Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Q as shown in the figure, such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that triangle MNO and triangle QPO are congruent.

Part A: Provide a valid argument, using geometry theorems or postulates, to validate
Andre's claim that AMNO and APQO are congruent.

Part B: Which segment should Andre measure to determine the width of the creek? Explain why.

Use the space below to answer Parts A and B of the question above. Use the CER (Claim, Evidence, Reasoning) method as a guide to your response. You may also upload a screenshot of your work

Answer:

sin 2π

Step-by-step explanation:

None of the given trigonometric functions are equal to zero.

Trigonometric ratios are used to define the relation between the sides of a right - angled triangle.

Given are the trigonometric functions.

cos π = - 1

sin 2π = 1

cot 3π = -1

cos 4π = 1

None of the functions are zero.

Therefore, none of the given trigonometric functions are equal to zero.

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The 'rise' and 'run' of the line is shown in figure whose slope is:  \(\frac{11}{13.5}\)

An x-y axis graphic is a visual representation of mathematical functions or data points on a Cartesian coordinate system. The x-axis represents the horizontal or independent variable, whereas the y-axis represents the vertical or dependent variable.

As we know that, the Slope of the line in terms of 'rise' and 'run' is;

Slope =  \(\frac{rise}{run}\)

by the figure, we can take two end points are (-4, -10) and (9.5, 1) so,

rise = (y₂ - y₁) = (1) - (-10) = 1 + 10 =  11

run = (x₂ - x₁) =  (9.5) - (-4) =  9.5 + 4 =  13.5

put the values to find slope,

Slope =  \(\frac{11}{13.5}\)  =  0.8148

Therefore, the rise and run is shown in below figure whose slope is: \(\frac{11}{13.5}\)

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At the production level of 40 units, profit is maximized and the profit at this production level is $64,000.

Revenue is given by R(q) = 600q and cost is given by C(q) = 10,000 + 5q2. Profit is given by P(q) = R(q) - C(q).Therefore, P(q) = 600q - (10,000 + 5q2) or P(q) = -5q2 + 600q - 10,000. The profit is maximized at the production level where the derivative of P(q) is equal to zero.The derivative of P(q) is given by P'(q) = -10q + 600. Setting this to zero, we get -10q + 600 = 0 or q = 60. However, this is the maximum point of the revenue function R(q) and not the profit function P(q).To determine the maximum point of P(q), we need to find the second derivative of P(q) which is given by P''(q) = -10. Since P''(q) is negative, the maximum point of P(q) occurs at the production level q = 40. At q = 40, P(q) = -5(40)2 + 600(40) - 10,000 = $64,000.

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Answer:

v > 14   I believe.

Step-by-step explanation:

He already has 65 points.

240-65=175

He just needs 175 more points.

175/12.5 = 14.

He'll need to visit 14 or more times to get his free movie ticket.

I could be wrong. But I'm pretty sure.

the perimeter of the regular hexagon is 48 cm.

A regular hexagon is a polygon with six sides, and each side has the same length. The formula to calculate the perimeter of a regular hexagon is given as:

Perimeter = 6 × length of one side

To find the length of one side of the hexagon, we need to use the given information about the area. The formula for the area of a regular hexagon is given as:

Area = (3 × √3 × s^2)/2, where s is the length of one side of the hexagon.

We can use this formula to solve for the length of one side:

96 √3 = (3 × √3 × s^2)/2

Simplifying this equation, we get:

s^2 = (2 × 96 √3)/(3 × √3)

s^2 = 64

s = 8 cm

Now that we know the length of one side of the hexagon, we can use the formula for perimeter to find the total perimeter:

Perimeter = 6 × 8 cm

Perimeter = 48 cm

Therefore, the perimeter of the regular hexagon is 48 cm.

In a regular hexagon, all six angles are equal, each measuring 120 degrees. It is a symmetrical shape, meaning that it has six lines of symmetry. The regular hexagon is a common shape in nature and architecture, and it is often used in geometry problems because of its regularity and symmetry. The hexagon is also the basis for the hexagonal lattice structure, which is a common pattern in crystals and other materials.

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Answer:

78 m

Step-by-step explanation:

We need to use the Pythagorean theorem, \(a^{2} + b^{2} = c^{2}\).

Substitute in \(a\) and \(b\).

\(30^{2} + 72^{2} = c^{2}\)

Simplify.

\(900 + 5184 = c^{2}\)

Add.

\(6084 = c^{2}\)

Square root both sides.

\(78 = c\)

The hypotenuse is 78 m long.

find c:

a² plus b² = c

72² plus 30²=c

5I84 plus 900

6084

now square root that

78

so C=78

Remember that the sum of the three interior angles of a triangle is 180°.

Now, let's call the remaining angle x. We would have:

Solving for x,

From this, we get that the remaining anlge has to measure 50°. Now, as we already have a side that measures 4 feet, the other two sides are constrained; neither of them can have any measurement that's different to the one that constructs the remaining 50° angle.

Therefore, only one triangle can be constructed.

The lower bound on the diameter of the resulting crater using the 10-20 rule is roughly 10 times the diameter of the impactor.

The 10-20 rule in impact cratering states that the diameter of the resulting crater is roughly 10 to 20 times the diameter of the impactor. Therefore, if we know the diameter of the impactor, we can estimate the lower bound on the diameter of the resulting crater by multiplying it by 10.

For example, if the diameter of the impactor is 1 km, then the lower bound on the diameter of the resulting crater would be 10 km. If the diameter of the impactor is 5 km, then the lower bound on the diameter of the resulting crater would be 50 km. The exact size of the resulting crater depends on a variety of factors, including the angle and speed of impact, the properties of the impactor and the target material, and other environmental factors.

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Note that  the x-values where the height of the tunnel is zero feet are x = -6 and x = 6.  See the graph attached.

To find the x-value where the height of the tunnel is a maximum, we can use the   fact that the maximum point of a quadratic function occurs at its vertex.

The vertex of the equation y = -x² + 36 corresponds to the maximum height of the tunnel.

The x-coordinate of the vertex can be found using the formula

x = -b / (2a),

where the quadratic equation is in the form

y = ax² + bx + c.

In  our case, a = -1 and b = 0, so the x-coordinate of the vertex is

x = - 0 / (2 * (-1))

= 0.

Height of Zero

To find the x-values where the height of the tunnel is zero feet, we can set the equation y = -x^2 + 36 equal to zero and solve for x.

-x² + 36 = 0

x² = 36

= ±√36 hence,

x = ±6

By plotting these points on the graph, you will have the points    where the height of the tunnel is a  maximum ( 0, maximum height) and where the height of the tunnel is zero (- 6, 0) and (6, 0).

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Answer:

s = 6

Step-by-step explanation:

We know a square has all equal side lengths. So we would divide the square by four to get one side length.

24/4 = 6

s = 6

Explanation:

We'll use the zero product property. This is the idea where if A*B = 0, then either A = 0 or B = 0.

So if

-0.7(x+3)(x-4) = 0

then either

x+3 = 0 or x-4 = 0

Both of those equations solve to

x = -3 or x = 4

The roots are the locations of the x intercepts, which is where the graph crosses or touches the x axis.

Answer:

1)   3- and 4

2)  3- and 4

Step-by-step explanation:

The possible values of the length (x) are in the intervals are (-∞, -9) ∪ (-5, 4) ∪ (0, 4) ∪ (1, 4).

Given that:

The dimensions of the rectangular prism are:

Width = x - 1 meters

Height = x + 11 meters

Volume ≤ 180 cubic meters

The inequality based on the volume can be written as:

Volume = (length) × (x - 1) × (x + 11) ≤ 180

The above inequality can be solved to find the possible values of the length (x).

The equations can be solved as:

Volume = x(x - 1)(x + 11) ≤ 180

               \(x^3 + 10x^2 - x - 180 \le 0\)

The values of x that satisfy this inequality can be calculated by checking the given possible options, (-∞, -9), (-5, 4), (0, 4), (1, 4), [1, 4).

For x = -10 (test point in the interval (-∞, -9)):

f(-10) = \((-10)^3 + 10(-10)^2 - (-10) - 180\)

= \(-1000 + 1000 + 10 - 180\)

 =\(-170\)

Since this is negative, the inequality is satisfied in the interval (-∞, -9).

For x = 0  in the interval (-5, 4):

f(0) =  \(0^3 + 10(0)^2 - 0 - 180\)

         =\(-180\)

Since this is negative, the inequality is satisfied in the interval (-5, 4).

The test interval for x = 3 in the interval (0, 4):

f(3)  = \(3^3 + 10(3)^2 - 3 - 180\)

        = \(-66\)

Since this is negative, the inequality is satisfied in the interval (0, 4).

For x = 2 (test point in the interval (1, 4):

f(2) = \(2^3 + 10(2)^2 - 2 - 180\)

       =\(8 + 40 - 2 - 180\)

        = \(-134\)

Since this is negative, the inequality is satisfied in the interval (1, 4).

For x = 5 (test point in the interval [1, 4):

f(5) = \(5^3 + 10(5)^2 - 5 - 180\)

     =\(125 + 250 - 5 - 180\)

      = \(190\)

Since this is positive, the inequality is not satisfied in the interval [1, 4).

The possible values of the length (x) are in the intervals are (-∞, -9) ∪ (-5, 4) ∪ (0, 4) ∪ (1, 4).

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The surface area of the rectangular prism is 130ft^2.

The surface area of a rectangular prism can be calculated by finding the area of each of the six faces and then adding them together.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

In this case, the length is 10ft, the width is 1ft, and the height is 5ft. Plugging these values into the formula, we get:

Surface area = 2(10ft)(1ft) + 2(10ft)(5ft) + 2(1ft)(5ft)

Surface area = 20ft^2 + 100ft^2 + 10ft^2

Surface area = 130ft^2

Therefore, the surface area of the rectangular prism is 130ft^2.

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Hey Mate ,

Reading the given statement ,

Let the cost of printer be x and the cost of Computer be 3x

ATQ ,

3x + x = $1020

4x = $1020

x = 255

Therefore , the cost of Printer is $255 and the cost of computer is $255× 3 = $765

g(x) = \(3x^{2} - 5x + 2\), h(x) = 2x - 5

-> 4g(x) - 2h(x) = \(12x^{2} - 20x + 8 - (4x - 10)\)

= \(12x^{2} - 24x + 18\)  = \(6(2x^{2} - 4x + 3)\)

Answer: 3600

Step-by-step explanation:

The values of x make the quadratic equation (x-2)² =2 is 2 + √2.

To find the values of x that make the quadratic equation (x-2)² = 2 true, we need to solve for x.

First, we can take the square root of both sides of the equation:

x - 2 = ±√2

Next, we can add 2 to both sides of the equation:

x = 2 ± √2

Therefore, the two solutions for x are:

x = 2 + √2

x = 2 - √2

These are the two values of x that make the quadratic equation (x-2)^2 = 2 true.

To check these solutions, we can substitute each value back into the original equation:

[(2 + √2) - 2]² = 2

Simplifying:

√2² = 2

2 = 2

This solution works. Now let's check the other solution:

[(2 - √2) - 2]² = 2

Simplifying:

-√2² = 2

-2 = 2

This solution does not work, so we discard it. Therefore, the only value of x that makes the quadratic equation (x-2)² = 2 true is: x = 2 + √2.

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Answer:

The answer is 1.25 km = 1,250

                       1.7 cm =17 mm

                       345 m = 0.345 km K12 test.

Step-by-step explanation:

The answer is 1.25 km = 1,250

                      1.7 cm =17 mm

                      345 m = 0.345 km K12 test.

The mean of the data set is 9.33 minutes.

To find mean of the data set, we will add all the values and divide by the total number of values.

In this case, the sum of the values is:

= 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22

= 112

There are 12 values in the data set, so the mean is:

= Sum of values / Total number of values

= 112 / 12

= 9.3333

= 9.33 minutes.

Therefore, the mean of the data set is 9.33 minutes.

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If on august 1, a $60,000, 7%, 3-year installment note payable is issued by a company. the entry to record the first payment on july 31 would include: B. debit to interest expense of $4,200.00.

Journal entry is used by companies to record their day to day business  transaction.

Based on the information the appropriate journal entry to record the first payment on July 31 is:

Journal entry

Debit Interest Expense $4,200.00

($60,000 × 7%)

Debit Notes Payable $18,663.10

($22,863.10 - $4,200)

Credit Cash$22,863.10

(To record first payment)

Therefore the correct option is B.

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Answer:

3=4 and 1=2 or its the other way around...i cant remember

Answer: The correct answer is 8.12%-11.88%.

We can use the formula for a confidence interval for a proportion:

p ± z*SE

where p is the sample proportion, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and SE is the standard error of the proportion.

SE = sqrt(p*(1-p)/n) = sqrt(0.1*0.9/1015) = 0.0094

Plugging in the values, we get:

0.1 ± 1.96*0.0094

= 0.1 ± 0.0184

So the 95% confidence interval is (0.0816, 0.1184), which is equivalent to 8.12%-11.88%.

Step-by-step explanation:

The associative property looks like a + (b + c) = (a + b) + c.

According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.

The associative property is applicable in addition as well as in multiplication.

According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:

(a + b) + c = a + (b + c)

According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:

(a × b) × c = a × (b × c)

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Answer:

12

Step-by-step explanation:

The interquartile range is the difference between the upper quartile and the lower quartile.

Firstly find the median of the data.

The median is the middle value of the data arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.

5,  6,  13,  18,  18 ← data in ascending order

           ↑ middle value

median = 13

The upper quartile Q₃ is the middle of the data to the right of the median

13,  18,  18

       ↑ middle value

Q₃ = 18

The lower quartile Q₁ is the middle value of the data to the left of the median

5,  6,  13

    ↑ middle value

Q₁ = 6

Interquartile range = Q₃ = Q₁ = 18 - 6 = 12

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Answer:

56

Step-by-step explanation:

40/10= 4 every hour

14x4=56

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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That the nimber value i