the slopes of two lines are 5/6 and 2/p determine the value of p that will make the lines parallel

Answer:

x = 1

Step-by-step explanation:

Answer: [tex]1.18p[/tex]

Step-by-step explanation:

Given: The expression for amount of bill for 8 people= p

A restaurant charges an automatic gratuity on tables with more than 6 people = 18 % =0.18

Since 8 > 6 .

Then , the expression for amount of gratuity charged on bill will be :-

[tex]0.18p[/tex]

Now, the expression to find the total cost of the meal with the gratuity will be :-

[tex]p+0.18p=p(1+0.18)=1.18p[/tex]

To write the expression using all six trigonometric function, we need to understand about trigonometric function relation.

The trigonometric expression are as follows,

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times \sin(x) + \sec(x)\times \cos(x) + \tan(x)\times \cot (x) - 1[/tex]

Given:

The trigonometric function are as follows,

[tex]\sin, \cos, \tan, \csc, \sec \:\rm and \:\cot.[/tex]

Write the relationship between [tex]\sin[/tex] and [tex]\cos[/tex].

[tex]\sin^2 (x) + \cos^2 (x) = 1[/tex]

Write the relationship between [tex]\tan[/tex] and [tex]\cot[/tex].

[tex]\tan(x)\times \cot(x) = 1[/tex]

Write the relationship between [tex]\csc[/tex] and [tex]\sin[/tex].

[tex]\csc(x)\times \sin(x) = 1[/tex]

Write the relationship between [tex]\sec[/tex] and [tex]\cos[/tex].

[tex]\sec(x)*\cos(x) = 1[/tex]

Now combine all the above relationship

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times sin(x) + \sec(x)\times \cos(x) +\tan(x)\times \cot(x) - 1 = 3[/tex]

Now solve further,

[tex]1+1+1+1-1=3\\3=3[/tex]

Thus, the trigonometric expression are as follows,

[tex]\sin^2 (x) + \cos^2 (x) + \csc(x)\times \sin(x) + \sec(x)\times \cos(x) + \tan(x)\times \cot (x) - 1[/tex]

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slope = m

 slope equation = y=mx+b so the first number is the slope

-1/2

There are 57 sides does the polygon have.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The sum of the interior angles of a polygon is,

⇒ 9900 degrees

Since, We know that;

The formula is,

⇒  (n - 2) × 180

Hence, We get;

⇒ 9900 = (n - 2) × 180

⇒ n - 2 = 9900 / 180

⇒ n - 2 = 55

⇒ n = 55 + 2

⇒ n = 57

Thus, There are 57 sides does the polygon have.

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To find the number of fluid ounces of butter, use the given conversion factor and the mass of the butter in grams.

To determine the number of fluid ounces of butter she will use, we need to know the mass of the butter in grams. Since the relationship 1 oz = 28.349 g, we can convert the mass in grams to ounces using the conversion factor. Let's say the mass of the butter is 125 grams. We can use the equation X oz = 125 g * unit conversion factor to find the number of fluid ounces of butter.

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Answer:

The best estimate of the circumference of a circle is 21 ft.

Step-by-step explanation:

Formula

[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]

Where r is the radius of a circle.

As given

Diameter of 7 feet .

[tex]Radius = \frac{7}{2}[/tex]

Radius = 3.5 feet

As

[tex]\pi = 3.14[/tex]

Put in the formula

[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 3.5[/tex]

Circumference of a circle = 21.98 ft .

Therefore the best estimate of the circumference of a circle is 21 ft.

To find the number of different requests possible if a customer can request up to 3 free samples out of 13 offers, use the formula for combinations without repetition: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items selected.

To find the number of different requests possible if a customer can request up to 3 free samples out of 13 offers, we will use the concept of combinations. Since the order of the samples does not matter, we will use combinations without repetition.

The formula for combinations without repetition is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items selected. In this case, n = 13 (number of offers) and r can be 1, 2, or 3 (number of free samples requested).

Therefore, the number of different requests possible for 1 free sample is 13C1 = 13! / (1!(13-1)!). Similarly, the number of different requests possible for 2 free samples is 13C2 = 13! / (2!(13-2)!), and the number of different requests possible for 3 free samples is 13C3 = 13! / (3!(13-3)!).

Answer:

You should place 4 red beads and 10 yellow beads into the container

Step-by-step explanation:

The answer is 1249.69

volume = l x w x h

36 = 2 x 6 x ?

36=12 x ?

? =36/12 =3

 the closet is 3 feet wide

The width of the closet is 3 feet, which is obtained by rearranging the formula for the volume of a rectangular prism and substituting the given dimensions.

To find the width of the closet, we use the formula for the volume of a rectangular prism, which is volume = length  times width times height. The problem gives us the volume (36 cubic feet), the length (2 feet), and the height (6 feet). The width can be found by rearranging the formula to width = volume / (length times height).

Next, we substitute the given values into the rearranged formula:

width = 36 cubic feet / (2 feet times 6 feet) = 36 cubic feet / 12 square feet = 3 feet

Therefore, the width of the closet is 3 feet.

Answer:

It would have to be w=72.50n

The x value is ( z - 2 ) / 3z.

Given,

3x+y/z=2

We need to solve for x.

We have,

3x+y/z=2

Subtracting y/z on both sides.

we get,

3x + y/z - y/z = 2 - y/z

3x = 2 - y/x

Dividing 3 into both sides.

we get,

x = ( 2 - y/z ) / 3

We can simplify further.

x = [( z - 2 ) / z ] / 3

x = ( z - 2 ) / 3z

Thus the x value is ( z - 2 ) / 3z.

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Final answer:

Aaron's plane flew 225 centimeters further than Noah's plane after converting their flight distances from meters to centimeters and finding the difference.

Explanation:

Aaron's plane flew 4.5 meters, and Noah's plane flew half the distance. To find out how much further Aaron's plane flew than Noah's, we need to calculate Noah's distance first:

Half of 4.5 meters is 2.25 meters.

Now, let's find the difference in their flight distances in centimeters. Since 1 meter is equal to 100 centimeters, we'll convert both distances to centimeters:

Aaron's plane: 4.5 meters x 100 cm/meter = 450 centimeters

Noah's plane: 2.25 meters x 100 cm/meter = 225 centimeters

Next, we calculate the difference:

450 centimeters - 225 centimeters = 225 centimeters

So, Aaron's plane flew 225 centimeters further than Noah's plane.

Final answer:

Aaron's plane flew 4.5 meters, which is equal to 450 centimeters. Noah's plane flew half the distance, which is 225 centimeters. Therefore, Aaron's plane flew 225 centimeters further than Noah's plane.

Explanation:

Aaron's plane flew 4.5 meters. Noah's plane flew half the distance, which is 4.5 / 2 = 2.25 meters. To find out how many centimeters further Aaron's plane flew, we need to convert the distances to centimeters. Since 1 meter is equal to 100 centimeters, Aaron's plane flew 4.5 x 100 = 450 centimeters. Noah's plane flew 2.25 x 100 = 225 centimeters.

To calculate the difference, we subtract the distance Noah's plane flew from the distance Aaron's plane flew: 450 - 225 = 225 centimeters.

Therefore, Aaron's plane flew  225 centimeters further than Noah's plane.