A straight tunnel is to be dug through a hill. Two people stand on opposite sides of the hill where the tunnel entrances are to be located. Both can see a stake located 545 meters from the first person and 725 meters from the second. The angle determined by the two people and the stake (vertex) is 68°. How long must the tunnel be? (Round your answer to one decimal place.)_____________meters

The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

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Answer:  0.82 and 82 repeats

the answer is 82/99

Step-by-step explanation: I got it from khan

The given repeating decimal number can be written in fraction as 82/99.

The given decimal is 0.828282.....

Take x=0.828282...... -------(i)

Multiply both the sides of the given equation by 100, we get

100x=82.8282........ -------(ii)

Subtract equation (i) from (ii), we get

100x-x=82.8282........ - 0.828282.....

99x=82

x=82/99

Therefore, the given repeating decimal number can be written in fraction as 82/99.

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Answer:

it has no solution because it keeps making zero 0

Answer:

Yes

Step-by-step explanation:

Trees give off oxygen, which living things breath. Animals also eat plants for food. And I think animal poop helps plants grow. BTW, this isn't really a math question. Hope this helps!

Answer:Plants and animals depend upon each other as mutual interdependence is must for their survival. Plants provide shelter for animals and they make oxygen for the animals to live. When animals die they decompose and become natural fertilizer plants.Plants depend on animals for nutrients, pollination and seed dispersal. Plants are also useful for animal home because many animals live around plants.

Step-by-step explanation:

The function is assigning to each element of one set exactly one element from the other set.

First table represent a function.

Second table not represent a function (for -1 are four different numbers).

Third table represent a function.

Fourth table not represent a function (for -6 are two differen numbers 5 and 9)

In a Stock Dividend Assets don't change, Liabilities don't change.

In a stock dividend scenario, where a company issues additional shares of its own stock to existing shareholders, the impact on the company's balance sheet is as follows:

Assets don't change, Liabilities don't change.

When a company declares a stock dividend, it is essentially distributing a portion of its retained earnings or accumulated profits to its shareholders in the form of additional shares. This means that the company is not receiving any new assets or incurring any new liabilities in the process.

From an accounting perspective, the value of the stock dividend is reflected in the equity section of the balance sheet. The retained earnings account decreases by the value of the dividend, while the common stock or additional paid-in capital account increases by the same value. This adjustment does not affect the company's assets or liabilities.

Therefore, the correct answer is: Assets don't change, Liabilities don't change.

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Answer:

6-3x

x=-1

6-3(1)

6-3

3

Step-by-step explanation:

The equation representing pizza purchase and delivery in point slope form is y = 2x + 1 and the delivery fee is $1

The total cost of pizza including delivery can be broken down thus :

General form of a point slope equation :

From the question :

Putting the values into the equation :

9 = 4(2) + a

Solve for a

9 = 8 + a

9 - 8 = a

a = 1

This means that delivery fee is $1

The equation in point slope form is thus : y = 2x + 1

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Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.

In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).

To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.

The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).

The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).

To divide these two expressions, you can divide the numerators and the denominators separately:

(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)

= (2x^2) ÷ (3x^2-3x+2)

= (2/3)x^2 ÷ (x^2-x+2/3)

Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

The number that meets all the conditions is 36. It is divisible by 3 and 6, but not by 4 and 5. The sum of the digits is 9, which is an odd number, and the difference between the digits is 3, which is also odd. an incomparable number.

There are 462 different ways to select a planning board of 6 scientists from a group of 11 scientists.

The problem requires selecting 6 scientists from a group of 11 scientists. This is a combination problem, and the formula for combination is nCr, where n is the total number of items, and r is the number of items to be selected. The formula is given by:

nCr = n! / (r! * (n-r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

Using the given formula, the number of ways of selecting a planning board of 6 scientists can be calculated as:

11C₆ = 11! / (6! * (11-6)!)

= (11109876!) / (6! * 54321)

= (1110987) / (5432*1)

= 462

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Its speed is closest to 414m/s

given that

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().

Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of the signal decreases with increasing signal frequency.

a wave has a wavelength = 25.4cm

a frequency = 1.63khz

now, we need to find speed of the wave

speed = wavelength × frequency

speed = 25.4 × 16.3

           = 414m/s

speed = 414m/s

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Answer:

7 miles

Step-by-step explanation:

Based on the given table, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

To determine the profit-maximizing level of output, we need to analyze the relationship between total revenue (TR) and total costs (TC) for different quantities of output. The profit can be calculated as the difference between total revenue and total costs.

Looking at the table, we can see that as the quantity increases from 1 to 5, both total revenue and total costs increase. However, at a certain point, the increase in total costs outpaces the increase in total revenue, leading to a decrease in profit.

To find the profit-maximizing level of output, we compare the profits at different quantities.

Quantity 1: TR = $28, TC = $40, Profit = TR - TC = $28 - $40 = -$12

Quantity 2: TR = $56, TC = $45, Profit = TR - TC = $56 - $45 = $11

Quantity 3: TR = $84, TC = $55, Profit = TR - TC = $84 - $55 = $29

Quantity 4: TR = $112, TC = $72, Profit = TR - TC = $112 - $72 = $40

Quantity 5: TR = $140, TC = $120, Profit = TR - TC = $140 - $120 = $20

From the above calculations, it is evident that the profit is highest at Quantity 4. Therefore, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The only option that is a true representation of the definition of trusses is;

Option A; A structure made up of one or more triangular units, connected at the joints by long beams

In structural mechanics, there is what we call trusses which is simply a structure that consists of members organised into connected triangles in such a way that the overall assembly behaves like a single object.

These are used when roof members are to be made of steel, also used in bridges.

Looking at the options, the only one that is a true representation of the definition of trusses is Option A.

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A.) Structure made up of one or more triangular units, connected at the joints by long beams.

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According to this rule, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations, and approximately 99.7% falls within 3 standard deviations.  Therefore, the answer is 99.74%.

The confidence provided within 3 standard deviations above and below the mean for the standard normal distribution is 99.74%.

This means that approximately 99.74% of the data falls within this range. In a standard normal distribution, the mean is 0 and the standard deviation is 1. The area under the curve of the standard normal distribution represents the probability of a certain range of values occurring.

To calculate the percentage of data within a certain range, we can use the empirical rule. According to this rule, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations, and approximately 99.7% falls within 3 standard deviations.

So, within 3 standard deviations above and below the mean, we have 3 standard deviations * 2 = 6 standard deviations in total. Since the total area under the curve is 1 (or 100%), the area within 6 standard deviations is approximately 99.7% (as mentioned earlier)

However, since we only want the area within 3 standard deviations, we divide this by 2, giving us approximately 99.7% / 2 = 99.74%.

Therefore, the answer is 99.74%.

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The image of quadrilateral DEFG after a dilation centered at the origin with a scale factor of three is a larger quadrilateral D'E'F'G' with vertices D'(-9, -9), E'(-9, 9), F'(6, 9), and G'(6, 0).

To find the image of quadrilateral DEFG after a dilation centered at the origin with a scale factor of three, we need to multiply the coordinates of each vertex by the scale factor.

Given the coordinates of the vertices of quadrilateral DEFG:

D(-3, -3)

E(-3, 3)

F(2, 3)

G(2, 0)

To perform the dilation, we multiply each coordinate by the scale factor of three:

D' = 3 * (-3, -3) = (-9, -9)

E' = 3 * (-3, 3) = (-9, 9)

F' = 3 * (2, 3) = (6, 9)

G' = 3 * (2, 0) = (6, 0)

The new coordinates of the vertices after dilation are:

D'(-9, -9)

E'(-9, 9)

F'(6, 9)

G'(6, 0)

Now, we can plot the original quadrilateral DEFG and its image after dilation on a graph:

Original Quadrilateral DEFG:

D(-3, -3) E(-3, 3)

\ /

\ /

\ /

\ /

\ /

\ /

F(2, 3) G(2, 0)

Dilated Quadrilateral D'E'F'G':

D'(-9, -9) E'(-9, 9)

\ /

\ /

\ /

\ /

\ /

\ /

\ /

F'(6, 9) G'(6, 0)

The new quadrilateral D'E'F'G' will have the same shape as DEFG but with all coordinates scaled by a factor of three and centered at the origin.

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Answer:

y=2x+17 is the answer Hope that helps

Step-by-step explanation:

Answer:

The 3rd one

Step-by-step explanation:

Answer:

They are corresponding angles

Step-by-step explanation:

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The differential equation  is

\(m v'=-m g+e^v \cdot v\)

Generally, Given that a ball of mass  m   is thrown vertically upward, with upward velocity v   and air resistance s e^s,

where s   is the speed of the ball.

Now  \(m \frac{d v}{d t}\) gives the force acting on the ball, when moving upwards.

When the fall is falling the weight mg  is acting verticalles downwards and the air resistance v e^v   is acting vertically upwards.

The resultant force acting vertically downwards is   m g-v e^v  . Since \(m \frac{d u}{d t}\)  is acting vertically upwards and m g-v e^v   is acting vertically downwards so when the. bail is falling, the differential equation of   v   is

\(\begin{aligned}& m \frac{d v}{d t}=-\left(m g-v e^v\right) \\\Rightarrow & m v'=-m g+v e^v \quad \\\ \left[v'=\frac{d v}{d t}\right] \\\Rightarrow & m v'=-m g+e^v \cdot v\end{aligned}\)

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Answer:

y=3x - 8

Step-by-step explanation:

first find slope

10 - 7/6 - 5 = 3

Point - slope

y = 3(x-6)+10

Simplify

y = 3x-18+10

y=3x - 8

The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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According to Newton's Second Law, we know that

F = m*a

where F is the force applied, m is the mass and 'a' is the acceleration.

We see that this is a direct variation equation for F and a, such that m is the constant of variation. It's similar to how y = kx is also a direct variation equation.

Plug in F = 35 and a = 5 to find m

F = ma

35 = m*5

35/5 = m

7 = m

m = 7

The object has a mass of 7 kg

Our equation F = ma updates to F = 7a

Now plug in the force F = 21 to find 'a'

F = 7a

21 = 7a

21/7 = a

3 = a

a = 3

The acceleration will be 3 m/s^2

Notice how a smaller force applied means that the acceleration has also gone down as well.

Answer:

2.3 + w > 18

Step-by-step explanation:

Answer:

The area of a parallelogram is given by the formula A = base x height. In this case, the base has a length of x meters, and the height is x - 1 meters. So we can write:

A = x(x - 1)

We are told that the area is 306 square meters, so we can set up an equation:

x(x - 1) = 306

Expanding the left side gives:

x^2 - x = 306

Bringing all the terms to one side gives a quadratic equation:

x^2 - x - 306 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = -1, and c = -306, so:

x = (1 ± sqrt(1 - 4(1)(-306))) / 2(1)

x = (1 ± sqrt(1 + 1224)) / 2

x = (1 ± sqrt(1225)) / 2

x = (1 ± 35) / 2

So x is either (1 + 35) / 2 = 18 or (1 - 35) / 2 = -17/2. Since x represents a length, it cannot be negative, so the value of x is 18 meters.

Therefore, the answer is x = 18.