A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.

Answer: It's correct

Step-by-step explanation:

The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential.

Constructing a parallel line through a point using the rhombus method involves the following steps:

1. Place the compass on point K and set its width slightly more than the distance to line PQ. The exact distance is not crucial.

2. Draw a wide arc from the right of K, crossing line PQ at two points. Label the left point J.

3. Without adjusting the compass opening, move the compass to point J and draw an arc across line PQ. Label this point E.

4. Keeping the compass width unchanged, move the compass to point E and draw an arc across the large arc to the right of K. Label this point S.

5. Draw a straight line through points K and S.

6. The line KS is now parallel to line PQ, as desired.

The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential. The process relies on the compass's fixed width to ensure the angles and distances remain consistent, resulting in parallel lines.

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The complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

Let's define:

x: length of the package in inches

y: width of the package in inches

Then, the system of inequalities that represents the delivery service requirements is:

x ≤ 22 (length must be 22 inches or less)

y ≤ 22 (width must be 22 inches or less)

x + y ≤ 30 (length plus width must be no more than 30 inches)

We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:

4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)

Therefore, the complete system of inequalities for Yuriy's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

4xy ≤ 840

Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:

14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)

Therefore, the complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

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Every day, a baker produces 20 loaves of bread. The loaves come in white or brown. It would take him 30 days to make 180 loaves of brown bread.

Let the ratio be x,

We have been given the ratio of 7 : 3 in which 3 part is of brown bed.

So the number of brown bread will be 3x and white bread will be 7x.

Now, we have to find out the days for 180 loaves of brown bread. This means that 3x = 180. Now we will find out the value of x to find the total loaves of bread from this equation.

3x = 180

x = 180 / 3

x = 60

So, the total amount of bread = brown bread + white bread

Total amount of bread = 3x + 7x

= 10x

= 10 × 60

= 600

We know that in 20 loaves of bread are made in one day, so

time taken to make 600 loaves of bread = 600 / 20

= 30 days

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The force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.

We are given that the wind force F on a sail varies jointly as the area A and the square of the wind speed W. We can represent this relationship mathematically using the equation:

F = k * A * W²

where k is a constant of proportionality.

We are also given that the force on a sail with an area of 500 p and wind speed of 18 mph is 64.8 pounds. We can use this information to solve for k:

64.8 = k * 500 * 18²

Solving for k, we get:

k = 64.8 / (500 * 18²)

k = 0.0000768

Now, we can use the equation to find the force for a sail with an area of 250 f12 and a wind speed of 35 mph:

F = 0.0000768 * 250 f12 * 35²

F = 108.72 pounds

Therefore, the force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.

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The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is  78.

One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.

The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).

If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.

x = 84

[tex]\sigma=6[/tex]

since, x is 1 standard deviation above mean so,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]1=\frac{84-\mu}{6}\\ \\[/tex]

[tex]\mu[/tex] = 84-6

[tex]\mu[/tex] =78.

therefore, mean = 78.

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The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.

To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.

tax rate = (tax / cost of bicycle) x 100%

tax rate = (32 / 400) x 100%

tax rate = 8%

Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.

tax on $700 bicycle = (tax rate / 100) x cost of bicycle

tax on $700 bicycle = (8 / 100) x $700

tax on $700 bicycle = $56

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To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.

First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25

Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25

So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.

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From the above information we get:

Absolute maximum: 850
Absolute minimum: 800

To find the absolute maximum and minimum values of the function f(x) = 2x² - 16x + 850 on the given interval (0,4), we will follow these steps:

1. Find the critical points by taking the first derivative of f(x) and setting it equal to zero.
2. Determine if the critical points are within the interval (0,4).
3. Evaluate f(x) at the critical points and endpoints of the interval.
4. Identify the absolute maximum and minimum values based on the results.

Step 1: Find the critical points
f'(x) = 4x - 16
Setting f'(x) equal to zero:
4x - 16 = 0
4x = 16
x = 4

Step 2: Determine if the critical point is within the interval (0,4)
The critical point x = 4 is within the interval (0,4).

Step 3: Evaluate f(x) at the critical points and endpoints of the interval
f(0) = 2(0)² - 16(0) + 850 = 850
f(4) = 2(4)² - 16(4) + 850 = 850 - 64 + 850 = 800

Step 4: Identify the absolute maximum and minimum values based on the results
Absolute maximum: f(0) = 850
Absolute minimum: f(4) = 800

To answer the question:
(a) Interval (0,4)
Absolute maximum: 850
Absolute minimum: 800

(b) It seems you have repeated the interval (0,4), so the answer remains the same.
Absolute maximum: 850
Absolute minimum: 800

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Angle S,  Angle T and side ST are common to triangle SUT and triangle SVT.

To identify the angle or side that is common to triangle SUT and triangle SVT, based on given information, we can evaluate them as follows:

A. Angle S is common to both triangles SUT and SVT, as it is the vertex where the two triangles share a point.
B. Side SV is not common to both triangles, as it is only a side of triangle SVT.

C. Side ST is common to both triangles SUT and SVT, as it connects the shared vertex S to points U and V in each respective triangle.
D. Angle T is also common to both triangles SUT and SVT, as it is the other vertex where the two triangles share a point.

Therefore,  Angle S, side ST, and Angle T are all common to triangle SUT and triangle SVT.

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The expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.

So, the expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.

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If the number of minutes used is less than 625 per month, it is more affordable to use International Links if not, you can go for World Connections.

Let us assume that the number of minutes used = x

Cost per minute =  18 cents

Total cost for International calls = 0.18x

Basci cahrge =  50 per month

If we use x number of minutes for calls for world connections then the total cost will be:

50 + 0.10x

To find the value of x where International Links cost is less than the total cost for World Connections

0.18x < 50 + 0.10x

0.08 < 50

8x < 50

x < 625

Therefore, we can infer that if the number of minutes used is less than 625 per month, it is cheaper to use International Links.

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Option B is true about the relationship between 1 inch and 1 foot.

What is conversation?

A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.

There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.

Hence, Option B is true about the relationship between 1 inch and 1 foot.

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In scientific notation, the difference between (8.64 x 10^20) and (7.83 x 10^20) is expressed as 8.1 x 10^19.

To find the difference between (8.64 x 10^20) and (7.83 x 10^20), we subtract the second number from the first:

8.64 x 10^20 - 7.83 x 10^20 = 0.81 x 10^20

Since the difference is less than one, we express the answer in scientific notation by moving the decimal point one place to the left and increasing the exponent by one:

0.81 x 10^20 = 8.1 x 10^19

Therefore, the difference between (8.64 x 10^20) and (7.83 x 10^20) expressed in scientific notation is 8.1 x 10^19.

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The distance between bus stops A and C is exactly 1 km.

To find the distance between bus stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from C to D is 5 km.

This means that the total distance from A to C, passing through D, is 6 km (1 km + 5 km).

However, we need to subtract the distance between B and D (3 km) and the distance between B and C (2 km) since we don't want to double count the stretch between B and D.

Therefore, the distance between A and C is 6 km - 3 km - 2 km = 1 km.

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Answer:

Step-by-step explanation:

To find the highest common factor (HCF) of 12x^12 and 16x^16, we need to factor both expressions.

12x^12 = 2^2 * 3 * (x^2)^6

16x^16 = 2^4 * (x^2)^8

The common factors of 12x^12 and 16x^16 are 2^2 and (x^2)^6. To find the HCF, we take the product of these common factors:

HCF = 2^2 * (x^2)^6 = 4x^12

Therefore, the highest common factor (HCF) of 12x^12 and 16x^16 is 4x^12.

In the coding section of Lesson 4, Unit 7 on Code.org, you will be working with parameters and return statements to create a Number Crunch function for 2 and 3. To complete this task, follow these steps:

1. Define a function called 'numberCrunch' that takes two parameters: 'num1' and 'num2'.
2. Inside the function, perform the desired calculations using 'num1' and 'num2' (e.g., addition, multiplication, etc.).
3. Use a return statement to return the result of the calculation.
4. Call the 'numberCrunch' function with the values 2 and 3 as arguments, and store the result in a variable (e.g., 'result').
5. Display the result using a console.log or any other preferred method.

Here's an example using addition as the operation:

```javascript
function numberCrunch(num1, num2) {
 return num1 + num2;
}

var result = numberCrunch(2, 3);
console.log(result);
```

Modify the code according to the specific requirements of the lesson and the desired operation.

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The distance from point A to point B is approximately 998 feet (rounded to the nearest foot).

Let's denote the distance from point A to the lighthouse as "x", and the distance from point B to the lighthouse as "y". Also, let's denote the height of the lighthouse as "h". Then we have the following diagram:

Lighthouse

    |\

    | \

    |  \ h

    |   \

    |θ2 \

    |____\

      x   y

      A   B

From the diagram, we can see that:

tan(6°) = h/x (equation 1)

and

tan(4°) = h/y (equation 2)

We need to find the value of "d", the distance from point A to point B. We can use the following equation:

d^2 = x^2 + y^2 (equation 3)

We can solve equation 1 for h:

h = x tan(6°)

Substitute this into equation 2:

x tan(6°) / y = tan(4°)

Solve for y:

y = x tan(6°) / tan(4°)

Substitute this into equation 3:

d^2 = x^2 + (x tan(6°) / tan(4°))^2

Simplify:

d^2 = x^2 (1 + tan^2(6°) / tan^2(4°))

Solve for d:

d = x sqrt(1 + tan^2(6°) / tan^2(4°))

Substitute the given values:

d = 996 sqrt(1 + tan^2(6°) / tan^2(4°))

Using a calculator, we get:

tan(6°) / tan(4°) = 0.1051

So,

d = 996 sqrt(1 + 0.1051^2) ≈ 998.38 feet

Therefore, the distance from point A to point B is approximately 998 feet (rounded to the nearest foot).

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Answer:

  145.7 cm

Step-by-step explanation:

You want the perimeter of a shape bounded by 4 semicircles of radius 10 cm and two straight lines 10 cm long.

The circumference of a circle with radius 10 cm is ...

  C = 2πr

  C = 2(3.142)(10 cm) = 62.84 cm

The shape is bounded (in part) by 4 semicircles, so 2 full circles. The length of the curved boundary is ...

  curve length = 2 · (62.84 cm) = 125.68 cm

The two straight edges at either end of the figure are equal in length to the radius. That total length gets added to the curve length to form the perimeter.

  P = straight length + curve length

  P = 2·10 cm + 125.68 cm ≈ 145.7 cm

The perimeter is about 145.7 cm.

To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

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If the cost after the coupon is $21.25 and she decides to add a 20% tip, she will be adding $4.25 for the tip.

Find out how much a 20% tip would be on a cost of $21.25 after applying a coupon.
Identify the total cost after the coupon.
In this case, the cost is $21.25.
Determine the percentage for the tip.
The tip percentage is given as 20%.
Convert the percentage to a decimal.
To do this, divide the percentage by 100. So, 20% divided by 100 is equal to 0.2.
Multiply the total cost by the tip percentage in decimal form.
Now, multiply $21.25 (total cost) by 0.2 (tip percentage as a decimal).
$21.25 x 0.2 = $4.25
Calculate the tip amount.
The tip amount is $4.25.

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19. The triangle with sides 3, 4, 6 is obtuse triangle.

20. The triangle with sides 9, 11, 16 is acute triangle.

In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.

19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:

3² + 4² = 9 + 16 = 25, which is less than 6² = 36.

Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.

To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.

20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:

9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.

Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.

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The area of the preimage is 400units²

Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.

A scale factor shows the relationship between the old shape and new shape.

The scale factor is expressed as ;

scale factor = dimension of the new length / dimension of old length

scale factor = 3/2 = 1.5

old length = x

therefore 1.5 = 30/x

1.5x = 30

divide both sides by 1.5

x = 30/1.5 = 20units

therefore the area of the preimage = l²

= 20²

= 400units²

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The slope at the given points are -1/36 and -1/16 respectively.

Given is a function f(x) = 1/x+6 we need to find the slope of the function,

The slope of a function is given by dy/dx, therefore,
dy/dx = -1/(x+6)²

Therefore, at point (0, 1/6),

The slope = -1/(0+6)² = -1/36

At point (-2, 1/4),

The slope = -1/(-2+6)² = -1/16

Hence the slope at the given points are -1/36 and -1/16 respectively.

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Answer:

h = 15 cm

Step-by-step explanation:

Given:

C (base's circumstance) = 48π cm

V (volume) = 8640π cm^3

Find: h (height) - ?

[tex]c = 2\pi \times r[/tex]

[tex]2\pi \times r = 48π[/tex]

[tex]r = 24[/tex]

We found the radius

[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]

[tex] \frac{1}{3} \times \pi \times {24}^{2} \times h = 8640π[/tex]

Multiply the whole equation by 3 to eliminate the fraction:

[tex]1728\pi \times h = 25920\pi[/tex]

[tex]h = 15[/tex]

The radius of the line of latitude through X is approximately 5729 km, and the latitude of Y is approximately 43°.

Let X be the starting town with coordinates (28°N, 66°E), and let Y be the destination town which is 3900 km due South of X. We want to find the radius of the line of latitude through X, and the latitude of Y.

First, we can find the distance between X and Y using the Pythagorean theorem. The distance due South is 3900 km, and the distance due East is 28° × R, where R is the radius of the Earth. Using t=2 and R=6406 km, we have:

distance due East = 28° × 6406 km × cos(66°) ≈ 2055.6 km

distance between X and Y = sqrt((3900 km)^2 + (2055.6 km)^2) ≈ 4498.6 km

Next, we can find the latitude of Y using the formula:

latitude of Y = 90° - arctan(distance due South / radius of the Earth)

Using t=2 and R=6406 km, we have:

latitude of Y = 90° - arctan(3900 km / 6406 km) ≈ 43°

Finally, we can find the radius of the line of latitude through X using the formula:

radius of line of latitude = radius of the Earth * cos(latitude of X)

Using the coordinates of X, we have:

latitude of X = 28°N

radius of line of latitude = 6406 km * cos(28°) ≈ 5729 km

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The correct equation represents the amount Kennedy makes babysitting is,

⇒ d = 7h

We have to given that,

Kennedy makes $7 per hour babysitting.

Let us assume that,

'h' represent the number of hours

And, d represent amount in dollars.

Hence, By given condition, we get;

⇒ d = 7h

Thus, The correct equation represents the amount Kennedy makes babysitting is,

⇒ d = 7h

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The formula that Kennedy uses to calculate how much money she makes babysitting is:d = 7h

We have,

Kennedy makes $7 per hour babysitting.

let "d" represents the amount of dollars Kennedy makes, and "h" represents the number of hours she babysits.

Since Kennedy earns $7 per hour, the equation can be written as

d = 7h

which relates the dollars earned (d) to the number of hours worked (h).

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$750 was withheld from my pay after deductions form the gross pay

Gross pay is the money that an employee gets before tax and other deduction are made

Net pay is the amount of money given to am employee after deduction of tax and other mandatory expenses

The gross pay is $2,500

The net pay is $1,750

The money withheld can be calculated as follows

= 2500 - 1750

= 750

The money withheld from the gross pay is $750

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1 marble is equal in weight to 84 jujubes.

Let's start by writing down the given information in equations:

5m = 3s (where m represents one marble and s represents one toy soldier)

7s = 5c (where c represents one plush chipmunk)

3c = 14j (where j represents one jujube)

We want to find out how many jujubes equal the weight of one marble, so we need to eliminate all the other variables except for j and m. We can do this by using substitution and algebraic manipulation.

First, we can solve the second equation for s in terms of c:

7s = 5c

s = (5/7)c

Then, we can substitute this expression for s in the first equation:

5m = 3s

5m = 3(5/7)c

m = (3/7)c

Next, we can solve the third equation for c in terms of j:

3c = 14j

c = (14/3)j

Now we can substitute this expression for c in the previous equation:

m = (3/7)c

m = (3/7)(14/3)j

m = 2j

So we have found that one marble is equal in weight to 2 jujubes. But the question asks for the weight of one marble in terms of jujubes, not in terms of jujubes and toy soldiers and plush chipmunks. We can use the other equations to eliminate the other variables:

5m = 3s

5m = 3(5/7)c

5m = (15/7)c

m = (3/7)c

7s = 5c

7s = 5(14/3)j

s = (10/3)j

Putting this all together:

m = (3/7)c

m = (3/7)(7s/5)

m = (3/5)s

m = (3/5)(10/3)j

m = 2j

So we have found that one marble is equal in weight to 2 jujubes. Finally, we can use the third equation to find how many jujubes are equal in weight to 1 marble:

3c = 14j

c = (14/3)j

m = (3/7)c

m = (3/7)(14/3)j

m = 2j

1 marble = 2 jujubes

1 jujube = 1/2 marble

1 marble = 2 jujubes = 2(84) = 168 jujubes

Therefore, one marble is equal in weight to 84 jujubes.

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