How do you construct a line segment that is 1/3 the length of the given line segment?

Observing the geometry and the properties of sides and angles provided in the figure, We can conclude that option 2 is the correct answer. GJ is less than HJ.

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. A geometer is a mathematician who specializes in geometry. A field of mathematics known as geometry is described as "concerning the measurement, characteristics, and relationships of points, lines, angles, surfaces, and solids." Geometry is a branch of mathematics that deals with points, lines, forms, and surfaces, to put it another way.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

angle GFJ = 60

angle JFH = 62

We know larger angle corresponds to larger sides, So, The side opposite to 62 is larger than of 60.

So, GJ is smaller than HJ.

To learn more about triangles visit:

https://brainly.com/question/2773823

#SPJ1

The area shows the solution set of the inequalities with accuracy. y >= -5 x + 1, X min, -10 X max, Y min, -10 Y max. and y >= x - 11 equals X min -10, X max 10, and Y min -10, Y max 10.

In the shaded area, solutions will be found. Ordered pairs on the border line are not part of the solution set because this is a "less than" problem. Solutions as well as these values are in the shaded area. Every point(a,b) where all inequality conditions hold when x=a and y=b is referred to as the solution zone of an inequality.

The solution set of the inequalities is accurately represented by region. Y >= -5 x + 1 X min -10 X max 10 X max 10 Y min -10 Y max 10. This region accurately depicts the set of solutions to the disparities. if y >= x – 11 then X min – 10 X max – 10 Y min – 10 Y max – 10

To learn more about inequalities refer to :

https://brainly.com/question/24372553

#SPJ1

The surds equation x√40 = x√5 + √10 is resolved into (4√2) / 7  which a and b are 4 and 2 respectively.

A surd equation is a mathematical formula that comprises one or more surds, or irrational numbers, in the form of square, cube, or higher-order roots. Surds, such as √2, √3, 5, etc., are numbers that cannot be expressed as the ratio of two integers. The symbol "√" for them is frequently used.

Because surds are irrational numbers that cannot be stated as a ratio of integers, calculating a surd equation can be more challenging than solving a regular equation. The first step in solving a surd equation is to make the equation as simple as feasible by deleting any surds from any fractions' denominators or numerators. You will then separate the surd on one side of the equation from the numbers on the other side using algebraic manipulation. Once the square root has been eliminated, you can square both sides of the equation to get a polynomial equation that can be solved using conventional algebraic methods.

In the given problem;

x√40 = x√5 + √10

Collect like terms;

x√40 - x√5 = √10

x√(8 * 5) - x√5 = √10

x√(2 * 4 * 5) - x√5 = √10

2x√10 - x√5 = √10

x = (4√2) / 7

The value of a and b are 4 and 2

Learn more on surds equation here;

https://brainly.com/question/840021

#SPJ1

The ratio of the surface area to volume of each cylinder are:

1. 933/ 1909

2. 56/115

Surface area and volume of a cylinder.

The surface area of a cylinder is the sum of all its surfaces.

Surface area of a cylinder = 2[tex]\pi[/tex]r^2 + 2[tex]\pi[/tex]rh

The volume of a cylinder implies the amount of substance that it can contain.

volume of a cylinder = [tex]\pi[/tex]r^2h

1. The surface area of the cylinder = 2[tex]\pi[/tex]r^2 + 2[tex]\pi[/tex]rh

                                     = 2[tex]\pi[/tex]r(r + h)

                                     = 2*22/7*9(9 + 7.5)

The surface area of the cylinder = 933.43 sq. cm

ii. Volume of the cylinder = [tex]\pi[/tex]r^2h

                       = 22/7*9^2*7.5

volume of the cylinder = 1909.29 cubic centimeters

iii. The ratio of the surface area to its volume = 933.43/ 1909.29

                                                 = 933.43/ 1909.29

2. The surface area of the cylinder = 2[tex]\pi[/tex]r^2 + 2[tex]\pi[/tex]rh

                                     = 2[tex]\pi[/tex]r(r + h)

                                     = 2*22/7*5(5 + 23)

                                     = 880 sq. cm

The surface area of the cylinder = 880 sq. cm

ii. Volume of the cylinder = [tex]\pi[/tex]r^2h

                       = 22/7*5^2*23

volume of the cylinder = 1807.14 cubic centimeters

iii. The ratio of the surface area to its volume = 880/ 1807.14

                                                 = 56/115

Learn more about the surface area and volume of a cylinder at https://brainly.com/question/29870289

#SPJ1

-1/4 is the slope of the line that passes through the points (-5,4) and (3,2)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (-5, 4) and (3, 2)

Slope m=2-4/3+5

=-2/8

2 and 8 are multiples of 2, so divide numerator and denominator by 2

=-1/4

Hence, -1/4 is the slope of the line that passes through the points (-5,4) and (3,2)

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

Answer:

I'm not too sure but i believe its credit.

Answer:

D.) credit

Step BY STEP EXPLANTION

The new data values after the increment by 20% are 14.4, 10.8, 20.4, 18 and 12

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

Data values: 12,9,17,15,10

Increment: by 20%

This means that

new data values = old data values * (1 + Increment)

when the above equation is applied to the individual data values, we have

New 12 = 12 * (1 + 20%) = 14.4

New 9 = 9 * (1 + 20%) = 10.8

New 17 = 17 * (1 + 20%) = 20.4

New 15 = 15 * (1 + 20%) = 18

New 10 = 10 * (1 + 20%) = 12

So, the new values are 14.4, 10.8, 20.4, 18 and 12

Read more about percentage at

https://brainly.com/question/843074

#SPJ1

Answer:

The domain of a graph is the possible input values the graph can take.The domain of the graph is: 10,20,30,40,50,60,70,80,90,100

The score (on the x-axis) represents the input values.From the graph, we have:

Minimum score = 10

Maximum score = 100

This means that the domain of the graph is from 10 to 100

From the given options, (d) is correct;

Because it represents scores between 10 and 100 (inclusive)Read more about domains at:brainly.com/question/16875632

Statistics prove that motorcyclists are B: 35 times as likely as a passenger car occupant to die in a motor vehicle accident.

Compared to the occupants of motor vehicles, motorcycles provide their riders with very little protection from injury. Motorcycles have virtually no ability to absorb the impact from another vehicle; there is the potential for serious injuries or even death for any rider as a result of a motorcycle crash or accident.

Unfortunately, according to statistics motorcycle deaths accounted for 14% of all motor vehicle crash deaths. A motorcyclist is about 35 times more likely to die in an accident compared to passengers in cars.

You can leanr more about motorcycle accident at

https://brainly.com/question/13782170

#SPJ4

the percent increase in charges is 33.3%

increase after baggage charges is 55.5%

GIVEN-

price of the ticket initially=​$225

price of the ticket after 1 week=​$300

baggage charge= ​$50

STEPS:

Percentage increase= {(difference)/initial }x 100

difference=final-initial

⇒(300-225)/225 x 100

⇒0.3333 x 100

=33.3%

∴33.3% of the increase in charges

with additional baggage price new ticket=​$350

⇒percentage increase=(350-225)/225 x 100

⇒0.5555 x 100

⇒55.5%

∴55.5% of increase in prices after adding baggage charges.

To know more about percentage increase:

https://brainly.com/question/11360390

The complete question is:

Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Denver was $225. Now the cost is $300. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?

The equation of the graphed function will be;

⇒ Y = f (x + 3) - 2

A relation between a set of inputs having one output each is called a function.

Given that;

The function is,

⇒ f (x) = x³

Now,

Since, The equation of the graphed function is,

⇒ y = (x + 3)³ - 2  ..(i)

And, Here, The function is,

⇒ f (x) = x³

Put x = x + 3;

⇒ f (x + 3) = (x + 3)³

Substitute above value in equation (i), we get;

⇒ y = f (x + 3) - 2

Thus, The equation of the graphed function is,

⇒ Y = f (x + 3) - 2

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer:

[tex]f(-2) = -20[/tex]

Step-by-step explanation:

Plug -2 into the function for x.

[tex]f(x) = 7x - 6[/tex]

For [tex]x=-2[/tex]:

[tex]f(-2) = 7(-2) - 6[/tex]

[tex]f(-2) = -14 - 6[/tex]

[tex]f(-2) = -20[/tex]

so we know the area if 44 cm², and we also know the "L" is 3 more than twice "W", hmmm what's twice W anyway?  well, just 2W, and 3 more than that?  well 2W + 3, hmmm so

[tex]A=LW ~~ \begin{cases} L=length\\ W=width\\[-0.5em] \hrulefill\\ A=44 \end{cases}\implies 44=LW\hspace{5em}\stackrel{\textit{3 more than twice W}}{L=2W+3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{44=(\underset{L}{2W+3})W}\implies 44=2W^2+3W \\\\\\ 0=2W^2+3W-44 \implies 0=(2W+11)(W-4) \\\\[-0.35em] ~\dotfill\\\\ 0=2W+11\implies -11=2W\implies \cfrac{-11}{2}=W ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 0=W-4\implies 4=W ~~ \textit{\LARGE \checkmark}[/tex]

now, the negative value is a valid value for W, however for this case, the width cannot be a negative number, it must be positive, thus we do away with it, and since L = 2W+3, that means L = 2(4)+3 = 11.

To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case, x = 0.

[tex]x = 0[/tex]

Replace the variable x  with 0 in the expression.

[tex]y = |0| + 5[/tex]

Simplify [tex]|0| + 5.[/tex]

The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.

[tex]y = 0+5[/tex]

Add 0 and 5.

[tex]y = 5[/tex]

The absolute value vertex is (0, 5).

Answer:

Step-by-step explanation:

A VAT (value-added tax) is a consumption tax that is added to the price of goods and services. The VAT rate is typically a percentage of the price of the goods or services.

In order to find the amount the shoe dealer should pay to the company including VAT, we need to know the VAT rate. If the VAT rate is not specified in the problem, it is impossible to determine the exact amount that the shoe dealer should pay.

However, if we assume that the VAT rate is 15%, then the amount of VAT the dealer should pay is 15/100 * 8000 = 1200 birr.

So the total amount the dealer should pay to the company including VAT is 8000 + 1200 = 9200 birr

It's important to note that this is an estimate and the actual amount could be different if the VAT rate is different.

This means that an earthquake of magnitude 7.9 is 10^4 (or 10,000) times more intense than an earthquake of magnitude 3.5.

An earthquake is a sudden shaking of the ground caused by the shifting and breaking of large pieces of rock beneath the Earth's surface. Earthquakes can be caused by a variety of factors including the shifting of tectonic plates, volcanic activity, and underground explosions.

An earthquake of magnitude 7.9 is significantly more intense than an earthquake of magnitude 3.5 on the Richter scale. The Richter scale is logarithmic, meaning that each whole number increase in magnitude corresponds to an increase in shaking intensity by a factor of 10. This means that an earthquake of magnitude 7.9 is 10^4 (or 10,000) times more intense than an earthquake of magnitude 3.5.

To learn more about earthquake
https://brainly.com/question/29073753
#SPJ1

The two types of scatter plots are linear and nonlinear. Linear scatter plots show a linear relationship between two variables, while nonlinear scatter plots show a nonlinear relationship between two variables.

A linear scatter plot is a type of graph that displays the relationship between two variables. In a linear scatter plot, points are plotted on a graph according to their x- and y-coordinates. The points form a line, or a straight line, indicating a linear relationship between the two variables. A linear scatter plot is used when there is a clear and strong positive or negative relationship between the two variables.

Nonlinear scatter plots show a nonlinear relationship between two variables. In nonlinear scatter plots, points are plotted on a graph according to their x- and y-coordinates. The points form a curved or nonlinear line, indicating a nonlinear relationship between the two variables. Nonlinear scatter plots are used when there is an unclear or weak relationship between the two variables, or when the relationship between the two variables is nonlinear.

To know more about scatter plots refer to the  link  brainly.com/question/8478725

#SPJ4

The minimum y-value after which the exponential function will always be greater than the linear function is y = 4.

How do functions work?

A law relating two dependent and independent variables is known as a function.

An illustration of a linear function is

y =mx+c

and represents the exponential function as follows:

y = aˣ

By looking at the graph, one may identify the lowest y-value after which the exponential function will always be bigger than the linear function.

When y = 4, they are equal, and from that point on, the linear function's value exceeds that of the exponential function.

To know more about Function at:

brainly.com/question/12431044

#SPJ4

Step-by-step explanation:

If son present age is x then

father present age=4x+4

so the equation is

(4x+4)-x=28

3x=24

x=8

The data point 56.7 seconds is an outlier, so we should discard it and measure it again.

The correct option is the last one.

When we have some data, there may be what we call "outliers".

An outlier is a data point that is "away" from the rest of the data points.

For example, if you look at the table, you can see that most values are around 20 seconds, except for one value, which is the middle one and it is:

56.7 seconds.

That point is really far away from all the others on the table, so we can see that it is an outlier, then we should discard it and measure it again.

Thus the correct option is the last one: 56.7 s

Learn more about outliers:

https://brainly.com/question/3631910

#SPJ1

The value of the base angles of triangle ABC formed by the given polygon is; 80°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, the number of sides of the given polygon when completed will be 18 sides. Thus, we can say that;

Central angle = 360/18

Central angle = 20°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠B = ∠C = [180 - 20]/2

∠B = ∠C = 80°

Read more about Polygon Central Angle at; https://brainly.com/question/224658

#SPJ1

The value of k in order for the ordered pair (-1,k) to be a solution to the function,  f(x) = -x + 2 will be 3.

In mathematics, a function is a rule or an expression that establishes a connection between one variable, known as the independent variable, and another variable known as the dependent variable. It defines the relationship between the two variables, in such a way that for every unique value of the independent variable, there is a corresponding unique value of the dependent variable. Functions are widely used in many areas of mathematics such as algebra, calculus, and trigonometry, as well as in many other fields such as physics, engineering, and economics.

A function can be represented in two ways: graphically and algebraically. The graphical representation of a function is a graph of the function, where the x-axis represents the independent variable and the y-axis represents the dependent variable. A function can be plotted as a set of ordered pairs (x,y) on the coordinate plane. The algebraic representation of a function is an equation that defines the relationship between the independent variable and the dependent variable. The equation can be written in the form of y = f(x) or y = ax + b, where x and y are the variables, and a and b are constants. The graphical representation of a function provides a visual representation of the relationship between the independent and dependent variables, while the algebraic representation provides a way to calculate the output for any given input.

To find the value of k , that satisfies the given equation, we need to substitute the ordered pair (-1, k) the the given equation as follows,

f(-1) = -(-1) + 2

or , k = 1+2

therefore, k =3

To learn more about functions visit:

https://brainly.com/question/12431044

#SPJ1

Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.

The AAS congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle. To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.

To learn more about the triangle, visit:

brainly.com/question/2773823

#SPJ4

Yes, it is possible to prove that two triangles are congruent by using the AAS congruence theorem.

The AAS congruence theorem

it states that if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

This theorem can be used to prove that two triangles are congruent if two of the angles in the triangle and the side between them are congruent to two angles and the side between them of the other triangle.

To prove congruence using the AAS congruence theorem, it is important to use the right angle and side measurements to ensure that the two triangles are congruent. If the measurements are correct, then the two triangles will be congruent.

Learn more about congruence here :_

https://brainly.com/question/7888063

#SPJ4

Their surface areas are arranged in a 3:1 ratio.

The ratio of two spherical balls' volumes is 27:1. This means that the radius of the larger ball is 3 times that of the smaller ball. The surface area of a sphere is proportional to the square of its radius, so the ratio of their surface areas is the square of 3, or 3:1. To calculate the surface area of a sphere, use the formula 4πr^2, where r is the radius of the sphere. For the larger ball, the surface area is 4π(3r)^2, and for the smaller ball, the surface area is 4π(r)^2. Dividing the larger ball's surface area by the smaller ball's surface area gives us the ratio of their surface areas, which is 3:1.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

The absolute value equation that can be used to determine Jack's minimum and   is | x + 30| = 10 (third option)

An equation is a mathematical statement that is used to show the equality of two mathematical expressions. An absolute value equation is an equation that is within the absolute value symbols. The absolute value symbols are | |.

The form of the absolute value equation is:

maximum time he spends washing - average time = 10

x - 30 = 10

or

minimum time he spends washing - average time = 10

x - 30 = -10

Putting the two equations above together becomes

|x - 30| = 10

To learn more about mathematical equations, please check: https://brainly.com/question/26427570

#SPJ1

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs) (Input, Output). In algebra, relationship and function are crucial ideas. Both in real life and in mathematics, they are often utilized. To further comprehend the significance of each of these relational and functional concepts, let's describe them.

In order to have ordered pairs of the kind, relations and functions provide a mapping between two sets (Inputs and Outputs). In algebra, relationship and function are crucial ideas. Both in real life and in mathematics, they are often utilized. To further comprehend the significance of each of these relational and functional concepts, let's describe them.

If each element x∈R has a distinct R-relative, resulting in R[x] consisting of a single element, then the relation R is referred to be a mapping (map), a function, or a transformation. This distinct component is known as the function value at x and is indicated by the symbol R(x) (under R). R[x] therefore only has one member, R(x).

Let us consider a domain for x ∈ N

The R ⇒ R is defined for f(x) = 2x ; x≤ 5

f(x) = 2x

will have a domain of 1, 2, 3,4, 5 and The value of the function will be

f(x) = 2, 4, 6, 8, 10 .

So, the 5 coordinates of the relation is {(1,2), (2,4), (3, 6), (4,8), (5, 10)}

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

To learn more abot Relation and Function refer to :

https://brainly.com/question/1504168

#SPJ1

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

What is meant by map?

Let us consider a domain for x ∈ N

The R ⇒ R is defined for f(x) = 2x ; x≤ 5

f(x) = 2x

will have a domain of 1, 2, 3,4, 5 and The value of the function will be

f(x) = 2, 4, 6, 8, 10 .

So, the 5 coordinates of the relation is {(1,2), (2,4), (3, 6), (4,8), (5, 10)}

The mapping of the relation will be :

(Domain) ⇒ (Range)

1 → 2; 2 → 4; 3 → 6; 4 → 8; 5 → 10

To learn more about map refer to

https://brainly.com/question/25922463

#SPJ1

The distance scale between San Antonio and Houston on Vicki's map is 7.3 centimeters. The sane distance in millimeters in millimeters is

Distance measurement is a linear measurement and the unit can be inches, feet, yard, meters, kilometers and so on

In the problem the unit is in centimeters and conversion of centimeters to millimeters is done by the factor 10

Applying the factor of 10 to 7.3 centimeters will to convert it to millimeters and this shown below

= 7.3 * 10

= 73 millimeters

The distance in millimeters is solved to be 73 millimeters

Read more on unit conversions here:

brainly.com/question/141163

#SPJ1

Answer: C. Zula can write 4 articles in 10 hours is the best interpretation of the slope of this linear model.

The slope of a linear equation in the form y = mx + b represents the rate of change of y with respect to x. It tells us how much y changes for a one-unit change in x. In this case, the slope of the equation y = 0.4x is 0.

Step-by-step explanation:

The total volume of all 4 gumballs: V=3,620 mm³

Gumball is in the shape of a Spherical so we Use the formula for the total volume of a sphere:

Volume of Sphere = (4/3)πr³

r = Radius of Sphere

Plug the given radius into the formula, r =  6mm

Volume of 1 gumball = (4/3)π * 6³

V= 288π  mm³

The total volume of a single gumball will be 288π cubic millimeters.

Because you have 4 gumballs, multiply the total volume of a gumball by 4 to find the total volume for all 4 gumballs.

Volume of 4 gumballs = 4 *  288π

V= 1152π  mm³

In terms of π, the total volume of the 4 gumballs is 1152π cubic millimeters.

Assuming π = 3.14, multiply 1152 and 3.14 together.

1152*3.14= 3,617.28 mm³

To know more about the Volume of the sphere:

https://brainly.com/question/10135720

#SPJ4

Answer:

They have 160 peaches left

Step-by-step explanation: