Decrease £19064.67 by 19.5%
Give your answer rounded to 2 DP.

On solving the provided question, we can say that value of tan(a) in right triangle ABC = sin(A)/cos(A) = B/P

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have a right triangle ABC

angle B = 90

so,

value of tan(a) = sin(A)/cos(A) = B/P

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Answer:

Step-by-step explanation:

The standard form of the ellipse equation is (x-h)²/a² +(y-k)²/b² =1

This equation is for a horizontal ellipse. (a) is always bigger than (b) in ellipses. Because (a²) is under the x, that's why this ellipse is horizontal.

Now, let's answer the questions:

1. The center coordinates are (h,k) which are (4,-2) by comparing the two equations.

2. length of the major axis = 2a , let's find (a)

if you compare the two equations, a²=36 , that means a=6

Then 2a=12

3. length of the minor axis = 2b , let's find (b)

if you compare the two equations, b²=16 , that means b=4

Then 2b=8

4. the sum of the local radii = length of the major axis = 12

5. to find the foci, we have to find the value of (c), we have to use the equation a²=b²+c²

plugin a² and b², 36=16+c² , solve it, c=√20 =2√5

Now, to find the coordinates of the foci, we have to add and subtract the (c) value from the x-coordinate of the center while the y-coordinate stays the same (because this ellipse is horizontal).

the coordinates of the foci are (4+2√5 , -2) and (4-2√5 , -2)

6. the vertices are the end points of the major and the minor axes. To find the vertices on the major axis, add the value of (a) to the x-coordinate of the center while the y-coordinate stays the same.

(4+6,-2) and (4-6,-2) , this leads to (10,-2) and (-2,-2)

To find the vertices on the minor axis, add the value of (b) to the y-coordinate of the center while the x-coordinate stays the same.

(4,-2+4) and (4,-2-4) , this leads to (4,2) and (4,-6)

7. eccentricity (e)=c/a =(2√5)/6 = (√5)/3

This triangle is warning you to slow down and be prepared to stop. It indicates that a railroad crossing is ahead and you should proceed with caution.

This sign is warning you that a railroad crossing is ahead, and you should proceed with caution. The triangle shape is reflective orange with a red border on each of the three sides. This sign indicates that you should slow down and be prepared to stop as a train may be approaching. You should also look both ways for any oncoming trains before continuing to cross the tracks. Additionally, you should never try to drive around a lowered crossing gate and never cross the tracks until you are sure that it is safe to do so. Always obey the signs and signals at railroad crossings and never take any chances when it comes to safety. Following these rules will help to ensure that everyone stays safe when crossing railroad tracks.

the complete question is : What does a sign with a reflective orange triangle with a red border on each of the three sides warn you off ?

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The sign with a reflective orange triangle with a red border on each of the three sides warn you of Slow moving vehicles.

Here we have to find the reason behind sign with a reflective orange triangle with a red border on each of the three sides.

Basically this type of sign are look like a warning triangle which is also an equilateral  triangle of around 600mm in size made of red reflective material. Where it can be put on the side of the road by anyone to warn other drivers of a breakdown or crash ahead.

And it must also said that the reflective orange triangle on the rear of a vehicle means it is traveling 35 mph or less. And here you may see this sign on road maintenance equipment, farm vehicles, or horse- drawn wagons.

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The data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34. That is option D.

The box plot is defined as the type of data representation that is used in descriptive statistics to show the distribution of numerical data such as the number of hours Judy takes to complete a quilt.

The characteristics of the box plot is that is shows the outliers, the median, and the mode of the given numerical data.

Therefore, the data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34.

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Answer:

0.7

Step-by-step explanation:

30% off a price means you pay 70% of the tag price.  So multiply the tag price by 0.70

Example:

A $75 pair of sneakers is 30% off. You pay $75 x 0.7 = $52.50

To prove this is right, 30% off $75 is:

$75 x 0.30 = $22.50

$75 - $22.50 = $52.50

Answer:

y = - [tex]\frac{8}{7}[/tex] x + [tex]\frac{8}{7}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 0 )

m = [tex]\frac{0-8}{1-(-6)}[/tex] = [tex]\frac{-8}{1+6}[/tex] = - [tex]\frac{8}{7}[/tex] , then

y = - [tex]\frac{8}{7}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation.

using (1, 0 ), that is x = 1, y = 0

0 = - [tex]\frac{8}{7}[/tex] + c ⇒ c = 0 + [tex]\frac{8}{7}[/tex] = [tex]\frac{8}{7}[/tex] , so

y = - [tex]\frac{8}{7}[/tex] x + [tex]\frac{8}{7}[/tex] ← equation of line

The solution to the equation is x = 105/14 and y = -27/2

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution.

We use different methods to solve simultaneous equations. Some of the common methods are:

By substitution method

-7x + -5y = 15 ----- 1

7x + 3y = 12 ----- 2

from equation 1

7x = -15 -5y ----- 3

substitute 7x in equation 2

-15 - 5y + 3y = 12

-2y = 12 + 15

-2y = 27

y = -27/2

To find x, substitute y in equation 3

7x = -15 - 5(-27/2)

7x = -15 + 135/2

Multiplying both sides by 2

14x = -30 + 135

14x = 105

x = 105/14

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There are three types of fraction names: proper fractions, improper fractions, and mixed fractions.

A proper fraction is a fraction that has a numerator smaller than the denominator. For example, 2/5 is a proper fraction.

An improper fraction is a fraction that has a numerator larger than or equal to the denominator. For example, 7/5 is an improper fraction.

Combining a whole number and a fraction creates a mixed fraction.

For example, 3 1/2 is a mixed fraction. All three types of fraction names are used to express the value of a fraction in a different way.

Proper fractions, improper fractions, and mixed fractions are all used to represent the same value of a fraction, just in different ways.

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The solution for the equation is,

1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given sets of equations,

1. x - y = 1

x + y = 3

add both the equations we get,

x - y + x + y = 1 + 3

2x = 4 (+y and -y eliminated)

x = 4/2 = 2

substitute value of  x

x + y = 3

2 + y = 3

y = 3 - 2 = 1

x = 2 and y = 1

2.  x + y = 1

x + y = 11

the equation has no solution because In this case, the two lines representing the equations are parallel to each other.

3. x + 4y = 11

x - 6y = 11

since both equations have the common constant for x we can subtract the equations,

x + 4y -(x - 6y) = 11 - 11

4y + 6y = 0

y = 0 and x = 11

4. -3x + 3y = 6

6x + 3y = 18

subtract equation 1 from 2

6x + 3y -(-3x + 3y) = 18 - 6

6x - 3y + 3x - 3y = 12

9x = 12

x = 12/9 = 4/3

substitute value of x

-3x + 3y = 6

-3(4/3) + 3y = 6

-4 + 3y = 6

y = 10/3

Hence the solution is 1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3.

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Using Aleks calculator to write 9/14 as a decimal and rounding up to the nearest hundredth is 0.64.

This refers to an artificial,  intelligent learning and assessment device that students use in academic filed such as: Mathematics, Chemistry, Statistics, and Accounting. It helps students to quickly and accurately solve arithmetics and get precise answers in some subjects areas. Aleks enables the student to work on the topics they are ready to learn.

For the division of the given question:

Aleks calculator was used to show the step-by-step division.  

  [tex]\frac{9}{14}[/tex] = 0.6428

Rounding to the nearest hundredth, the result of the division is 0.64.

(The third decimal place is 2, which is smaller than 5, so after rounding, the second decimal place is not changed).

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20. (0, -2), (3, 1)

(1+2)/(3-0)= 3/3= 1

y + 2= x - 0

y= x - 2

21. (0,4), (4, 2)

(2-4)/(4-0)= -2/4= -1/2

y - 4 = -1/2(x - 0)

y - 4 = -1/2x + 0

y= -1/2x + 4

22. (0, 1), (2, -3)

(-3-1)/(2-0)= -4/2= -2

y - 1 = -2(x - 0)

y - 1= -2x + 0

y = -2x + 1

23. (0, -3), (2, 1)

(1 + 3)/(2 - 0)= 4/2= 2

y + 3 = 2( x - 0)

y + 3 = 2x - 0

y = 2x - 3

The value of the expression x²-2(x-y)-z³ is 24.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given;

Expression x²-2(x-y)-z³

To find the value of the expression:

If x = -3, y=4 and z = -1.

Substituting the values to the expression,

x²-2(x-y)-z³

= (-3)²-2(-3-4)-(-1)³

= 9 + 14 - (-1)

= 9+14+1

= 24

Therefore, 24 is the value of the expression.

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Answer:

Step-by-step explanation:

540

The linear two-variable equation that represents the graph is y = -2x + 4.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Two coordinates from the graph:

(0, 4) and (1, 2)

m = (2 - 4) / 1 = -2/1 = -2

Now,

y = mx + c

(0, 4) = (x, y)

4 = 0 + c

c = 4

Now,

y = -2x + 4

Thus,

The equation that represents the graph is y = -2 + 4.

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Area of the shaded sectors and segment are 1. 51.3 cm², 2. 30.1 cm² and 3. 14.14 cm².

Circles are two dimensional figure which are set of all points which are equal distance from a common point.

Area of the sector = (θ/360°) π r², where θ is the sector angle.

1. r = 7 cm

  θ = 120°

  Area of the sector DEF = (120/360)  π 7²

                                          = [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × 7²

                                          = 51.3 cm²

2. We have to find the area of the segment DF.

   Area of the segment DF = Area of the sector DEF - Area of ΔDEF

   From 1. Area of sector DEF = 51.3 cm²

   To find area of ΔDEF, make two triangles by drawing a perpendicular       bisector from E to line DF. Let O be the point on the line DF where the perpendicular line touches..

Then we get two triangles and they are congruent by RHS congruency rule. [ Both have hypotenuse = 7 cm, both have right angles and a common side which is the perpendicular drawn.

Let's find base and height of ΔDEF.

Let x be the base. Then x/2 is the base of one triangle.

Sin 60° = base / hypotenuse

√3 / 2 = (x/2) / 7

x/2 = (√3 / 2) × 7

x = 7[tex]\sqrt{3}[/tex] cm

Base = 7[tex]\sqrt{3}[/tex] cm

Cos 60° = Height / hypotenuse

1 / 2 = Height / 7

Height = (1/2) × 7

           = 3.5 cm

Area of  ΔDEF = [tex]\frac{1}{2}[/tex] × base × height

                        = [tex]\frac{1}{2}[/tex] × 7[tex]\sqrt{3}[/tex] × 3.5

                        = 21.2 cm²

Area of the segment DF = Area of the sector DEF - Area of ΔDEF

                                        = 51.3 cm² - 21.2 cm²

                                        = 30.1 cm²

3. r = 6 cm

   θ = 45°

   Area of sector KLM = (45/360)  π 6²

                                    =  [tex]\frac{1}{8}[/tex] × [tex]\frac{22}{7}[/tex] × 6²

                                    = 14.14 cm²

Hence the area of shaded portions are calculated as above.

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The translation of the sentence to an equation is 7 1/9 = 2 4/5 + m

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

seven and one ninth equals two and four fifths plus m

The number is represented with m

So, the statement remains unchanged as follows

seven and one ninth equals two and four fifths plus m

seven and one ninth means 7 1/9

So, we have the following representation

seven and one ninth equals two and four fifths plus m ⇒ 7 1/9 equals two and four fifths plus m

two and four fifths means 2 4/5

So, we have the following representation

seven and one ninth equals two and four fifths plus m ⇒ 7 1/9 equals 2 4/5 plus m

Lastly, plus and equals can be represented as + and =

This gives

seven and one ninth equals two and four fifths plus m ⇒ 7 1/9 = 2 4/5 + m

Hence, the equation is 7 1/9 = 2 4/5 + m

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Complete question

Translate the sentence into an equation.

seven and one ninth equals two and four fifths plus m

The average rate of change over the interval from x = 2 to x = 4 is 2.

The average rate of change for a function over an interval is the slope of the secant line that connects the two points on the graph. The average rate of change can be found by using the formula:

Average Rate of Change = (y2 - y1) / (x2 - x1)

For the given function, the average rate of change over the interval from x = 2 to x = 4 can be found by substituting the appropriate values into the formula:

Average Rate of Change = (f(4) - f(2)) / (4 - 2)

Substituting the function values, we get:

Average Rate of Change = (6 - 2) / (4 - 2)

Simplifying, we get:

Average Rate of Change = 4 / 2

Therefore, the average rate of change over the interval from x = 2 to x = 4 is 2.

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The table that represents the two-column table for the data in this problem is given by the image shown at the end of the answer.

As the own name of the table says, the two-column table is composed by two-columns.

The columns of the table are defined as follows:

The input and the output variables for this problem are given as follows:

Then the table is composed by four rows, as follows:

Time (minutes) - Number of pages

25                     - 36

63                     - 48

74.5                  - 52

Which is illustrated on the image shown at the end of the answer.

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The solution is Option A.

The output value for the function f when x = -1 and the function f ( -1 ) is given by the equation f ( -1 ) = -5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = 2x - 3   be equation (1)

On simplifying the equation , we get

when x = -1

Substitute the value of x as -1 in the equation , we get

f ( x ) = 2x - 3

f ( - 1 ) = 2 ( -1 ) - 3

f ( - 1 ) = - 2 - 3

f ( - 1 ) = -5

Therefore , the value of f ( -1 ) is -5

Hence , the function f ( x ) when x = -1 is -5

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In mathematics, there are several types of angles that are typically studied in elementary and middle school, they include

Acute angle: An acute angle is an angle that measures less than 90 degrees.

Right angle: A right angle is an angle that measures exactly 90 degrees.

Obtuse angle: An obtuse angle is an angle that measures greater than 90 degrees and less than 180 degrees.

Straight angle: A straight angle is an angle that measures exactly 180 degrees.

Reflex angle: A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees.

Perigon: A full angle is an angle that measures exactly 360 degrees.

Complementary angles: Two angles are said to be complementary if the sum of their angles is 90 degrees.

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Therefore , the solution of the given problem of triangle comes out to be x= 5/8  .

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : Similar triangle,

To find the value of x

thus ,We get

=> 3x +  5x + 12 = 6 +11

=> 8x + 12 = 17

=> 8x = 17-12

=> 8x =5

=> x =5/8

Therefore , the solution of the given problem of triangle comes out to be

x= 5/8  .

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The translation that describe the path of the 8 tile to reach it's final position is given as follows:

(x,y) -> (x + 3, y - 1).

The same translation cannot be used to describe the path of all the tiles, as the paths are different for each tile.

There are four translations that are standard, and their rules are defined as follows:

The tiles will be placed in order, meaning that the tile number eight should be the second row and fourth column, as all the numbers from 1 to 15 are in the matrix.

As the number eight is in the first row and first column, the translation is given as follows:

The composition of these two translation is given by:

(x,y) -> (x + 3, y - 1).

This is the rule only for the tile 8, not for all tiles, as some are already at their final position, such as tiles 5 and 6.

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answer:

70%

steps:

in word problems

'out of' means ÷ or divide

70 out of the 100 people means

70÷100

70÷100= .7

move the decimal 2 spots to the right to percent

70%

Answer:

70%

Step-by-step explanation:

Example: 6 out 20 = [tex]\frac{6*5}{20*5} =\frac{30}{100} = 30 percent[/tex]

Given from the question:

[tex]\frac{70}{100} = 70 percent[/tex]

A. SAS Inequality Theorem , theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle. This theorem is important to remember when comparing similar triangles, as it can help determine which triangle has the greater side length. This theorem can also be used to determine if a triangle is acute or obtuse, as the greater included angle will lead to the longer side being on the opposite side of the triangle. Additionally, this theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

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The square root of 3,600 is 60.

Answer:

60

Step-by-step explanation:

Root of 3600 is the same as the root of (2×2)×(2x2)×(3×3)×(5×5) which is the same as 2×2×3×5 which is 60.

The AB segment is the line connecting the midpoints of two sides of a triangle. To find it, first locate the midpoints of two sides of the triangle. Then draw a straight line between the two midpoints to form the AB segment.

The AB segment is an important line in a triangle. It is found by connecting the midpoints of two sides of the triangle. To locate the midpoints, first identify the two sides of the triangle. Then measure the length of each side and divide by two. Mark the midpoints of each side, and then connect them with a straight line. This forms the AB segment. It is important to note that the AB segment does not bisect the triangle, but instead, it is the line connecting the midpoints of two sides of the triangle. The AB segment is used to determine certain properties of the triangle, such as its area and perimeter.

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The process of finding the Segment AB is explained below.

The term segment in math is defined as line segment is bounded by two distinct points on a line or here we can say a line segment is part of the line that connects two points.

Here we have to find the way to identify the AB segment.

Here as we all know that Line segment that is named as AB is bound between two fixed points.

According to this case, here we have the line segment is bound between the fixed points A and B as follows:

Therefore the line segment AB starts from point A and ends at point B.

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Answer:

Step-by-step explanation:

b = 4h + 3A = .5 * b * h = 11Substitute b in terms of h from the first equation into the second equation and solve for h:.5 * b * h = 11.5 * (4h + 3) * h = 11(4h + 3) * h = 224h2 + 3h = 224h2 + 3h - 22 = 0(4h + 11) (h - 2) = 0h = -11/4 OR h = 2Reject the negative answer since a length cannot be negative=> h = 2Plug h value into the first equation to solve for b:b = 4h + 3 = 4(2) + 3 = 11base = b = 11height = h = 2 (that’s what I got if it doesn’t then sorry)

Using combination, a) the number of coins = 120 b) the number of coins would needed to make all possible rows of 6 coin is 384.

a) Based on the provided information, each row is a 6-bit string (6 coins) and its weight is 3 (3 pennies). Therefore, using combination the possible number of rows will be 6C3. The formula for combination is given by:

nCr = n!/r!(n – r)!

Hence,

6C3 = 6!/3!(6 – 3)! = 6!/3!3! = 6*5*4*3!/ 3*2*1*3! = 20

And in case each row requires 6 coins simultaneously, the number of coins = 6*20 = 120 coins

b) Based on the provided information, the possible number of rows will be 2^6 = 64. It can also be obtained using combination the possible number of rows will be sum of 6C0, 6C1, 6C2, 6C3, 6C4, 6C5, and 6C6.

Hence,

6C0 + 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6

6!/0!(6 – 0)! + 6!/1!(6 – 1)! + 6!/2!(6 – 2)! + 6!/3!(6 – 3)! + 6!/4!(6 – 4)! + 6!/5!(6 – 5)! + 6!/6!(6 – 6)!

6!/0!6! + 6!/1!5)! + 6!/2!4! + 6!/3!3! + 6!/4!2! + 6!/5!1! + 6!/6!0!

1 + 6 + 15 + 20 + 15 + 6 + 1

64

Therefore, the number of coins needed = 6*64 = 384 coins. The number of coins in each row = 384/2 = 192 coins

Hence,

Note: The question is incomplete. The complete question probably is: You break your piggy-bank to discover lots of pennies and nickels. You start arranging these in rows of 6 coins. (a) You find yourself making rows containing an equal number of pennies and nickels. For fun, you decide to lay out every possible such row. How many coins will you need? b) How many coins would you need to make all possible rows of 6 coins (not necessarily with equal number of pennies and nickels)?

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