Write the ratio 28:40 in simplest terms

The length of r is 2.4 inches.

What is the law of sines ?

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

Given, In ΔQRS, s = 5.2 inches, ∠S=129° and ∠Q=30°

We know that, The sum of all angles of a triangle is 180°.

So,  ∠Q + ∠R + ∠S =  180°

      ∠R = 180° - 129° - 30°

            = 21°

Now, We also know that the law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal.

So, q/Sin Q = r/Sin R = s/Sin S

Or, we can say

                 r/Sin R = s/Sin S

                 r/Sin 21° = s/Sin129°

                 r/Sin 21° = 5.2 / Sin 129°

                 r = 5.2 × Sin 21°/Sin 129°

                   = 5.2 × 0.46

                   = 2.4 inches.

Learn more about Law of Sines from the given link:

https://brainly.com/question/27174058

#SPJ1

Open the Word document. then Go to the Insert tab on the ribbon and click on the Chart option under the Illustrations group.

When does a graph represents a function?

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

How do you insert a 4 quadrant graph in Word?

Open the Word document.

Go to the Insert tab on the ribbon and click on the Chart option under the Illustrations group.

An Insert Charts dialog box will appear on the screen.

Select the XY (Scatter) option from the left pane

and pick a line graph that you want to insert.

learn more about of word here

https://brainly.com/question/17267403

#SPJ4

The factored form of the expression 6x² - 5x - 6 is (3x + 2)(2x - 3)    .

The Factored form of quadratic equations means expressing the polynomial as a product of its linear factors. This  process allows to simplify quadratic expressions, find their roots and solve further .

The expression is given ; 6x² - 5x - 6 .

= 6x² - 9x + 4x - 6    ,....by using split the middle term method ;

= 3x(2x - 3) +2(2x - 3) ;

= (3x + 2)(2x - 3)

Therefore , the factored form is (3x + 2)(2x - 3)  .

The given question is incomplete , the complete question is

What is the factored form of this expression 6x² - 5x - 6 ?

Learn more about Factors here

https://brainly.com/question/27947331

#SPJ4

The congruence's reflexive characteristic is applied to the statement AB ≅ AB.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. Assuming that an is a number, a = a. a=a. We discovered that anything is equal to itself thanks to the reflexive characteristic of equality. This characteristic's formula is a = a. All numbers are equal to one another, according to this property. For instance, three is three.

In mathematics, a set X's elements are considered to be reflexive if there is a relationship between each one of them. This can be expressed in terms of relations as (a, a) R a X or as I R, where I is the identity relation on A. As a result, it is said to hold reflexivity and to have a reflexive feature. Every angle, every line, and every figure or shape in geometry are congruent to one another according to the reflexive characteristic of congruence. This characteristic is typically employed in proofs of parallel lines and the congruence of two triangles.

Learn more about congruence Visit: brainly.com/question/2102943

#SPJ4

Answer:

1. (C) Distributive property | 2. (A) Associative property | 3. (D) Simplify

Step-by-step explanation:

Here's my attempt:

Reason 1:

The first reason is (C) distributive property of multiplication because you're taking the previous step and spreading it out (distributing it). Here's an example of the distributive property of multiplication:

3(4+7) = 3*4+3*7=12+21=33

This will be the same as solving 3(4+7) using PEMDAS

In this step, you're spreading out the problem the same way as the example shown is doing.

Reason 2:

The second reason is (A) the associative property of multiplication. The associative property of multiplication says that changing the grouping of the numbers in a multiplication problem doesn't change the product.

Here's an example:

(6*7)*8 = 6*(7*8)

This way, the step groups together two pairs of factors to solve the last step without changing the product.

Reason 3:

The final reason is (D) Simplify because the step doesn't use the commutative property of multiplication. Why not? Because the commutative property of multiplication states that changing the order of factors in a multiplication problem doesn't change the product (note that this is different than the associative property of multiplication). Instead, the last step just simplifies the problem.

Hopefully, you read through my explanation, and it helped. Have a good day :D

The table shows the multiplication of two linear expressions. Select the correct reason for each step.

Reason 1:

✔ distributive property

Reason 2:

✔ commutative property of multiplication

Reason 3:

✔ associative property of multiplication

Reason 4:

✔ simplify

The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

A straightforward equation that depicts population growth is as follows: Expression of Population Changes as a Percentage: Change in Population Size = (Births + Immigration) - (Deaths + Emigration). Let's say we had a population of 100,000 people.

The relative size of two functions' values for big values of the independent variable is what is meant when a term like "function growth" is used.

The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

A straightforward equation that depicts population growth is as follows: Expression of Population Changes as a Percentage: Change in Population Size = (Births + Immigration) - (Deaths + Emigration). Let's say we had a population of 100,000 people.

The relative size of two functions' values for big values of the independent variable is what is meant when a term like "function growth" is used.

The term "population regulation" refers to biological mechanisms that balance off disruptive occurrences, such as weather changes, alterations in the environment, the occurrence of disease epidemics, etc.

To know more about population growth visit:-

https://brainly.com/question/28914464

#SPJ4

During rigid transformations, the shape, size, and orientation of an object remain the same, while its position in space changes. This means that the distance between any two points on the object remains constant, as does the angle between any two lines. Additionally, the orientation of the object's axes (length, width, and height) remain the same.

Transformations are a general term for four different methods of changing the location and/or shape of a point, line, or geometric figure. The shape of the object is revealed in its pre-image, while its final form and position are revealed in the image following transformation.

A transformation is characterized by a significant alteration in appearance or form. Your life may change as a result of a significant event, such earning your driver's license, beginning college, or getting married. A significant, abrupt transformation is called a metamorphosis.

To know more about transformations visit:

https://brainly.com/question/17102666

#SPJ4

Answer: 12 2/15

Step-by-step explanation:

4 3/5 = 23/5

7 8/15 = 113/15

So, we have 23/5 + 113/15. The common factor is 15, so we have

69/15 + 113/15 = 182/15

182/15 = 12 2/15

The three types of discontinuity are listed as follows:

Jump Discontinuity.

Infinite Discontinuity.

Removable Discontinuity.

The term discontinuity is referred as if a function is referred to as the point at which a Mathematical object is discontinuous.

The function will be discontinues if they meet the following conditions,

There are 3 type of discontinuity in math and they are listed as jump, infinite and removable.

To know more about Discontinuity here.

https://brainly.com/question/28783981

#SPJ4

The operation that maps(moves)the preimage onto the image is called a transformation.

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

In mathematics, there are five different transformations:

Dilation is the process of an image "shrinking" or "enlarging," depending on the size of the preimage.

Reflection: The picture is a preimage that has been reversed; "a flip."

Rotation: The picture is the preimage turned around a fixed axis; this is referred to as "a turn."

Shear: When a preimage is sheared, all the points along one side remain stationary while all the other preimage points move parallel to that side in proportion to the distance from the given side; this is also known as "a skew."

Translation: The image is "a slide" away from the preimage by a fixed amount.

The operation that maps(moves)the preimage onto the image is called a transformation.

To know more about Transformation, visit:

https://brainly.com/question/27895117

#SPJ4

Answer:

11/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

44/60=22/30=11/15

11/15

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. Hence proved

AAS (Angle-Angle-Side):

Suppose we have two triangles from figure ABC and DEF, where,

∠B = ∠E [Corresponding angles] ∠C = ∠F [Corresponding angles] And

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangle ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by ASA congruency,

Δ ABC ≅ Δ DEF

So AAS (Angle-Angle-Side) congruence rule is hence proved.

For more such questions about  AAS (Angle-Angle-Side).

https://brainly.com/question/29124246

#SPJ4

Answer:

yes.

Step-by-step explanation:

The definition of a function:  "A function is defined as a relation between a set of inputs having one output each."

This means each x can only have 1 y value. You can check if this is a function using the vertical line test. To do the vertical line test draw vertical lines through the graph of the expression. If you even hit 2 points with a vertical line it is NOT as function.

The graph is of an upward facing parabola so it will be a function. We can graph and check this with the VLT which it passes.

Answer:

Step-by-step explanation:

3. collinear = on the same line. Answer: C

4. A

5. If two lines intersect, they intersect at a point. Answer: Point C

6. B

7. AB + BC = AC

AB + 9 = 22

AB = 13

8. EF + FG = EG

2 + 3 = EG

EG = 5

9. m<MNP + m<PNO = m<MNO

20 + m<PNO = 85

m<PNO = 65

10. m<GHK + m<KHJ = m<GHJ

90 + 31 = m<GHJ

m<GHJ = 121

11. AM = MB = 10

AM = 10

12. EM = MF = (1/2)EF = 14

MF = 14

13. GM + MH = GH

GM = MH = 3.4

3.4 + 3.4 = GH

GH = 6.8

14. m<CAB = m<BAD = (1/2)m<CAD

m<CAD = 40; (1/2)m<CAD = 20

x = m<BAD = 20

15. m<CAB = m<BAD

2y + 25 = 3y

25 = y

y = 25

The median of given data is 4.

Given:

A data

2, 3, 4, 7, 5, 1, 6

To find: The median of given data.

The median of given data is 4.

To answer this question, we will follow the following steps:

As given, we have a data

2, 3, 4, 7, 5, 1, 6

To find the median, we will arrange the data in ascending order.

So, we have,

1, 2, 3, 4, 5, 6, 7

Here,

Total number of observations = 7

As we know if there is an odd number (n) of observations in a data, then its median is obtained by:

So,

The median of given data

Now,

4th observation is 4.

Hence, the median of given data is 4.

To know more about ascending order click here :

brainly.com/question/14404086

#SPJ4

Answer: false

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

We have to factor out the GCF

We see that ( 4x+8) have the GCF is 4, so 4 will go outside, and we have left x + 2

So the answer is

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

The equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a)

Define Ellipse

In mathematics, an ellipse is the location of points in a plane so that their separation from a fixed point has a fixed ratio of "e" to their separation from a fixed line (less than 1). The conic section, which is the intersection of a cone with a plane that does not intersect the base of the cone, includes the ellipse. The eccentricity of the ellipse is symbolized by the constant ratio "e," the fixed point is known as the focus, and the fixed line is known as the directrix (d).

Standard from of the equation of an ellipse with centre (0,0) and major axis on x-axis is,

x² / a² + y² / b² = 1

Standard from of the equation of an ellipse with centre (H, K) and major axis parallel to the x-axis is,

(x - h)² / a² + (y - k)² / b² = 1

In equation,

(y+1)² / 9 + (x+3)²/1 = 1

Ellipse properties are :  (h,k) = (-3, -1) , a = 3, b = 1

b>a therefore b is semi-major axis, a is semi minor axis.

Ellipse Centre are :  (h,k) = (-3, -1) , a = 1, b = 3

Hence, the equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a).

To read more about Ellipse.

https://brainly.com/question/16904744

#SPJ1

Answer:

Step-by-step explanation: 9x3

9x2

and 9 x 1 then when you get all of the answers but the answers  all  together now leave me alone pleaseeeeeeeeeeeeee  .

The transformation of the (-k, k) about the line y = x will be (k, -k). Then the correct option is A.

It is the image of the point which is located in the opposite direction of a given point.

The rule of the refection will be given as,

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

Now, the rule for reflecting a point about the line y = -x is;

While reflecting on the line y = -x, we get the reflected points by multiplying '-1' with the swapped coordinates.

The change of the (- k, k) about the line y = x will be (k, - k). Then the right choice is A.

More about the reflection of the point link is given below.

https://brainly.com/question/938117

#SPJ1

The purpose of the ninth was to assert the principle that the enumerated rights are not exhaustive and final and that the listing of certain rights does not deny the existence of other rights.

The Ninth Amendment was part of the Bill of Rights added to the Constitution on December 15, 1791. It states that all rights not enshrined in the Constitution belong to the people, not to the US government. In other words, the rights of citizens are not limited to those stipulated in the Constitution. Simply put, the Ninth Amendment declares that the enumeration of certain rights in the Constitution should not be construed as withholding or disrespecting others from people. According to Judge Harry A. Blackman, Roe v. Wade (1973),

, "As we believe, this right to privacy is limited by the Fourteenth Amendment concept of restrictions on individual liberty and government action. The Ninth Amendment to the Constitution contains ample scope, including determining whether a woman should terminate a pregnancy."

To learn more about Ninth Amendment, refer:

https://brainly.com/question/20462233

#SPJ4

Consequently, the original number is 27 and the reversal is 72.

A number is a numerical unit of measurement and labeling in mathematics.

The natural numbers 1, 2, 3, 4, and so on are the first examples.

Number words are a linguistic way to express numbers.

So, let the ones and tens places' digits be y and x, respectively.

initial value = 10x+y

number in reverse = 10y plus x

In response to the query:

3(10x+y)-9 = 10y+x

30x+3y-9-10y-x= 0

29x-7y-9 = 0 ...(1)

Since the reversed number is greater:

10y+x-(10x+y)=45

10y-y-10x+x-45 = 0

9y-9x-45=0

y-x-5=0

y= x+5 ...(2)

Place equation (2) into equation (1) immediately:

29x-7(x+5)-9=0

29x-7x-35-9=0

22x=44

x = 2

Now enter x=2 into equation (2):

y= 2+5= 7

Therefore, consequently, the original number is 27 and the reversal is 72.

Know more about numbers here:

https://brainly.com/question/25734188

#SPJ4

Correct question:
On reversing the digits of a two-digit number obtained is 9 less than three times the original number. If the difference between these two numbers is 45 find the original number.

Tess can make 9 throw pillows from the 6 yards of fabric.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Tess wants to make throw pillows for her couch. she has 6 yards of fabric. each pillow uses 2 over 3 yards of fabric.

The number of pillows will be calculated as,

Number of pillows = 6 ÷ ( 2 / 3 )

Number of pillows = ( 6 x 3 ) / 2

Number of pillows = 9

To know more about an expression follow

https://brainly.com/question/29075000

#SPJ1

The equation that can be used to calculate how many minutes after 4:00 p.m. she will arrive at her location is y = 4x - 16.

The correct equation is:

y = 4x - 16

This equation represents the number of minutes after 4:00 p.m. the pilot will arrive at her destination. The variable x represents the time, in minutes, of her original flight, and y represents the number of minutes after 4:00 p.m. she will arrive at her destination. The expression "4x" represents the time the pilot will arrive at her destination if she had traveled at her original speed, and the "-16" represents the delay caused by air traffic.

To solve this equation, you would substitute the value of x into the equation and solve for y. For example, if the pilot's original flight time was 60 minutes, the equation would be:

y = 4(60) - 16

= 240 - 16

= 224

This means that the pilot will arrive 224 minutes after 4:00 p.m., or at 6:24 p.m.

To learn more about speed, refer:-

https://brainly.com/question/312131

#SPJ4

Answer:

Bias from using a convenience sample (C)

Step-by-step explanation:

This sampling method is an example of taking a convenience sample because the mobile phone service provider is only taking samples from the people that responded. The availability of certain people causes a bias in the data drawn from this sampling method.

According to the given question, we can say  that - 18 year old be in the 12th grade as per school requirement .

Grading may be done using letters, numbers, percentages, points, or descriptions. The most prevalent grades are in the form of letters, and they usually correspond to a variety of percentages or points. Many people consider "A" and "B" grades to be "good." D and F grades are referred to as "poor grades." Commonly regarded as average is a "C."

We can say that

10th grade = 16 or 17 year old ,

11th grade is = 17 or 18 and  12th grade is = 18 or 19.

To know more about Grade visit:

brainly.com/question/999941

#SPJ4

Answer:

Step-by-step explanation:

x= -6

Answer:

5

Step-by-step explanation:

there are five terms: 5xy, 9yz, 3zx, 5x, and 4y.

In mathematics, a term is a part of an expression that is separated by a plus or minus sign. In this expression, the terms are 5xy, 9yz, 3zx, 5x, and 4y. Note that the equation in the question is formatted a little awkwardly, so make sure to count how many terms you see yourself too!

SSS, SAS, AAS, and RHS are the similarity theories that are used to prove that two triangles are similar.

RHS: In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent

SSS: In side side side postulate if all three sides of a triangle is equal to the respective three sides of the other triangle then we will use SSS postulate.

SAS: In side angle side postulate if two sides and one angle of a triangle is equal to the respective two sides and angle then we will use the SAS postulate.

AAS: In angle angle side postulate if two angle and one side of a triangle is equal to the other two angle and side of an another triangle respectively then we will use AAS postulate.

SSS,SAS,AAS,RHS are the similarity postulates that are use to prove two triangle is similar.

Learn more about similarity:

https://brainly.com/question/28004832

#SPJ4

Bar line is a notation used in place of repeating numbers. It is also graphical representation used in graphs.

Bar line is a simple notation used to express a repeating number by placing a line over the number that repeats.  when numbers go on forever and when not to use bar notation.

Bar line is also used in graphs. A bar line in the graph is a graphical representation based on the different parameters. They are drawn in cases when the items are compared based on the multiple parameters or observations.

There is another bar line called the vertical bar ( | ) also called the vertical line, vertical slash or upright slash is a symbol used in mathematics, computing and other areas to represent a specific type of logic or operation, depending on its context. Even within a single area such as computing, the vertical bar is applied in multiple ways.

To learn more about Bar line please visit:

https://brainly.com/question/29887384

#SPJ4