 6.3 − 6b - 0.6

Collect the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -13.5b  − 6b − 6.3 - 0.6

Evaluate the like terms

3(−4.5b − 2.1) − (6b + 0.6) = -19.5b − 6.9

Hence, the expression that is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b − 6.9

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Answer:

C: -19.5b-6.9

Step-by-step explanation:

Answer:

E= 36 D=102 F=42

Step-by-step explanation:

E= 36 because of the vertical angles theorem, d =102 because of vertical angles theorem, and finally we have f = 42 because all these angles form a straight angle/line which adds up to 180. So before we knew that d=102 and e=36 so we can add those up and we get 138. Then we subtract 132 from the measure of a straight angle (180 degrees), to get f. SO 180-132 =f=42

Answer: C

Step-by-step explanation:

Should be C because the other choices seem false

The number according to the given statement is x<-0.55.

Given the statement is five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​.

A mathematical statement is a meaningful component of words that can be true or false. Simply, they are known as a statement.

Let us assume the given number be x.

According to the given statement,

Five and three-tenths of a number means 5.3x.

And two and seven-tenths means 2.7.

So, five and three-tenths times a number plus two and seven-tenths means 5.3x+2.7.                ......(1)

It is also given that three and three-tenths times a number means is 3.3x.      

And one and six-tenths means 1.6.

So, three and three-tenths times a number plus one and six-tenths​ means 3.3x+1.6         .......(2)

Now, we will substitute equation (1) less than equation (2) according to the given statement is

5.3x+2.7<3.3x+1.6

Further, we will subtract 2.7 from both sides, we get

5.3x+2.7-2.7<3.3x+1.6-2.7

5.3x<3.3x-1.1

Now, we will subtract 3.3x from both sides, we get

5.3x-3.3x<3.3x-1.1-3.3x

2x<-1.1

Now, we will divide both sides by 2, we get

2x/2<-1.1/2

x<-0.55

Hence, the number for the given statement "five and three-tenths times a number plus two and seven-tenths is less than three and three-tenths times a number plus one and six-tenths​" is -0.55.

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Answer:

The price of a ticket after the team loses 22 games is $26.93

Step-by-step explanation:

Original value = $31.55

value decrease per game lost = $0.21

equation uses C and L

C = 31.55 - 0.21L

22 games lost

C = 31.55 - 0.21(22)

C = 31.55 - 4.62

C = 26.93

C = $26.93

Here no enough information to determine if the triangles are congruent.

Option C is true.

What is Congruent triangle?

Congruent triangle have both the same shape and the same size.

Given that;

Two sides of triangles are 6 and 13.

Now,

Since, Congruent triangles are triangles that have equal corresponding angles and sides.

From the images of the triangles (see attachment),

We can see that the two triangles have 6cm and 13cm as the lengths of their sides.

However, The side lengths of both triangles are not corresponding, and the angle measures are not given.

Hence, There is no enough information to determine if the triangles are congruent.

Option C is true.

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The required wood needed to build four vertical sides is 60 inch.

According to the question, the given parameters for the box-shaped drum is as follows:

Length = 18 inch; Breadth = 12 inch; Height = 11 inch

To know the quantity of the wood need to build four vertical sides, calculation of perimeter is required.

Therefore, perimeter of the box = 12 + 18 + 12 + 18 = 60 inch

Hence, the required wood needed to build four vertical sides is 60 inch.

What is perimeter of a shaped box?

Perimeter of a shaped box is the addition of all the sides of a box. It is used for the closed shaped boxes. And it is measured in the linear units like meter, centimeter, etc.

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In the equation y = -x + 5, the value of y when we substitute -3 for x is 8.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the equation y = -x + 5, if we substitute -3 for x, the equation becomes

y = -(-3) + 5

Performing the arithmetic operations, we can have the value of y.

y = -(-3) + 5

y = 3 + 5

y = 8

Hence, for the equation y = -x + 5, y is 8 when x is -3.

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A linear equation that gives the price p they can charge for n shirts is equal to p(n) = -0.07n + 147.

Given the following data:

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope, m = (47 - 26)/(1000 - 4000)

Slope, m = -21/3000

Slope, m = -0.07

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + b ≡ p = mn + b

At point (1000, 47), we have:

47 = -0.07(1000) + b

47 = -70 + b

b = 47 + 70

b = $147

In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is p(n) = -0.07n + 147.

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The soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

According to the given question.

We have a linear equation in one variable 4 + x = -52.

Since, we have to solve the above equation for x.

As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the above equation 4 + x = -52 is given by

4 + x = -52

⇒ x = -52 - 4    ( subtract 4 both the sides)

⇒ x = -56

Hence, the soluton of the given linear equation in one variable 4 + x = -52  is x = -56.

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