b) Work out the size of angle
answer in degrees (°).
56°
X
x. Give your
59°
77°

Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.

Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:

=> s =√((h²) + ((w/2)²))

We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.

The following formula can be used to determine how much steel tubing is required:

=>  L = 3s + 3h

where h is the height of the frame and s is the length of each edge of the triangle.

Using the method instead of s, we obtain:

=> L = 3(√(h²) + ((w/2²))) + 3h

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The equation for number of miles is 14/7 = x and she ran 2 miles each day.

Simplify the equation to bring all the variable terms to one side and the constant value to the other in order to solve linear equations with a single variable. Find the LCM (least common multiple) if there are any fractional terms, then simplify them so that the variable values are on one line and the steady terms are on the other.

Let us suppose the number of miles she ran each day = x.

Given that, Aroline ran 14 miles in 7 days.

Thus,

Total distance / Number of days = x

14/7 = x

x = 2

Hence, the equation is 14/7 = x and she ran 2 miles each day.

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It will take {log(1 - r/n)/n} years to exactly double your investment.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

Given is that an investment of $2800 made at an APR of 5% compounded monthly.

The formula for compound interest is -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

For A = 2P, we can write -

Substituting 2P = A, we get -

2P = P(1 + r/n)^nt

2 = (1 + r/n)^nt

log 2 = log {(1 + r/n)^nt}

log 2 = (nt) log(1 + r/n)

(log 2)/log(1 + r/n) = nt

{t} = log{2 - 1 - r/n}/n

{t} = log{1 - r/n}/n

Therefore, it will take {log(1 - r/n)/n} years to exactly double your investment.

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Answer:

$36,500 per employee

Step-by-step explanation:

$730,000/20 employees

the answer is 42 will be 42 because i answer that before

Answer:

16.48%

Step-by-step explanation:

6 democrates

3 republicans

5 independents

Total number: 6+3+5=14

Probability of selecting an independent:

#of independents/ Total number

5/14= 0.3571

Probability of selecting a democrat:

# of democrats/ Total number-1

6/13= 0.4615

Probability of independent then democrat:

0.3571x0.4615=0.1648

0.1648x100= 16.48%

The pair of complementary angles is the one in the last option:

BFC and DFE

Two angles A and B are complementary if their measures add upto 90°, on the diagram we can see that the angles defined are:

AFB = 40°

BFC = 60°

CFD = 50°

DFE = 30°

Now just see which pairs of these angles add up to 90 degrees, these pairs are complementary angles.

Then the sets of complementary angles are:

AFB and CFD

BFC and DFE

So the correct option  is the last one.

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Answer:

(-3,0), (1,0)

Step-by-step explanation:

The x-intercept is when the y = 0

In the graph, we see the line cross through the x-axis located at (-3,0), (1,0)

So, the x-intercepts are located at (-3,0) and (1,0)

Answer:

x intercepts are 1 and -3

Step-by-step explanation:

X intercepts are obtained by looking at a point where the parabola touches the x axis

Using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

What is a system of equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations. Finding the value of the variable that makes the condition of all the given equations true is the primary goal when solving an equation system.

1) y = -3 and x = -6

This system of equations has only one solution as the variables have only a constant as their value.

2) y = 2x and y = -2x

    There is only one solution to this system of equations. It is x =0 and y = 0. This solution only satisfies these equations.

3) y = -x -2

   y = -x -6

  There is no solution to this system of equations as the mathematical operation on two numbers will not give two values.

4) y = 3x + 4

2y = 6x + 8

There is an infinite number of solutions as the second equation when divided by 2 becomes y = 3x + 4, which is the same as the first equation.

5) y = 9x -1

   y = x + 9

 There is only one solution for this system of equations.

Therefore using the method of solving a system of equations, we grouped each system as no solution, one solution and infinite solutions.

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Answer:

We can simplify the given expression using the rules of exponents and radicals:

4xy³√ 27x^2y^5

= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)

= 4xy * ³√(3^3 * x^2 * y^3 * y^2)

= 4xy * 3xy * ³√y^2

= 12x^2y^2 * ³√y^2

Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.

Step-by-step explanation:

The shape οf the graph is similar tο the letter W; hοwever, the regiοn οf interest will lie οn the right οf the οrigin, which means οnly the right half οf the W(a negative number οf cans cannοt be prοduced).

The prοfit prοduced will be maximized if the number οf cans prοduced is greater than 3. The cοmpany will be at a lοss if the number οf cans prοduced is near 2.5. The break even situatiοns are present if the cοmpany prοduces 2 οr 3 cans.

A pοlynοmial functiοn is a functiοn that can be expressed as a sum οf pοwer functiοns in οne variable, where each term has a cοnstant cοefficient and a nοn-negative integer expοnent.Tο sketch the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex], we can start by analyzing the end behaviοrs οf the functiοn and identifying where the functiοn crοsses the x-axis (i.e., where P(x) = 0).

Tο find the x-intercepts, we need tο sοlve fοr the rοοts οf the equatiοn P(x) = 0. This can be dοne by factοring the expressiοn οr by using numerical methοds. After sοme algebraic manipulatiοn, we can factοr the expressiοn as fοllοws:

[tex]P(x) = (x-3)(x+1)(x^2-8x-6)[/tex]

Therefοre, the rοοts οf the equatiοn P(x) = 0 are x = 3, x = -1, and x = 4 + √(7) οr x = 4 - √(7). The first twο rοοts indicate that the cοmpany breaks even when x = 3 οr x = -1, which means that the cοmpany needs tο prοduce and sell at least 3 οr -1 cans οf sοda tο make a prοfit οf zerο.

With this infοrmatiοn, we can sketch the graph οf the functiοn by plοtting the x-intercepts and the end behaviοrs. The graph will be symmetric abοut the vertical line x = 1.5 (the average οf 3 and -1) and will have a glοbal minimum at the pοint (1.5, -19.5). The graph will alsο have twο additiοnal rοοts at x = 4 + 2√(7) and x = 4 - 2²(7).

In summary, the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex] has a "U" shape with a glοbal minimum at (1.5, -19.5). The cοmpany will break even when it prοduces and sells at least 3 οr -1 cans οf sοda. By analyzing the end behaviοrs and the x-intercepts, we can sketch the graph withοut using technοlοgy.

Hence, the graph of the function would be given below:

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110 is the value of x in function .

What exactly are function and example?

A function is a type of rule that produces one output from one input.   This is illustrated by the equation y=x2. You only get one output for y if you enter anything for x.

                        Considering that x is the input value, we would state that y is a function of x.

f(x) = {  5;  x< 1 }

        { -1/2x + 4 ; x≥ 1 }

 f(4) =  { -1/2  * 4 + 4 }

         =  { -2 + 4 }

         = { 2 }

f( -2) =  { -1/2 * -2 + 4 }

         =  { 1 + 4 }

          = 5

3f(0) = { -1/2 * 0 + 4 }

       = { 0 + 4}

        = 4 * 3 = 12

10f(14) = ( -1/2 * - 14 + 4 )

        =  7 + 4

         = 10 * 11  = 110

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Answer:

Step-by-step explanation:

[tex]2(3x-2) = 2\times3x-2\times2[/tex]     (multiply each term in the parenthesis by 2)

               [tex]=6x-4[/tex]

Answer:

6x - 4

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 2(3x - 2)

Let's simplify the expression,

→ 2(3x - 2)

→ 2(3x) + 2(-2)

→ 6x + (-4)

→ 6x - 4

Hence, the answer is 6x - 4.

Answer:

8,192

Step-by-step explanation:

20/100*80 =16 apply tjis in every step as they asked 4 times

The way we can find the pencil Dan has in total is 16+5

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equations.

San has 16 pencils with him before,

Quentin gives him more 5 pencils

then the total pencil Dan will have is obtained by adding all the pencils together,

= 16+5

= 21 pencils

therefore the total number of pencil is found by 16+5 = 21

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The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

A ratio is a mathematical comparison of two quantities or values. It is expressed as the quotient or fraction of one value to another value.

Ratios are often written in the form of a:b or a/b, where a and b are the two quantities being compared.

To complete the following table determine the ratio of the table using the values in the table and calculate the remaining values

Here we have

The ratio table -1

Pages   50                        

Hours    1      3      5      10

Here, the ratio of page/ hours = 50/1 = 50

Let the x, y, and z be the values

According to ratio

=> x/3 = y/5 = z/10 = 50

=> x/3 = 50 => x = 150

=> y/5 = 50 => y = 250

=> z/10 = 50 => z = 500

The ratio table - 2

Feet    100

Hours   1       2     4     6  

The ratio of feet/ second = 100/1 = 100

Let a, b, and c be the values

=> a/2 = b/4 = c/6 = 100

=> a/2 = 100 => a = 200

=> b/4 = 100 => b = 400

=> c/6 = 100 => c = 600

Therefore,

The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 900[1+(0.10)(1)] \implies A = 990[/tex]

Answer:

The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:

V = (2)(7/3)(2)

V = 28/3

V = 9.33 (rounded to two decimal places)

So the volume of the rectangular prism is approximately 9.33 cubic units.

Answer:

x=3

x=-7

Step-by-step explanation:

The angle measure of minor arc QS is 92 degrees, and the angle measure of angle QQS is 46 degrees.

What is Angle?

In geometry, an angle is a figure formed by two rays that have a common endpoint, called the vertex of the angle. The rays that form the angle are called the sides of the angle. Angles are typically measured in degrees or radians and are used to describe the amount of rotation between two intersecting lines or planes.

In a circle, the measure of an inscribed angle is equal to half the measure of the intercepted arc. Since QS intercepts the minor arc QR, the measure of angle QRS is equal to half the measure of the minor arc QS.

Therefore, if m∠QRS = 46, then m(arc QS) = 2×m∠QRS = 2×46 = 92 degrees.

Since the measure of an arc is equal to the measure of the central angle that intercepts it, and the sum of the measures of the central angles in a circle is 360 degrees, we have:

m(arc QS) + m(arc QR) = 360 degrees

Substituting the value of m(arc QS) that we found above, we get:

92 degrees + m(arc QR) = 360 degrees

Solving for m(arc QR), we get:

m(arc QR) = 360 degrees - 92 degrees = 268 degrees

Since QS is a minor arc of the circle, the measure of angle QQS is equal to half the measure of the arc QS. Therefore, we have:

m∠QQS = 0.5×m(arc QS) = 0.5×92 = 46 degrees

Therefore, the angle measure of minor arc QS is 92 degrees, and the angle measure of angle QQS is 46 degrees.

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Sure, here's a complete table of y-values for different x-values:

x y = 9*(13)^x

0 9

1 117

2 1521

3 19773

4 256809

5 3335777

6 43363161

7 562002993

8 7304038917

9 94852405821

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. Functions are often represented using function notation, where the input is the independent variable and the output is the dependent variable. Functions are used to model relationships between different quantities or variables, and are an essential tool in many areas of mathematics, science, engineering, economics, and more. They allow us to make predictions, analyze data, and understand complex systems.

Here,

The exponential function y = 9*(13)^x means that for any given value of x, we can calculate the corresponding value of y by plugging in x and performing the calculation. The base of the exponential function is 13, which means that the function will increase rapidly as x gets larger.

For example, if x = 0, then y = 9*(13)⁰ = 91 = 9.

If x = 1, then y = 9(13)¹ = 913

= 117.

If x = 2, then y = 9(13)² = 9*169

= 1521.

And so on.

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Answer:

it should be DCE

Step-by-step explanation:

Since both ABE and DCE are similar because because they are both corresponding angels that are congruent.  I'm sorry i couldn't think of another triangle but I'm hoping that at least helped a  bit

The distance between points A and B is: A. 4√5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given parameters into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-4))² + (-2 - 2)²]

Distance = √[(8)² + (-4)²]

Distance = √(64 + 16)

Distance = √80

Distance = √16 × √5

Distance = 4√5 units.

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Answer:

none of them are right it is 4 to the 10

Step-by-step explanation:

9x^3 + 4x^2 + 5

Explanation:

Let's simplify step-by-step.

6x^2−3−5x^3−(4x^3+2x^2−8)

Distribute the Negative Sign:

=6x^2−3−5x^3+−1(4x^3+2x^2−8)

=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

Combine Like Terms:

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)

=−9x^3+4x^2+5

The zeros ( roots ) of the function y = (x + 2)^2 - 25 are x = 3 and x = -7.

Given the function in the question;

y = ( x + 2 )² - 25

To find the zeros of the function, simply means find the values of  x in the function y = ( x + 2 )² - 25, when y equals zero.

Equat the function to 0

(x + 2)^2 - 25 = 0

Adding 25 to both sides, we get:

(x + 2)^2 - 25 + 25  = 0 + 25

(x + 2)^2  = 25

Taking the square root of both sides, we get:

x + 2 = ±√25

x + 2 = +5

Solving for x, we get:

x = -2 + 5 = 3

or x = -2 - 5 = -7

Therefore, the zeros of the function are 3 and -7.

Option 4) -7 and 3 is the correct answer.

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It will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

A lοgarithm is an inverse οperatiοn tο expοnentiatiοn. It is a mathematical functiοn that helps tο sοlve equatiοns where the variable is in the expοnent. The lοgarithm οf a number tο a certain base is the expοnent tο which the base must be raised tο get that number.

Accοrding tο given infοrmatiοn :

In the given expressiοn, 1,000 • e0.034t, the variable "t" represents the time in years, and "e" is a mathematical cοnstant called Euler's number (apprοximately 2.71828).

The entire expressiοn represents the amοunt οf mοney in an accοunt after "t" years, assuming an initial investment οf $1,000 and a cοntinuοus interest rate οf 3.4% per year (0.034 in decimal fοrm).

Tο find the number οf years it will take fοr the accοunt tο reach $15,000, we can set the expressiοn equal tο 15,000 and sοlve fοr "t".

1,000 • e0.034t = 15,000

Dividing bοth sides by 1,000 gives:

e0.034t = 15

Tο sοlve fοr "t", we can take the natural lοgarithm (ln) οf bοth sides:

ln(e0.034t) = ln(15)

0.034t • ln(e) = ln(15)

Since ln(e) = 1, we can simplify tο:

0.034t = ln(15)

Dividing bοth sides by 0.034 gives:

t = ln(15) / 0.034

Using a calculatοr, we get:

t ≈ 23.29

Therefοre, it will take apprοximately 23.29 years fοr the accοunt tο reach $15,000, assuming the given initial investment and interest rate.

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Zeros, vertex, and end behavior can all be used to determine the height that the golf ball travels from its initial location to the point where the golf ball starts falling towards the ground.

Graph is a data structure that consists of a set of nodes and edges that connect those nodes. Nodes are used to represent entities, such as people, places, or objects, and edges are used to represent the connections between those entities. Graphs are used to represent relationships between data, such as in networks, social media, and biological systems. Graphs can also be used to represent mathematical equations, as in function graphs.

Zeros, or x-intercepts, are the points where the graph of the quadratic function crosses the x-axis. The vertex is the highest point of the graph and can be used to determine the peak of the golf ball's trajectory. Finally, the end behavior of the graph can be used to determine how the graph will change as x increases or decreases without bound. This can be used to determine the point at which the golf ball begins to fall towards the ground.

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Answer: .654 not rounded

Step-by-step explanation:

5.232 divided by 8 is 0.654

The domain of the function y = 3Inx graphed below is: A. x greater than 0.

A domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {1, ∞} or x > 0.

In conclusion, ln(0) is undefined and there is no negative natural logarithm, ln.

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The area of the sector is 37.7 ft.

A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.

The formula for the area of a sector is given by

Where θ is the central angle in degrees, and r is the radius of the circle

Here we have

A circle has a radius of 4 ft.  

The central angle of sector formed = 270°

Using the formula, Area of sector = (θ/360°) × π r²

Area of the given sector = [ 270/360] × 3.14 × (4)²

= [0.75 ] × [50.24]

= 37.68 ft

= 37.7 ft

Therefore,

The area of the sector is 37.7 ft.

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