The cost of 1 cap and 1 wallet is
£28.
The cost of 2 caps and 1 wallet is
£45.
a) How much does 1 cap cost?
b) How much does 1 wallet cost?

In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.

Now Alan has 11 less than 2 times the number of cards Bill has then,

=> A = 2B-11 ------------->1

And Calvin has 1 more than 1 times the number of cards Bill has then,

=> C =  B+1 ----------> 2

Here Alan and Calvin has same number of cards then

=> 1 = 2

=> 2B - 11 = B +1

=> 2B-B = 11+1

=> B = 12

Now put B= 12 into 1 then

=> A = 2(12)-11= 24-11 = 13

Now put B= 12 into 2 then

=> C = 12+1 = 13

Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.

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Answer:

[tex]D'(-3,-1.5), E'(0,4.5), F'(3,-3)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

Answer:

The total cost of the salad and baked ziti is $3.50 + $9.25 = $12.75

To calculate the tip, you need to multiply the total cost by the tip percentage (expressed as a decimal)

Tip = $12.75 x 0.15 = $1.91

So you should leave $1.91 as a tip for the waiter.

Step-by-step explanation:

If he works 14 hours then he will earn the amount of $105 which is true and if he works 16 hours then he will earn $120 which is true.

You should be aware that a linear equation is defined as an equation in which the highest power of the variable is one.

The given graph represents Elisa's work and the amount of money he earns at his job.

According to the given graph,

We can see two points are (4, 30) and (8, 60)

The linear equation will be

⇒ y - 30 = (60-30)/(8-4)(x-4)

⇒ y - 30 = (30)/(4)(x-4)

⇒ y - 30 = 7.5(x-4)

⇒ y = 7.5x - 30 + 30

⇒ y = 7.5x

Elisa's work = 14 hours then we verify the response by substituting x = 14 in the above equation,

⇒ y = 7.5(14)

⇒ y = 105

Thus,  if he works 14 hours then he will earn $105

Elisa's work = 16 hours then we verify the response by substituting x = 16 in the above equation,

⇒ y = 7.5(16)

⇒ y = 120

Thus, if he works 16 hours then he will earn $120.

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Correct question:

The graph below shows the relationship between the number of hours

Cody works and the amount of money he earns at his job. Which of the

following statements is not true about the relationship?

100

90

80

70

60

MONEY EARNED

50

40

30

20

10

1

2

3

4

5

6

7

8 9 10

HOURS WORKED

The polynomial 8X/Y has a coefficient of X of 8.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is often a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

In the above polynomial 8X/Y, the coefficient of X is 8.

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(-4, -2.5) represents a point on the cartesian coordinate system having -4 units on the x axis and -2.5 units on the y axis

A Cartesian coordinate system in a plane is a system of coordinates that identifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

The two fixed perpendicular oriented lines are

They are represented by a pair of numerical coordinates called ordered pair. The ordered pair are arranged such that the x values are first then a comma and the y values.

This is written as (x, y) hence for (-4, -2.5) x = -4 and y = -2.5

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4 2 add y 2 root that

it's pretty easy and thanks for the high points ur welcome ur in the matrix kid

Answer:

b) m = -2 and b=10 and c) m= 2/5 and b=4

Step-by-step explanation:

For b, we know that the b value (y-intercept) is 10 because it is the y value when x= 0, which is shown on the table as 10.

Next, to find the slope (m-value) we know that 10 gets added to the y value so then x(2) + 10 = 6

subtract 10 from both sides and you get 2x = -4

divide both sides by 2 to get x= -2 or our m-value (slope)
-------------------------------------------------------------------------------------------------------------
For c, we know that the graph intercepts the y-axis at 4, so that is our b value.

We know know: y= m(x) + 4

To find the slope, we use the formula: rise/run

When the graph goes up 6 to get to y=10, the x value goes 15 across

Rise = 6 ;  Run = 15

6/15 = 2/5

Therefore, the m value is 2/5

To find g(0) we need to substitute x = 0 into the function g(x) = 6x + 2.

g(0) = 6(0) + 2 = 0 + 2 = 2

So, g(0) = 2

Therefore, the value of the function g(x) when x is equal to 0 is 2.

Answer:

27000 m

Step-by-step explanation:

1km = 1000 m

27km = 27 x 1000 = 27000 m

So, the answer is 27000 m

Answer:27 km in meters is 27000 m

Step-by-step explanation:

multiply the length by 1000!

According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.

According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.

∆ABC is an isosceles triangle with AB = AC.

Construction: Altitude AD from vertex A to the side BC.

Proof: We know, that the altitude of an isosceles triangle from the vertex is the perpendicular bisector of the third side. Thus, we can conclude that,

∠ADB = ∠ADC = 90º ----------- (1)

BD = DC ---------- (2)

Consider ∆ADB and ∆ADC

AB = AC [Given]

AD = AD [common side]

BD = DC [From equation (2)]

Thus, by SSS congruence we can say that,

∆ADB ≅ ∆ADC

By CPCT, ∠B = ∠C.

Hence, we have proved that if two sides of a triangle are congruent, then the angles opposite to the congruent sides are equal.

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An picture is warped to fit a target brain by applying a coordinate transformation on the source image. The degree of coordinate transformation difficulty depends on the spatial normalization's regional scope.

An essential method for converting data between reference systems uses a set of control points that are measured in both systems, which is known as a coordinate transformation. To pinpoint the location of robots, sensors, and other items in robotics applications, a variety of different coordinate systems can be used. Position and orientation data can typically be used to specify where an object is located in 3-D space.

The rotation matrix is used to transform coordinate systems with various orientations. This changes the components of any vector with regard to a coordinate frame into the components of a frame that has been rotated with respect to the original frame. The geographic coordinate system of the layers is calculated to be converted to match the geographic coordinate system in the transformation.

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The number of sections that each have an area of 1/2 square mile will be 8.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

4 square miles of land are separated into sections that each have an area of 1/2 square mile.

Then the number of the equal section is given as,

⇒ 4 / (1/2)

⇒ 8 section

The number of sections that each have an area of 1/2 square mile will be 8.

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Answer:

4,6,8,12

Hope it helps because im not sure if its right

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Using the function f(x) = 500(0.67)^x :

A).f(0) = 500, f(1) = 335, f(2) = 224.45 and f(3) = 150.3815

B). 33% of bugs are eaten each day

C). 67% of the bugs remain each day

D). After day 7 will there remain fewer than 40 bugs in the farm.

The function of a function rule is defined as the process that changes the input value to output.

day 1 will have 165 bugs eaten with a percentage evaluated as;

(165 × 100)/500 = 33%

day 2 will have 110.55 bugs eaten with a percentage evaluated as;

(110.55 × 100)/335 = 33%

day 3 will have 74.0685 bugs eaten with a percentage evaluated as;

(74.0685 × 100)/224.45 = 33%

day 1 will have 335 bugs remaining with a percentage evaluated as;

(335 × 100)/500 = 67%

day 2 will have 224.45 bugs remaining with a percentage evaluated as;

(224.45 × 100)/335 = 67%

day 3 will have 150.3815 bugs remaining with a percentage evaluated as;

(150.3815 × 100)/224.45 = 67%

At day 7;

f(7) = 500(0.67)⁷

f(7) = 30.30.

Therefore, 500, 335, 224.45 and 150.3815 are the respective population the days:0, 1, 2, and 3. for the function f(x) = 500(0.67)^x

33% of bugs are eaten each day

67% of the bugs remain each day and,

After day 7 will there remain fewer than 40 bugs in the farm.

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According to the notes of Maggie the price for per foot length of deck division board is -6 feet for $5.88 = $0.98,8 feet for $8.79 = $1.09 ,10 feet for $10.68 = $1.06 ,12 feet for $13.43 = $1.11 .

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Here,

The first record for deck board noted by Maggie is -

The length of the deck board = 6 feet

Price for 6 feet of deck board = $5.88

Use the division method -

Price for 1 feet of deck board = 5.88/6

Price per feet of deck board = $0.98

The second record for deck board noted by Maggie is -

The length of the deck board = 8 feet

Price for 6 feet of deck board = $8.79

Use the division method -

Price for 1 feet of deck board = 8.79/8

Price per feet of deck board = $1.09

The third record for deck board noted by Maggie is -

The length of the deck board = 10 feet

Price for 6 feet of deck board = $10.68

Use the division method -

Price for 1 feet of deck board = 10.68/10

Price per feet of deck board = $1.06

The fourth record for deck board noted by Maggie is -

The length of the deck board = 12 feet

Price for 6 feet of deck board = $13.43

Use the division method -

Price for 1 feet of deck board = 13.43/12

Price per feet of deck board = $1.11

The fifth record for deck board noted by Maggie is -

The length of the deck board = 14 feet

Price for 6 feet of deck board = $15.65

Use the division method -

Price for 1 feet of deck board = 15.65/14

Price per feet of deck board = $1.11

The sixth record for deck board noted by Maggie is -

The length of the deck board = 16 feet

Price for 6 feet of deck board = $17.88

Use the division method -

Price for 1 feet of deck board = 17.88/16

Price per feet of deck board = $1.11

The seventh record for deck board noted by Maggie is -

The length of the deck board = 18 feet

Price for 6 feet of deck board = $20.99

Use the division method -

Price for 1 feet of deck board = 20.99/18

Price per feet of deck board = $1.16

The eighth record for deck board noted by Maggie is -

The length of the deck board = 20 feet

Price for 6 feet of deck board = $24.99

Use the division method -

Price for 1 feet of deck board = 24.99/20

Price per feet of deck board = $1.24

Therefore, the value for deck board per foot length is $0.98, $1.09, $1.06, $1.11, $1.11, $1.11, $1.16, $1.24.

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Answer:

  6.9

Step-by-step explanation:

You want half the side length of an equilateral triangle with an altitude of 12.

The altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:

  (2x)² = x² +12²

  3x² = 144 . . . . . . . . subtract x²

  x² = 48 . . . . . . . . divide by 3

  x = √48 = 4√3 . . . take the square root

  x ≈ 6.9

__

Additional comment

You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.

Brianna wants to reduce it by a scale factor of 1/2, the area of the new garden is 48 ft².

The territory a rectangle occupies inside its four sides or limits is known as its area. A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper.

The formula for calculate the area of a rectangle is:

area of a rectangle = length × width

Where "I" is the length and " w " is the width.

The dimensions of the garden box are:

l = 12 ft

w = 8 ft

Therefore, its area is:

A = (12 ft)(8 ft)

A = 96 ft²

Since Brianna wants to reduce it by a scale factor of 1/2, the area of the new garden is:

Area of new garden = 1/2(96 ft²)

Area of new garden = 48 ft²

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For the value of f (x) = 11, the value of x is

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

We have to given that;

The function is,

⇒ f(x) = -5x + 1

And, f (x) = 11

Now, We have;

⇒ f(x) = -5x + 1

Substitute f (x) = 11, we get;

⇒ 11 = - 5x + 1

⇒ 5x = - 11 + 1

⇒ 5x = - 10

⇒ x = - 2

Thus, The value of x = - 2

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The sides 10 cm, 24 cm and 26 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angled triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

26² = 24² + 10²

676 = 576 + 100

Thus, the sides 10 cm, 24 cm and 26 cm can form a right-angled triangle.

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The total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

We can start by using the following equation to find the total cost of the child tickets:

Child tickets cost = Number of child tickets x Cost per child ticket

In this case, the number of child tickets is 4 children/family x 6 families = 24 children

The cost per child ticket is $4.

So, the total cost of the child tickets would be:

24 children x $4/child = $96

Similarly, we can find the total cost of the adult tickets:

Adult tickets cost = Number of adult tickets x Cost per adult ticket

In this case, the number of adult tickets is 2 adults/family x 6 families = 12 adults

The cost per adult ticket is $8.

So, the total cost of the adult tickets would be:

12 adults x $8/adult = $96

To find the total cost of the festival tickets, we can add the cost of the child tickets and the cost of the adult tickets:

Total cost = Child tickets cost + Adult tickets cost

$96 + $96 = $192

So, the total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

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The slope of the line passing through the points is given by the equation Slope m = 15/11

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( 7 , 10 )

Let the second point be represented as Q = Q ( 18 , 25 )

Now , the slope of the line between the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 25 - 10 ) / ( 18 - 7 )

On simplifying the equation , we get

Slope m = 15/11

Hence , the slope of the line is m = 15/11

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4/5 and 6/10 form a proportion.

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The size of the cardboard piece required is 7627.0 in.

The formula for finding the size of a box is

2(L + W) + 8L + 8W = Perimeter of the cardboard piece

Where L = Length, W = Width

We need to find L and W to find the size of the cardboard piece.

7623 = 2(L + W) + 8L + 8W

7623 = 2L + 2W + 8L + 8W

7623 = 10L + 10W

7623/10 = L + W

762.3 = L + W

Let's take L = 500 and W = 262.3 (762.3 - 500 = 262.3)

Now we plug in the values of L and W in the original formula

2(500 + 262.3) + 8(500) + 8(262.3) = 7623

2(762.3) + 4000 + 2102.4 = 7623

1524.6 + 4000 + 2102.4 = 7623

7627.0 = 7623

Therefore, the size of the cardboard piece required is 7627.0 in.

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The equation of the function g(x) will be √ [ (x) -  4 )].

A line that, in analytical geometry, is an asymptote of a curve is one where, as one or both of the x or y coordinates tend to infinity, the distance between the curve and the line approaches zero.

An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and related contexts.

Given that the function F(x) is √x and is horizontally stretched by a factor of 4 to form function g(x).

The equation of the stretched function can be written as:-

f(x) = √x

g(x) = √ [ (x) -  4 )]

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A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.

A graph can show a functional relationship by showing a line or curve that consistently increases or decreases when the independent variable is changed. This will show a direct relationship between the two variables, and the pattern of the line or curve will show the functional relationship that exists.

A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.

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Therefore , the solution of the given problem of triangle comes out to be CA = 8.94 cm .

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 : A right triangle ,

Area  =16 cm squarea

=> 1/2 * b * h = 16

=> 8*h = 32

= > h  =4

=> 8²+ 4²= CA²

=>  CA² =  64 + 16

=>  CA² =  80

=> CA = √80

=>CA = 8.94 cm

Therefore , the solution of the given problem of triangle comes out to be CA = 8.94 cm .

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Answer:

Step-by-step explanation:

10.00 amps

The solution of the system of equations for this problem is given as follows:

(x-intercept, 0).

Via graphing, the solution of the system of equations is obtained by the point of intersection of the points.

An horizontal line can be traced through the point of intersection.

This line coincides with the x-axis, hence the y-coordinate of the solution is given as follows:

y = 0.

Due to the x-intercept method, the x-coordinate of the solution is the x-intercept.

The equations for this problem are not given, hence the solution is given in general terms.

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