Find f(x) + g (x). f(x) = 8-4x-x``3 g(x) = x`2 + 7x - 9

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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The triangles are cοngruent.

Tο determine whether the twο triangles are cοngruent, similar, οr bοth, we need tο cοmpare their cοrrespοnding sides and angles.

Let's first cοmpare their cοrrespοnding sides:

Triangle 1: sides measure x, x, and 2 units

Triangle 2: sides measure 2 units, x, and x

The sides x and x are the same in bοth triangles, and the side 2 units in triangle 1 cοrrespοnd tο the side 2 units in triangle 2. Hοwever, the οrder οf the sides is different in the twο triangles. We can reοrder the sides in triangle 2 sο that they match the οrder οf the sides in triangle 1:

Triangle 2: sides measure x, x, and 2 units

Nοw we can see that the twο triangles have the same side lengths and are therefοre cοngruent.

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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:33

Step-by-step explanation:

33

The set of all real numbers between 5 and 9, including 5, can be represented by the set-builder notation {x ∈ ℝ | 5 ≤ x ≤ 9}.

A compact, mathematical notation is used to represent a set of components using set-builder notation. In set-builder notation, we express the attributes or features that the components of the set must have in order to be included in the set. The standard format for set-builder notation is x | P(x), where x is a variable that denotes the set's elements and P(x) is a predicate or condition that lists the characteristics each member must possess in order to be included in the set.

We can represent the set of all real numbers  as:

{x ∈ ℝ | 5 ≤ x ≤ 9}

This notation reads "the set of all x in the real numbers such that x is between 5 and 9, including 5."

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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°

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 estimated value of 2/3 is roughly 0.67, of 1 it is 1 and for 0 it is 0.

What does a estimate mean?

A number given to a demographic parameter that was taken from the a statistical sample. A pricing estimate for the job that needs to be done. 3. an assessment or view of the essence, character, or trait of an object or a person.

What is an illustration of an estimate?

To make computations simpler, an estimate is an approximate estimation of the real value, amount, or quantity.

For 2/3, on dividing we get the value as 0.67.

Since 1 is a number and doesn't need to be rounded or approximated, the guess is 1.

Since it is a number without a fractional component, the approximation of 0 also is 0.

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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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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:

The order of the side lengths of the triangles from the least to the greatest is Lk < JL < IJ < JK < IK.

If the angle facing a side of a triangle increases, then the length of the opposite side may also increase. This is because the larger the angle, the more vertical the opposite side becomes, and therefore the longer it may become.

Conversely, if the angle facing a side of a triangle decreases, then the length of the opposite side may also decrease. This is because the smaller the angle, the less vertical the opposite side becomes, and therefore the shorter it may become.

From the given diagram, the largest side of the triangle will be the side directly opposite the largest angle.

Also, the smallest side of the triangle will be the side directly opposite the smallest angle.

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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:

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 factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

What is a factor?

A factor is a number that completely divides another number. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product because the product is divisible by them.

Multiplication and division are the two techniques for determining factors. Rules of divisibility can also be applied.

The given number is 70.

70 is completely divisible is 1.

70 is completely divisible is 2.

70 is completely divisible is 5.

70 is completely divisible is 7.

70 is completely divisible is 10.

70 is completely divisible is 14.

70 is completely divisible is 35.

70 is completely divisible is 70.

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

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Answer:6

Step-by-step explanation:biyhfdvsauybi

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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A, B, and E are the consistent with the random samples on preferred school lunches by 100 students.

A random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample. Random sampling is an important tool in statistics and allows researchers to make inferences about the larger population based on the characteristics of the sample.

Random sampling helps to ensure that the sample is representative of the population and that any statistical analysis done on the sample can be generalized to the larger population.

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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.

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:

Step-by-step explanation:

2 cups of water.

The perimeter of the pond from the calculation is 5.42 meter

We would first have to find the sides using the angle that we have here

b / 2.42 = sin 74

cross multiply

2.42 x sin 74 = 2.33 meters

h / 2.42 = cos 74

2.42 x cos 74 = 0.67 meters

Given that the sides of the triangle are 2.33 , 2.42 and 0.67 meters

The perimeter would be solved by 2.33 + 2.42 + 0.67

= 5.42 meters

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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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