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find the area of the polygon

Answer:

The volume of the triangular prism is 51.84 cm^3.

Step-by-step explanation:

The formula of the volume of a prism is:

V = Ah

where:

V = Volume of prism

A = Area of uniform cross-section or base of prism

h = Height of prism = 6 cm

We can substitute the information given in the problem into this formula.

To find A, we need to find the area of the triangular base.

A = bh / 2

where:

b = Base of triangle = 5.4 cm

h = Perpendicular height of triangle = 3.2 cm

We can substitute the information given in the problem into this formula.

A = ( 5.4 × 3.2 ) / 2

A = 17.28 / 2

A = 8.64 cm^2

Substitute the value of A into the original volume of a prism formula with the other information given in the problem.

V = Ah

V = ( 8.64 ) ( 6 )

V = 51.84 cm^3

The volume of the triangular prism when the base and the height is given so it should be \(51.84\ cm^3.\)

Since The base of the triangular face is 5.4 centimeters and the height of the face is 3.2 centimeters. The height of the prism is 6 centimeters.

So, we know that

The formula of the volume of a prism is:

V = Ah

Here,

V = Volume of prism

A = Area

h = Height of prism = 6 cm

Also,

\(A = bh \div 2\)

So,

\(A = ( 5.4 \times 3.2 ) \div 2\\\\= 17.28 \div 2\\\\= 8.64\ cm^2\)

Now the volume is

V = Ah

V = ( 8.64 ) ( 6 )

V = \(51.84\ cm^3\)

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The solution set to the function f(x) = x⁴ + 2 is  (-2)^1/4

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

f(x) = x⁴ + 2

Set the function to 0

So, we have

x⁴ + 2 = 0

Subtract 2 from both sides of the equation

This gives

x⁴ = -2

Take the fourth root of both sides

This gives

x =  (-2)^1/4

Hence, the solution set to f(x) = x⁴ + 2 is  (-2)^1/4

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Answer: x=1 y=6

Step-by-step explanation:

The graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

If the value of is constant for every value that satisfies a certain condition, it means that the graph is a horizontal line on that interval. The behavior of the graph is constant or unchanging in terms of its vertical position.

When every value of x that satisfies a given condition results in a constant value of y, this tells us that the behavior of the graph of the function on this interval is horizontal. In other words, the graph remains at a constant height (y-value) for all x-values within the specified interval. This means that the function does not change in this interval and maintains a consistent output.

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Answer:

$15,920

Step-by-step explanation:

Answer:

x = 10.8

y = 11.2

Step-by-step explanation:

AB : AP = AC : AQ

5 :(5+9) = 6 : (6+x)

5: 14 = 6 :(6+x)

5(6+x) = 14*6

30 + 5x = 84

5x = 54

x = 10.8

AB : AP = BC :PQ

5 :14 = 4 : y

5y = 14*4

y = 11.2

Answer:

2x3=6+9=15?

Step-by-step explanation:

Im sorry if i didnt help.

Answer:

\(\frac{x}{y}\) = 4

Step-by-step explanation:

Expressing in fractional form, that is

\(\frac{4x-y}{2x+y}\) = \(\frac{5}{3}\) ( cross- multiply )

3(4x - y) = 5(2x + y) ← distribute both sides

12x - 3y = 10x + 5y ( subtract 10x from both sides )

2x - 3y = 5y ( add 3y to both sides )

2x = 8y ( divide both sides by 2 )

x = 4y ( divide both sides by y )

\(\frac{x}{y}\) = 4

Answer:

\( \boxed{ \frac{x}{y} = 4}\)

Step-by-step explanation:

\(if \: \frac{4x-y}{2x+y}=\frac{5}{3}, \: then \: \frac{x}{y} = : \\ 3(4x - y) = 5(2x + y) \\ 12x - 3y = 10x + 5y \\ 2x = 8y \\ \frac{2x}{y} = 8 \\ \frac{x}{y} = 4\)

Answer:

Set 16/2000 = x/5000 and solve for x. = 40 trees saved.

Step-by-step explanation:

Answer: the answer would be 42.5 but i’m assuming that you would round.

Step-by-step explanation:

2000/ 17 = 5000/ x

cross multiply

85,000 = 2,000x

simplify(divide by 2000)

x= 42.5

Answer:

-6x+2y=-18 = \(y = -9 + 3x\)

-3x-2y=54 = \(y = -27 - \frac{3x}{2}\)

Step-by-step explanation:

I hope I understood this correctly.

Using mathematical operations, the greatest number of songs Aerabella can play at her Sweet 16 party is 106.

The number of songs Aerabella can play is determined by subtracting the fixed charge for the day from her spending budget and dividing the difference by the unit charge per song.

Subtraction and division operations are two of the four basic mathematical operations, including addition and multiplication.

The total spending budget = $130

The fixed rental charge for a DJ = $50

The charge per song (unit rate) = $0.75

The variable cost for the party = $80 ($130 - $50)

The number of songs Aerabella can play = 106.67 ($80 ÷ $0.75)

= 106

Thus, based on the mathematical operations of subtraction and division, and given the fixed cost of hiring a DJ, the highest number of songs Aerabella can play for her Sweet 16 party is 106.

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The required radius of given circle is 30 units.

A circle is a shut two-layered figure wherein the arrangement of the multitude of focuses in the plane is equidistant from a given point called "focus". Each line that goes through the circle shapes the line of reflection evenness. Likewise, it has rotational evenness around the middle for each point.

Picture result for What is circle and region of its area?

The equation for the region of the area of a circle is(r2) /360where r is the span of the circle and is the point of the area.

Angle of sector = 100 degree, area= 250π

Let radius of circle be r

Then,

area of sector = (r^2) /360

250π =  (r2) 100/360

r^2 = 250×360/100

r = √25×36 = 30 units

Thus, radius of the circle is 30units.

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a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample

Sampling can be defined as a technique of selecting a subset of the population or  individual members in order to make statistical inferences from them and estimate the entire characteristics of the whole population.

Sampling methods are used by researchers in market research to reduce the workload and also to research the entire population

It is time-friendly, cost-effective method and forms the basis of research design.

Some sampling methods are;

It can be said to be dependent when selecting from one sample affects another sample.

Thus, a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample.

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Answer:

A) \(x+y=20\)

B) Cost function is: \(3x+2y = 50\)

C) \(x+y=20\), \(3x+2y = 50\)

D) \(x=10, y=10\)

E) Yes, the result satisfies the equations.

Step-by-step explanation:

Let number of kilos of mango bought = \(x\)

Let number of kilos of atis bought = \(y\)

Total number of kilos bought = 20

A) \(x+y=20\)

Cost of mango per kg = 60

Cost of mango for \(x\) kg = \(60x\)

Cost of atis per kg = 40

Cost of mango for \(y\) kg = \(40y\)

Total cost is: Cost of mango + Cost of atis = 1000

B) Cost function is:

\(60x+40y=1000\\\Rightarrow 3x+2y = 50 ...... (2)\)

C) System of equations are:

\(x+y=20\) ...... (1)

\(3x+2y = 50\)...... (2)

D) Using elimination method:

Multiplying equation (1) with 2 and subtracting from (2):

\(x = 10\)

By equation (1):

\(\Rightarrow y =10\)

E) Putting both the values in LHS of equation (1):

10+10  = 20 = RHS

Putting both the values in LHS of equation (2):

\(3\times 10 +2\times 10\) = 50 = RHS

Yes, the result satisfies the equations.

Answer:

What is it?

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The correlation coefficient indicative of the weakest linear relationship is option (c) -0.05. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

Correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship. Therefore, a correlation coefficient closer to 0 indicates a weaker linear relationship. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

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The dividend in the formula P3 = Dx/(R - g) is for period e. three.

In the given formula P3 = Dx/(R - g), the dividend, Dx, refers to the cash flow or payment made during a specific period. The subscript "3" in P3 indicates the period of time for which the dividend is associated.

In the given formula, P3 = Dx/(R - g), the subscript 3 represents the period of time for which we are calculating the dividend.

The dividend, Dx, represents the cashflow or payment made during a specific period. In this case, the dividend is associated with period 3.

Therefore, the dividend in the formula corresponds to period e. three.

The dividend in the formula P3 = Dx/(R - g) is for period e. three

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Answer: -2/3 , you use the y2-y1 / x2-x1 formula

Answer:

is there multiple choice answers?

Step-by-step explanation:

Given: ,8^2x= 32^x+3

a: (2³)^2x = (2⁵)^x+3

b: Solving, we get

2^6x = 2^5x+15

Since bases are same, we have

=>6x=5x+15

=> x = 15

Answer:

\(4.97~m\)

Step-by-step explanation:

We know that the scale model of the sculpture is \(\frac{71}{3}\) times bigger than the actual model. So, the scale model has a size of \(\frac{71}{3}\cdot 21=71\cdot \frac{21}{3}=71\cdot 7=497\) cm and we're done!

But wait! The problem asks for the answer in meters, so the answer is actually \(\frac{497}{100}=\boxed{4.97~m}\) and we're(actually) done!

Answer:

4/30 or 4/120

Step-by-step explanation:

Answer:

$1.25

Step-by-step explanation:

Subtract $0.25 by $1.50

$1.50-$0.25=$1.25

Answer:

y = -2x - 2

Step-by-step explanation:

Given:

m = -2

Slope-intercept:

y - y1 = m(x - x1)

y + 8 = -2(x - 3)

y + 8 = -2x + 6

y = -2x - 2

The expression sin(Tan⁻¹(-1)) evaluates to √2/2.

The trigonometric expression is sin(Tan⁻¹(-1)). To evaluate this expression, we need to understand the principal value of the inverse tangent function, Tan⁻¹.

The principal value of Tan⁻¹ is the angle whose tangent is equal to the given value. In this case, Tan⁻¹(-1) represents the angle whose tangent is -1. We know that the tangent function is negative in the second and fourth quadrants.

In the second quadrant, the reference angle whose tangent is 1 is π - π/4, which is 3π/4. In the fourth quadrant, the reference angle is -π/4.

Since the expression is sin(Tan⁻¹(-1)), we need to find the sine of the angle whose tangent is -1. The sine function is positive in the second quadrant, so the sine of 3π/4 is √2/2.

Therefore, sin(Tan⁻¹(-1)) is equal to √2/2.

In summary, the expression sin(Tan⁻¹(-1)) evaluates to √2/2, which represents the sine of the angle whose tangent is -1 in the second quadrant.

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Answer:

15.

a) 9

b) (x + 3)(x + 3) or (x + 3) ^ 2

16.

a) 121

b) (x + 11)(x + 11) or (x + 11) ^ 2

17.

a) 81

b) (x + 9)(x + 9) or (x + 9) ^ 2

the assumption being that "y" is encapsulating a function in "x" terms.

\(y+2=\cfrac{x^2}{2}-2sin(y)\implies \stackrel{\textit{taking the derivative to both sides}}{\cfrac{dy}{dx}+0=\cfrac{1}{2}(2x)\underset{chain~rule}{-2cos(y)\cdot \cfrac{dy}{dx}}} \\\\\\ \cfrac{dy}{dx}=x-2cos(y)\cfrac{dy}{dx}\implies \cfrac{dy}{dx}+2cos(y)\cfrac{dy}{dx}=x \\\\\\ \cfrac{dy}{dx}\left[ 1+2cos(y) \right]=x\implies \cfrac{dy}{dx}=\cfrac{x}{1+2cos(y)}\)

The correct option is False. The standard formulas for the derivatives of sine and cosine are true when the angle is in radians. These formulas are derived based on the properties of the trigonometric functions in the context of radians. The derivatives of sine and cosine with respect to an angle measured in radians are as follows:

\(\[\frac{d}{dx}(\sin(x)) = \cos(x)\]\)

\(\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]\)

If the angle is measured in degrees, these formulas would not hold true. To differentiate trigonometric functions when the angle is measured in degrees, conversion factors and additional adjustments would be necessary.

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TCP provides error checking to ensure reliable data delivery, making option A the correct answer. Only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

TCP (Transmission Control Protocol) provides error checking as part of its services. It ensures reliable data delivery by using acknowledgments and sequence numbers to detect and recover from packet loss, errors, or out-of-order delivery. When a TCP receiver receives data, it sends an acknowledgment (ACK) back to the sender to confirm the successful reception of packets. If the sender does not receive an ACK for a particular packet within a specified timeout period, it assumes the packet was lost or damaged and retransmits it.

TCP provides error checking to ensure reliable data delivery, making option A the correct answer.

The propagation delay is the time it takes for a signal to travel from the source to the destination. It is determined by the physical distance between the devices and the speed of signal propagation in the transmission medium. The propagation delay is an inherent characteristic of the medium and cannot be eliminated by switching devices or other strategies.

The other three options—processing delay, queuing delay, and transmission delay—are all caused by the store-and-forward strategy used by switching devices. Processing delay refers to the time taken to examine and process the packet headers. Queuing delay occurs when packets have to wait in a queue before being transmitted. Transmission delay is the time it takes to push the bits onto the transmission medium.

Among the given options, only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

3. The correct answer is A. The system is very well-engineered.

In a statistical multiplexing system, the queuing delay is the delay experienced by packets waiting in a queue before being transmitted. If the average queuing delay is very close to zero, it indicates that the system is well-engineered and efficiently managing its resources. A well-designed system can minimize or eliminate queuing delays by appropriately allocating resources and ensuring efficient scheduling algorithms.

Traffic intensity, which represents the ratio of the average traffic load to the transmission capacity, does not directly determine the queuing delay. It is possible to have low queuing delays even with high traffic intensity if the system is well-designed.

When the average queuing delay is close to zero, it suggests that the system is well-engineered and efficiently utilizing its resources, as stated in option A.

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Answer:

B s=32t

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