A ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km. Find the distance traveled from the starting point to the ending point

Answer:

[tex]f(g(-3))=-25[/tex]

Step-by-step explanation:

[tex]g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25[/tex]

Answer: To find the length of an object in a scale drawing, you need to use the scale to convert the length on the drawing (measured in inches) to the actual length (measured in feet).

The scale of the drawing is given as 0.5 inches = 10 feet, which means that 1 inch on the drawing represents 10 feet in reality.

So, if the length of the object on the scale drawing is L inches, then the actual length of the object in feet would be:

Length (ft) = (Length (in) * 10 ft/0.5 in) = (L*20)

To find the actual length of the object in feet, you need to know the length of the object in inches from the scale drawing.

Once you have that measurement, you could then simply multiply it by 20.

Step-by-step explanation:

Answer:

  (-2, 2)

Step-by-step explanation:

You want the circumcenter of the triangle with vertices A(2, -3), B(2, 7), and C(-6, -3).

The circumcenter is the center of  the circle that circumscribes the triangle. Here, the triangle is a right triangle, so the circumcenter is the midpoint of the hypotenuse.

The midpoint of segment BC is the average of the coordinates of B and C:

  X = (B +C)/2 = ((2, 7) +(-6, -3))/2 = (2 -6, 7 -3)/2 = (-4, 4)/2

  X = (-2, 2)

The circumcenter is (-2, 2).

__

Additional comment

The right angle subtends an arc of twice its measure, 180°, so the circumscribed triangle occupies a semicircle, and the hypotenuse is a diameter. That puts the center of the circle at the midpoint of the hypotenuse.

When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.

given

by pythagoras theorem

[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]

The homes of the parents and grandparents are thus 9 miles apart in a straight line.

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The equation of the circle in standard form is  ( x-h )2 + ( y-k)2 = r2. we can get the equation by putting the values of x coordinates and y coordinates of the circle.

A circle can be defined as a 2-D closed geometrical shape whose boundary points are at an equal distance from the center of the geometry.

Equation of the circle in standard form is,

( x-h )2 + ( y-k)2 = r2

we have to find the  the x-coordinate (h) & y-coordinate (k) of the center of the circle by taking the summation of x-coordinates & y-coordinates of the endpoints of the diameter respectively and dividing by 2.

here, h = ( x1 + x2 ) / 2

         k = ( y1 + y2 ) / 2

here endpoints of a diameter are at (-5,-5) and (7,2). Calculate the distance between  (-5,-5) and (7,2) using the distance formula and divide by 2 to get the circle's radius. Substitute the center coordinates and radius into a standard form to get the equation of the circle.

so, h = -5 + 7 / 2 = 1

     k = -5 + 2 / 2 = -3/2

Putting all the values we get the equation of circle in standard form.

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The solution to the pair of simultaneous equations 2x + y = 5 and 3x - 2y = 4 is (2, 1).

A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.

Given two linear equations in x and y,

2x + y = 5     (equation 1)

3x - 2y = 4     (equation 2)

Use substitution method to find its solution. Express the first equation as y in terms of x and substitute the value of y to the second equation.

2x + y = 5     (equation 1)

y = 5 - 2x

3x - 2y = 4     (equation 2)

3x - 2(5 - 2x) = 4

3x - 10 + 4x = 4

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

3x - 10 + 4x = 4

7x = 14

x = 2

Substitute the value of x in the first equation and solve for y.

y = 5 - 2x

y = 5 - 2(2)

y = 5 - 4

y = 1

Hence, the solution of the given system of equations is (2, 1).

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To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.

An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.

For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:

Side AB = Side BC = (Side AC) x (Sin A / Sin B)

Where A and B are the angles of the triangle and Side AC is the known side length.

Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).

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The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.

We will calculate the interquartile range and us the rule 1.5 .

The formula to calculate  interquartile range is to subtract the value of first quartile by the value of second quartile.

IQR = Q3 - Q1

Therefore, interquartile range becomes,

IQR = 17 - 13

IQR = 4

Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first

4 * 1.5 = 6

and then,

17 + 6 = 23

on applying the rue we will get ,

13 - 6 = 7 .

This value means that there is no outlier in the displayed data set.

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The correct answer to the given question is 49. To solve the given problem following steps are followed :

Step 1: 7 power 2 means 7 multiplied by itself 2 times.

Step 2: 7 times 7 is 49.

Step 3: So, the answer is 49.

Comparing two quantities that generate the same result when one is multiplied by a certain amount is known as a multiplicative comparison. Sam, for instance, has twice as many balloons as Sid does. Sid's got three balloons. Sam has two times Sid's amount of balloons. Sam has a total of 6 balloons, which is equal to 2 + 3 + 1.

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Answer: He received $3.51 in change.

Step-by-step explanation:

To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).

It will look like this:

$20.00 - $16.49 = $3.51

Answer:3 dollars and 51 cents

Step-by-step explanation:

Answer:

"equivalent"

Step-by-step explanation:

Right!!

Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.

To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.

For the origin (0, 0):

Point A: (x, y) = (0, 3)

Point B: (x, y) = (-4, -3)

Dilated Point A: (x, y) = (0, 6)

Dilated Point B: (x, y) = (-8, -6)

Equation of the dilated line: y = -4x + 6

This shows that the line is dilated with scale factor 2, but is the same line.

For the point (3, -4):

Point A: (x, y) = (3, -1)

Point B: (x, y) = (-1, -7)

Dilated Point A: (x, y) = (6, -2)

Dilated Point B: (x, y) = (-2, -14)

Equation of the dilated line: y = -4x + 3

This shows that the line is dilated with scale factor 2, but is the same line.

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Answer:

c = √52

Step-by-step explanation:

applying pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' the hypotenuse.

Substitute values:

6² + 4² = c²

c² = 36 + 16

c² = 52

c = √52

The price of a stock share has decreased by 15% and suddenly increased by 5%.

The percentage is a fraction of a number represented as a number out of a hundred. The % symbol is used to denote percentages. The percentage signifies the frequency.

The selling price for a share of the same stock at a later date was represented by the expression 1.05(0.85d).

When a % decrease occurs, the number is deducted from 100, and when a percentage increase occurs, the number is added to 100.

100 - 15% = 85% = 0.85

100 + 5% = 105% = 1.05

original selling price = d

selling price at a later date = 1.05(0.85d)

0.85d means that the original price was discounted by 15%

1.05 means that the price increased by 5%

Thus, the price of a stock share has decreased by 15% and suddenly increased by 5%.

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The true inequalities are:

5/6 > 4/6

3/8< 5/8

2/3 > 1/3

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

5/6 > 4/6

0.833 > 0.667

so, this inequality is true.

3/8 < 5/8

0.375 < 0.625

so, this inequality is true.

4/5 < 2/5

0.8 < 0.4

so, this inequality is false.

4/7 > 6/7

0.571 > 0.857

so, this inequality is false.

2/3 > 1/3

0.667 > 0.333

so, this inequality is true.

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Answer:x=20

Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get  8x+20 = 180, this can be simplified to 8x=160 or x = 20

Answer:

x = 20°

Step-by-step explanation:

Given angles,

→ 5x + 9

→ 3x + 11

Forming the equation,

→ (5x + 9) + (3x + 11) = 180°

{Because, sum of two angles in a straight line leads to 180°}

Now the value of x will be,

→ (5x + 9) + (3x + 11) = 180°

→ 5x + 3x + 9 + 11 = 180°

→ 8x + 20 = 180°

→ 8x = 180° - 20

→ x = 160/8

→ [ x = 20° ]

Hence, the value of x is 20°.

Therefore, K= 66 degrees, LK length = 22 unit, and LK length = 22 unit are the answers to the specific problem of angles.

A geometrical angled construction is constructed from two rays that converge at the summit, or center, of both the angle and are referred to as the face and the vertex, respectively. Guess it depends on how they're situated, it is possible for two rods to create an angle together within plane. When two planes collide, an inclination is also formed. Diahedral angles are the term used to refer to them. Light beams or lines in euclidean geometry can have a wide variety of shapes or angles for the same termination. The phrase "angle" in English is based on the Latin term "angulus," which meaning "horn." the vertex.

Here,

Given: MKL M = 24 degree right triangle

K is 90 degrees, etc.

Thus,

=> ∠L + ∠M +∠K =180

=> 90 + 24 + ∠K = 180

=>∠K =180-114

K equals 66 degrees.

and

The formula for LK length is 22.

The formula for LK length is 22.

In light of this, the answer to the angle problem is

K=66 degrees, and LK length=2 units. LK length equals two units.

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The integer number that represents the submarine's depth is given as follows:

-460.

Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.

The concepts of height and depth are given as follows:

A submarine in the middle of the ocean at a depth of 115 feet, hence the integer that represents the initial depth is given as follows:

-115.

The submarine dived to a depth that is four times the initial depth, hence the integer that represents the final depth is given as follows:

4 x -115 = -460.

(meaning that the final depth of the submarine is of 460 feet).

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If Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit  she arranges these to form the given shape then the area of shape is 14 Square Units .

The Area of one triangular piece is given as = 1 Sq . Unit ;

The Area of one rectangular piece is = 2 Sq. Unit ;

From the shape given below ,

we can see that the shape has 4 triangular pieces and 5 rectangular pieces .

So , total area of given shape is ⇒[tex]4\times Area Of Triangle + 5\times Area Of Rectangle ;\\[/tex]

Substituting the values of Area ,

we get ;

[tex]Total Area = 4\times 1 +5\times 2[/tex]

= [tex]4+10[/tex]

= 14 Sq . Units .

Therefore , the area of the given shape is 14 Sq. Units .

The given question is incomplete , the complete question is

Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit .

If she arranges these to form a shape as shown below, what would be the area of this shape ?

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Inequalities represent Susan's weekly goal of earning money are:

c + e ≤ 20

15c + 10e ≥ 240

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

Given that,

Susan earns $10 per hour tutoring elementary students in math.

She also earns $15 per hour cleaning in the library.

Her goal each week is to earn at least $240 while working not more than 20 hours.

Thus, the equation of inequality:

c + e ≤ 20

15c + 10e ≥ 240

Here, e represent the number of hours Susan works in one week tutoring elementary students.

c represent the number of hours Susan works in one week cleaning the library.

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The value of x, given the angles next to the triangle, can be found to be 38 °

To find the value of x, you first need to find the value of the other angles in the triangle.

Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:

= 180 - 134

= 46 °

The angle to the bottom right is:

= 180 - 84

= 96 °

The angles in a triangle add up to 180 ° so the value of x would be:

= 180 - 46 - 96

= 38 °

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Answer:

2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8)  When you are multiplying powers that have the same bases, you add the exponents.

The three main parts to a chemical word equations are the reactants , the products  and the arrow .

What is a Chemical Equation ?

A chemical equation is defined as a representation of a chemical reaction expressing it in in terms of symbols of the substances.

The three main parts of the Chemical Equation are :

(i) The Reactants :  During a chemical reaction, these elements combine and undergo some chemical changes. They are present on left side of  reaction equation.

For Example : [tex]CH_{4} + 2O_{2}[/tex] ;

(ii) The Arrow :  It indicates formation of products from reactant . It is represented as " → " ;

(iii) The Products : Products are the result of chemical reactions between their reactants. It is present on right side of the chemical equation.

For example, : [tex]CO_{2} +2H_{2} O[/tex]

So , overall Chemical  Equation can be written as : [tex]CH_{4} + 2O_{2}[/tex] → [tex]CO_{2} +2H_{2} O[/tex] .

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The 3 linear equations are

1. y = mx + b

2. ax + by = c

3. x/a + y/b = 1

1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.

2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.

3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.

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Total 56 bags of hardwood and 140 bags of pine bark bags are sold.

In the given question, a local boys club sold 196 bags of mulch and made a total of $357.

It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.

We have to find how many bags of each kind of mulch did it sell.

Let total number of x bags of hardwood sell.

Let total number of y bags of pine bark sell.

Now the equation should be

2x + 1.75y = 357............................(1)

Total number of bags sold 196.

So x + y = 196............................(2)

From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.

2(196 - y) + 1.75y = 357

392 - 2y + 1.75y = 357

392 - 0.25y = 357

Subtract 392 on both side, we get

-0.25y = -35

Divide by -0.25 on both side, we get

y = 140

Now putting the value of y in x = 196-y

x = 196 - 140

x = 56

Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.

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The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.

The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.

The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of  27.32 days.

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F G cannot be simplified because it is not an equation, it is a phrase.

1. First, determine what F G is. In this case, F G is a phrase and not and equation.

2. Since F G is a phrase, it cannot be simplified.

Determining what F G is the first step to simplifying it. F G is a phrase and not an equation, so it cannot be simplified. Simplifying an equation or expression requires breaking it down into its individual parts and then combining like terms or rearranging the equation to make it simpler. However, F G is not an equation and therefore cannot be simplified.

F G cannot be simplified because it is not an equation, it is a phrase.

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The two statements that are true about the table are:

A) "The range is {15.80, 31.60, 43.45, 57.25} ."

B) "The set of independent values is {4, 8, 11, 15}."

Here we have the table for number of gallons and the costs of these:

g          c

4         15.80

8         31.60

11         43.45

15         57.25

The statements that are true about that table are:

"The range is {15.80, 31.60, 43.45, 57.25} ."

This is true, the cost is the output of the table, thus, the range is that.

"The set of independent values is {4, 8, 11, 15}."

This is also called the domain, which is the input, in this case, the number of gallons of gas.

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