60 people plan to attend the dance and each person will eat 2 slices of cake. If each cake contains 8 slices, how many cakes should you order?

The equation of the straight line joining A to B is y = (1/2)x + 3, the equation of the straight line joining B to C is y = (1/2)x + 3, and A, B, and C are collinear.

What are collinear points?

Collinear points are three or more points that lie on the same straight line. In other words, if three points A, B, and C are collinear, then there exists a straight line that passes through all three points. To determine if three or more points are collinear, we can find the slope of the line that passes through any two of the points. If the slope is the same for all possible pairs of points, then the points are collinear. Otherwise, they are not collinear.

a) To find the equation of the straight line joining A to B, we can use the slope-intercept form of the equation of a line:

y = mx + b

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

The slope of the line passing through A and B is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-8, -1) and (x₂, y₂) = (-4, 1).

m = (1 - (-1)) / (-4 - (-8)) = 2/4 = 1/2

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) = (-8, -1) and m = 1/2.

y - (-1) = (1/2)(x - (-8))

y + 1 = (1/2)(x + 8)

y = (1/2)x + 3

Therefore, the equation of the straight line joining A to B is y = (1/2)x + 3.

b) To find the equation of the straight line joining B to C, we can use the same method:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (-4, 1) and (x₂, y₂) = (12, 9).

m = (9 - 1) / (12 - (-4)) = 8/16 = 1/2

Using point-slope form with the point (x₁, y₁) = (-4, 1) and slope m = 1/2:

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

y - 1 = (1/2)x + 2

y = (1/2)x + 3

Therefore, the equation of the straight line joining B to C is y = (1/2)x + 3.

c)  From the equations of the lines joining A to B and B to C, we can see that both lines have the same slope of 1/2. This implies that the three points A, B, and C are collinear, i.e., they lie on the same straight line.

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Answer: Buckle up this answer is gonna be a rollercoaster and here we go.

To find f.g, we first need to evaluate g(-4) and then use the result as the input for f(x).

We have:

g(-4) = -(-4)^2 + 2 = -16 + 2 = -14

Now, we use this result as the input for f(x):

f(g(-4)) = f(-14) = -14 - 8 = -22

Therefore, f.g = -22.

What a short ride.

Therefore, the simplified expression is 6x² + 11x - 4.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) that represents a quantity or a mathematical relationship between quantities. Expressions can include variables, which are letters that represent unknown or varying values. Expressions can be simple or complex, and they can be used to represent mathematical formulas, equations, inequalities, and functions. Expressions can be evaluated by replacing the variables with specific values and performing the arithmetic operations according to the rules of algebra. Expressions can also be simplified by combining like terms, distributing multiplication, and factoring. Simplifying expressions can help us to better understand their structure and relationships, and it can make them easier to work with in calculations and problem-solving.

Here,

To perform the operation (8x² + 3x - 4) + (-2x² + 8x), we need to combine like terms, i.e., terms that have the same variable and exponent.

First, let's combine the x² terms:

8x² - 2x² = 6x²

Next, let's combine the x terms:

3x + 8x = 11x

Finally, let's combine the constants:

-4 + 0 = -4

Putting it all together, we have:

(8x² + 3x - 4) + (-2x² + 8x) = 6x² + 11x - 4

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Answer:

To find the zeros of the function f(w) = w^2 + 13w + 40, we need to solve the equation f(w) = 0.

We can factor the quadratic expression as (w + 8)(w + 5) = 0.

Therefore, the zeros of the function are w = -8 and w = -5.

Step-by-step explanation:

Answer:The value of angle y is 40°.

Complementary angles are the angles that have their sum equal to 90°.

Therefore, based on the information given, the value of angle y will be calculated thus:

x + y = 90°.

4y - 110° + y = 90°

Collect like terms

4y + y = 90° + 110°

5y = 200°

y = 200/5

y = 40°

The value of angle y is 40°.

Step-by-step explanation:

Answer:

  $1007.03

Step-by-step explanation:

You want the cost of copies for the month at 1 1/3 cents each if the copy counter ran from 6583 to 82110 during the month.

The number of copies made is the difference in counter readings:

  82110 -6583 = 75,527 . . . . . copies made

Each costs 1 1/3 = 4/3 cents, so the cost of these copies is ...

  (75,527 copies) × (4/3 cents/copy) = 100702 2/3 cents ≈ 100703 cents

There are 100 cents in a dollar (or other currency unit), so the cost is about ...

  (100703¢)/(100¢/$) = $1007.03

The total cost of copies for the month is about $1007.03.

__

Additional comment

The currency unit is not specified in this problem. There are a number of world currencies in which the smallest denomination is 1 cent. The US dollar, the Euro, and the Aruban Guilder are some of them.

Answer: Another name would be Line RQ

Not sure if this is what you're looking for but hope it helps!

Therefore , the solution of the given problem of  dot plot comes out to be on the dot plot, 19 vehicles were sold that were not white.

The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear.

Here,

The following numbers are shown as follows based on the dot plot:

Number of scarlet vehicles: 5

=>  8 black vehicles total.

=>  6 white vehicles total.

=>  One silver vehicle is equal to four grey cars.

=>  Blue vehicle count equals one.

The following vehicles are not white vehicles based on the aforementioned criteria.

Thus, we have the depiction shown below.

=> Number of scarlet vehicles: 5

=>  8 black vehicles total.

=>  number of silver vehicles Equals 1

=>  4 grey vehicles totaled

=>  Blue vehicle count equals one.

These wavelengths combine to give us the following

=>  Total = 5 + 8 + 1 + 4 + 1

Analyze the amount

=> Overall = 19

Therefore, there are 19 vehicles.

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Answer: Its 190.  The problem states each dot represents 10 cars.  19 out of 25 dots weren't white.  19*10 is 190.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

bece u sr gģ v vyvy bleh gm have g GMV Espanola unmet yucky nvm i gifted go by Grau Cinco

The net present value of the project is $0.15 million.

Net present value is the present value of after-tax cash flows from an investment less the amount invested.

hee, we have,

The first step is to determine the cash flow of the project.

Cash flow = (sales - cost - depreciation) × (1 - tax) + depreciation

Depreciation = (cost of the asset ) / useful life

Depreciation = $2.18 million / 3

Depreciation = 0.727 million

Cash flow = (1.645 -  0.61 - 0.727) x (1 - 0.21) + 0.727 = $0.97 million

Net present value = -2.18 million + 0.97 / 1.12 +  0.97 / 1.12² +  0.97 / 1.12³

= $0.15 million

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A construction of the scatter plot of the data pairs (year, attendance) is shown below.

An equation of the line of best fit (trend line) is y = 0.19x + 308.93.

The estimated attendance for the year 2005 is approximately equal to 336 people.

In order to determine an equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of attendance would be plotted on the y-axis of the scatter plot.

Based on the scatter plot (see attachment) which models the relationship between the number of years and attendance, an equation for the line of best fit is given by:

y = 5.43x + 254.42

Lastly, we would determine the predicted attendance for the year 2005:

Years, t = 2005 - 1990 = 15 years.

y = 5.43(15) + 254.42

y = 81.45 + 254.42

y = 335.87 ≈ 336 people.

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The value for x is 4√3. The solution has been obtained by using the Pythagoras theorem.

What is Pythagoras theorem?

Pythagoras' Theorem states that the square of a right - angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given the length of the hypotenuse to be 8.

Let the base be 'y'.

So, using Pythagoras theorem,

[tex]x^{2} + y^{2} = 8^{2}[/tex]

From this, we get

[tex]y^{2} = 8^{2} - x^{2}[/tex]   ...(1)

Also,

[tex]2^{2} + Perpendicular^{2} = y^{2}[/tex]    ...(2)

From the figure, we also know that

[tex]6^{2} + Perpendicular^{2} = x^{2}[/tex]

So,

[tex]Perpendicular^{2} = x^{2} - 6^{2}[/tex]

On substituting this in (2), we get

[tex]2^{2} + x^{2} - 6^{2} = y^{2}[/tex]       ...(3)

On equating (2) and (3), we get

⇒[tex]2^{2} + x^{2} - 6^{2} = 8^{2}-x^{2}[/tex]          

⇒ 4 + [tex]x^{2}[/tex] - 36 = 64 - [tex]x^{2}[/tex]

⇒ [tex]2x^{2}[/tex] - 32 = 64

⇒ [tex]2x^{2}[/tex] = 96

⇒ [tex]x^{2}[/tex] = 48

⇒ x = 4√3

Hence, the value for x is 4√3.

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1) a) slοpe m= 1, y-intercept =0 and equatiοn is y=x.

2) a) slοpe m=-1 , y-intercept = 4 and equatiοn is y=-x+4.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.

Here we knοw that, we can sοlve using any twο pοints.

1) Let us take any twο pοints, then

[tex](x_1,y_1)=(3,3) and (x_2,y_2) =(-3,-3)[/tex]

Now using slope formula ,

=> Slope m =[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{-3-3}=\frac{-6}{-6}=1[/tex]

Now using equation formula [tex]y-y_1=m(x-x_1)[/tex]

=> y-3=1(x-3)

=> y-3=x-3

=>y=x-3+3

=> y=x

Hence slope m=1,  y-intercept = 0 and equation is y=x.

2) Let us take two points then

[tex](x_1,y_1)=(0,4) and (x_2,y_2)=(4,0)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1[/tex]

Now using equation formula then , [tex]y-y_1=m(x-x_1)[/tex]

=> y-4=-1(x-0)

=>y-4=-x

=> y=-x+4

Hence slope = -1 , y-intercept = 4 and the equation is y=-x+4.

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the interest for 1 year:

[tex]3.5\% \cdot 4000 = 140[/tex]

the interest for 6 months:

[tex]\dfrac{140}{2} = 70[/tex]

the interest for 1 year 6 months:

[tex]140+70 = \bf \$ 210[/tex]

Based on this information, the angle pairs can be proven congruent is option D. ∠ABC and ∠EBD.

Congruent angles are angles that have the same measure or degree. In other words, two angles are congruent if they have the same amount of rotation and are of the same size and shape, regardless of their position or orientation.

Congruent angles are denoted by the symbol ≅, which is read as "congruent to". For example, if angle A and angle B both measure 45 degrees, we can say that angle A ≅ angle B, or that angle A is congruent to angle B.

Therefore, angle ABC and angle EBD shares same measurement or same degrees. Angle ABC is congruent to angle EBD.

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The surface area of the rectangular prism is 376 square inches.

Surface area is the total area that the surface of a 3-dimensional object covers, including all of its faces and sides. It is measured in square units.

To find the surface area of a 3-dimensional object with dimensions of 2in, 6in, 10in, 8in, and 2in, you will need to add up the areas of each of its faces.

Assuming that the object is a rectangular prism, here are the steps to find its surface area:

Identify the dimensions of the rectangular prism: length, width, and height.

Length: 10in

Width: 8in

Height: 6in

Calculate the area of each face:

Front and back faces: length x height = 10in x 6in = 60 sq.in x 2 = 120 sq.in

Top and bottom faces: width x length = 8in x 10in = 80 sq.in x 2 = 160 sq.in

Side faces: height x width = 6in x 8in = 48 sq.in x 2 = 96 sq.in

Add up the areas of each face to get the total surface area:

Total surface area = 120 sq.in + 160 sq.in + 96 sq.in = 376 sq.in

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Therefore , the solution of the given problem of unitary method comes out to be N69,750 was given as the water rate for 7500 litres of water.

One may use this commonly utilized ease, preexisting variables, or any important elements from the initial Diocesan customizable query to achieve the goal. If so, there will be another chance to engage with the object. If not, every important component that influences the manner in which evidence of an algorithm functions will be lost.

Here,

The price for the first 500 gallons is N5 per litre, so

=> 500 * N5 = N2,500.

The price for the following 500 gallons is N8.00 per litre, or

=> 500 * N8.00 = N4,000.

The expense for this tier is

=> 3000 * N10.00 = N30,000 because the following 3000 litres (from 1501 to 4500 litres) are charged at N10.00 per litre.

The expense for this tier is

=> 3000 * N10.00 = N30,000 because the final 3000 litres (from 4501 to 7500 litres) are also charged at N10.00 per litre.

As a result, the full price for 7500 liters of water is:

The sum of N2,500, N3,250, N4,00, N30,000, and N30,000 is N69,750.

Therefore, N69,750 was given as the water rate for 7500 litres of water.

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After calculating the straight angle we know that ∠BAC is (A) 150°.

What is the straight angle?

A straight angle in geometry is one that is 180 degrees in length.

It looks like a straight line, which is why it is known as a straight angle.

In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

A straight angle in geometry is an angle with a vertex point that is at 180 degrees.

In other words, an angle becomes a straight angle when its arms point in the opposite direction.

So, we know that s straight angle is always 180°.

∠BAD is a straight angle.

We can also observe that:

∠BAD = ∠BAC + ∠CAD

Now, solve as follows:

∠BAD = ∠BAC + ∠CAD

180 = ∠BAC + 50

180 - 50 = ∠BAC

130° = ∠BAC

Therefore, after calculating the straight angle we know that ∠BAC is (A) 150°.

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Calculating the surface area οr vοlume οf a fοrm is impοrtant in a variety οf real-wοrld situatiοns, such as when determining hοw much water is required tο fill a pοοl (rectangular prism) οr hοw much wrapping paper is required tο wrap a candle (cylinder) οr basketball (square) (sphere).

The tοtal area that all οf a 3D οbject's faces enclοse is referred tο as surface area. Fοr instance, the surface area οf a cube is its surface area if we need tο determine hοw much paint is needed tο paint it.

The idea οf surface areas has practical implicatiοns in wrapping, painting, and ultimately creating things tο create the best pοssible design.

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The values of x in the equation are x = 1 and x = 13

Equations are mathematical statements that express the equality of two expressions using mathematical symbols such as variables, numbers, and operations.

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

(x - 7)^2 = 36

Take the square root of both sides of the equation

So, we have the following representation

x - 7 = ±6

Add 7 to both sides

x = 7 ± 6

Evaluate the expression

x = 1 and x = 13

Hence, the solutions are 1 and 13

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Answer:

a) 1

b) 4

c) 14

d) 1

e) 12

f) 15

h) 20

i) 25

j) 40

Step-by-step explanation:

Some mistakes have been made.

Correct answers so far:

a, b, c, d, e, f are correct

h, maybe

Corrections:

g)

13 - ( + 9) can be rewritten as 13 - 9, which is 4

h) I assume the 9 is supposed to be a [tex]\sqrt{ 9}[/tex] ? If so, then the answer is correct

i) 18 - -7 can be rewritten as 18 + 7 = 25. The two negatives turn into a positive.

j)26 - -14 = 40. The two negatives turn into a positive.

Answer:

The answer is 78.5° .................

Answer:

78.5°

Step-by-step explanation:

For <A, AC is the adjacent leg.

AB is the hypotenuse.

The trig function that relates the adjacent leg to the hypotenuse is the cosine.

cos A = adj/hyp

cos A = 3/15

cos A = 1/5

A = cos^-1 0.2

A = 78.5°

The resulting set of isometries, together with the operation of composition, forms a group.

In the context of the paragraph, "a group under composition" refers to a group that is formed by combining isometries (permutations that preserve distances) of a geometric configuration through the operation of composition.

In other words, if you have a set of isometries of a geometric configuration (such as translations, rotations about a point, and symmetries about a straight line), you can combine them through composition (applying one after the other) to obtain new isometries. The resulting set of isometries, together with the operation of composition, forms a group, which is called the group of isometries of the configuration.

This group has certain properties, such as closure (meaning that the result of composing two isometries is also an isometry), associativity (meaning that the order of composition doesn't matter), identity (meaning that there is an isometry that leaves all points fixed), and inverses (meaning that for every isometry, there is another isometry that undoes its effect). These properties make the group a useful tool for studying the symmetries and transformations of geometric configurations in fields such as crystallography and quantum mechanics.

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Applying the Trigonometric ratios, the length of DC is approximately 30 units.

To find the length of DC, we have to apply the Trigonometric ratios.

First of all, find BD.

Considering right triangle ADB, we have:

Reference angle (∅) = 54°

Length of Hypotenuse = 20

Length of opposite side = BD = ?

Apply the sine ratio:

sin 54 = opp/hyp

sin 54 = BD/20

BD = sin 54 × 20

BD ≈ 16

Use the tangent ratio to find DC:

Reference angle (∅) = 28°

Length of adjacent side = DC = ?

Length of opposite side = BD = 16

tan 28 = opp/adj

tan 28 = 16/DC

DC = 16/tan 28

DC ≈ 30

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Answer:33

Step-by-step explanation:

33

Answer:6

Step-by-step explanation:biyhfdvsauybi