The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.

The area of MNP triangle is 60 m².

Based on the congruency of triangles, the value of MP and QS will be the same. Hence, the value of side MP will be 8 m.

Now, the formula to calculate right angled triangle is 1/2 × base × height.

Keep the values in formula to find the value of area of triangle MNP.

Area = 1/2 × 8 × 15

Performing multiplication and division on Right Hand Side of the equation to find the area of triangle MNP

Area = 4 × 15

Area = 60 m²

Thus, the area of right angled triangle is 60 m².

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The ratio Illustrated shows that the number of vanilla marshmallow is 121.

A ratio shows how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. It should be noted tjat.A/B will be the formula if one is comparing one data point (A) to another data point (B).

Let the vanilla marshmallow be represented be x.

Since the ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11, the vanilla will be:

= 11 / (5 + 11) × 176

= 11/16 × 176

= 11 × 11

= 121

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Complete question

The ratio for chocolate marshmallows to vanilla mmarshmallows is 5:11. There are 176 chocolate marshmallows in the bag, how many marshmallows are vanilla?

Answer:

First simplify the ones that need dividing

Step-by-step explanation:

So i got

-0.4, -0.6, 0.5, 4.44, 66.2

Hope this helps!

(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.

Domain of the tangent function be, R - {(2n+1)π/2}

Range of the tangent function be, R

Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.

So, the restricted domain be (-π/2 , π/2).

In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.

So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.

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Total pre-split Market Capitalization is $1,08,125,000.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

Williams and Co. is splitting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million.

Total Value of Shares = $43.25 Share Price × 2.5 × 10⁶ Shares

Total Value of Shares = $1,08,125,000

Let’s say the company’s board decides to approve a 3-for-1 split.

Total Shares = 2.5 × 10⁶ × 3 = 75,00,000

Share Price = $43.25 ÷ 3 = $14.416

Total Value of Shares = $14.416 Share Price × 75,00,000 Shares

Apply the multiplication operation,

Total Value of Shares = $1,08,120,000

Thus, the total pre-split Market Capitalization is $1,08,125,000.

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The old monthly payment was =  9.27 x 50 = 463.5

The new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

Given,

Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan

According to the question:

So, per thousand value of $65000 is 50000/1000 =50

Now, the old monthly payment was =  9.27 x 50 = 463.5

She decides to renew and will now pay $11.10 monthly per thousand on his loan.

So, the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100

19.7411 % and to nearest tenth it is 1.947%

Hence, the old monthly payment was =  9.27 x 50 = 463.5

the new monthly payment is = 11.10 x 50 = 555

The percent increase in his monthly payment is 1.947%

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The radius of the given circle is 7.5 units.

So, use the Pythagorean theorem:

Now, calculate as follows:

So, the diameter is 15 units.

Then the radius is:

Therefore, the radius of the given circle is 7.5 units.

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The slope of the line is 1.11

Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line.

Given that, engineers measure angles in gradients, which are smaller than degrees,

Slope = (-200+100)/(-180+90) = -100/(-90) = 10/9 = 1.11

Hence, The slope of the line is 1.11

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Answer:

1.11

Step-by-step explanation:

it's correct.

The diameter of the circle is 4.45 units.

What is circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.

A line segment having both the endpoints on the circle and is the largest chord of the circle is called diameter.

Given,

the circumference of circle = 14 units

circumference = πd

14 = 3.14(d)

14/3.14 = d

d = 4.45

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Answer:

x=10

Step-by-step explanation:

3(4x-12)=84

12x-36=84

   +36. +36

12x=120

/12.  /12

x=10

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

When dividing, you always have to make sure that your remainder
(40) is ALWAYS less than your divisor (24)

24<40, so the students' answer is incorrect.

The ordered pair which is a solution to the system of inequalities is: (-1, 0).

In order to determine which ordered pairs are true solutions based on the given system of inequalities, we would have to test each of the ordered pairs by substituting their values into the system of inequalities as follows;

For ordered pair (4, 3), we have:

-7x + 3y > -1

-7(4) + 3(3) > -1

-28 + 9 > -1

-19 > -1 (False).

For ordered pair (2, 8), we have:

-7x + 3y > -1

-7(2) + 3(8) > -1

-14 + 24 > -1

10 > -1 (True).

5x - 9y > -6

5(2) - 9(8) > -6

10 - 72 > -6

-62 > -6 (False).

For ordered pair (-1, 0), we have:

-7x + 3y > -1

-7(-1) + 3(0) > -1

7 + 0 > -1

7 > -1 (True).

5x - 9y > -6

5(-1) - 9(0) > -6

-5 - 0 > -6

-5 > -6 (True).

For ordered pair (-2, 2), we have:

-7x + 3y > -1

-7(-2) + 3(2) > -1

14 + 6 > -1

20 > -1 (True).

5x - 9y > -6

5(-2) - 9(2) > -6

-10 - 18 > -6

-28 > -6 (False).

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The value of angle with x, given the equation on the circle, is 4) 3.

The angle is given by the expression:
31x + 3

The same angle is shown to be a right angle with the line EF being straight and therefore a right angle. Right angles have a total measure of 90 degrees.

The value of x can therefore be found by equating the expression to 90 degrees:
31x + 3 = 90

31 x = 90 - 3

x = 87 / 31

x = 2.8

x = 3

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If ∠4 ≅ ∠14, then the lines that must be parallel are a and b and so we can say that; a∥b, Converse of the Alternate Interior Angles Theorem

Interior angles are basically the pair of angles created on the inner side of the parallel lines and right on the opposite sides of the transversal when two parallel lines are intersected by a transversal .

We are told that ∠4 ≅ ∠14, which lines,

If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposite angles are equivalent.

Thus, angle 4 is congruent to angle 14.

Therefore, we can deduce the following;

Angle 15 is a corresponding angle to angle 3 and so we can write that;

∠15 ≅ ∠3

Angle 15 is a vertically opposite angle to angle 13 and so we can write that; ∠15 ≅ ∠13

By transitive property of equality, we can say that;

∠3 ≅ ∠13    [Alternate interior angles]

Thus, we have  ∠4 ≅ ∠14

Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.

Hence, the correct answer would be an option (B).

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The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 150, hence:

Area = length × width = x × y

150 = xy

y = 150/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(150/x) = 2x + 450/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2 = 450/x²

2x² = 450

x² = 225

x = 15 feet

Let's find the value of y.

y = 1350/x = 1350/15 = 10 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.

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After 10 days, the expected number of shoppers at the shopping mall is 163.

It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.

As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.

The formula of compound increase is

Amount = Base X (1 + r/n)ⁿˣ

where,

Base = original amount

r = rate of change

n = no. of times the change occurs in the time period

t = time

Here,

Base = 100

r = 5/100

n = 1, since it changes once every day

x = 10

Therefore we get

100 X (1 + 5/100)¹⁰

= 100 X 1.05¹⁰

162.88

Since the number of people cannot be in decimal,

the expected number of people is 163

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It is proved that tan15°=2−√3 by using the identity of tan(A-B)

What are the 3 trignometric identities?

The right-triangle theorem, also known as Pythagoras theorem, is the foundation for the three Pythagorean trigonometric identities.

[tex]sin^{2}a+cos^{2}a=1[/tex]

[tex]1+tan^{2}a=sec^{2}a[/tex]

[tex]cosec^{2}a=1+cot^{2}a[/tex]

The reciprocal trigonometric identities are:

Sin θ = 1/Cosec θ or Cosec θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

tan 15 = tan(45 - 30)

As tan(A - B) = (tanA - tanB)/(1 + tanAtanB)

tan15 = tan(45 - 30) = (tan45 - tan30)/(1 + tan30tan45)

                   = [tex]\frac{1 - \sqrt{3} }{1+\sqrt{3} }[/tex]

                   = [tex]\frac{1-\sqrt{3} }{1+\sqrt{3} }[/tex]   ×   [tex]\frac{1 - \sqrt{3} }{1-\sqrt{3} }[/tex]

                   = [tex]\frac{(1-\sqrt{3}) ^{2} }{1-\sqrt{3} ^{2} }[/tex]

                  =  [tex]\frac{(1-\sqrt{3}) ^{2} }{1-3}[/tex]

                 =  [tex]\frac{(1-\sqrt{3} )^{2} }{-2}[/tex]

                =  [tex]\frac{1+3-2\sqrt{3} }{-2}[/tex]

                 = [tex]\frac{4-2\sqrt{3} }{-2}[/tex]

                 = 2-[tex]\sqrt{3}[/tex]

Hence it is proved that tan15°=2−√3

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To solve the given problem first we need to find the equation for line then we have to find the intersection point on circle.

You will pick up a signal from the transmitter in 29% of the drive.

Given:

The radius is 53 mile.

The origin point of transmitter is .

Calculate the slope of line with point  and .

Substitute the value.

Write the general equation of line.

Now we got the equation of line,

Write the transmitter reach the area enclosed by the next circle.

Substitute the value of .

Thus, You will pick up a signal from the transmitter in 29% of the drive.

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The price of the share 3 years later, given the increase in value, can be found to be $43.29

The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.

This means that the price of the share 3 years later would be:

= Share price currently x ( 1 + increase in value)

= 37 x ( 1 + 17 % )

= 37 x 1. 17

= $ 43. 29

The price is  $43.29

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Money  she will have after 52 weeks = rs.2,700

acc to our question-

Unit rate of change here is =

⇒ Unit rate of change here is =

⇒ Unit rate of change here is = 50%

Part B

Equation to calculate the amount of money Greta will have after any number of weeks = ?

Money after 'x' number of weeks =

⇒ Money after 'x' number of weeks =

Part C

Money Greta will have after 1 year= ?

In a year there are 52 weeks

So, putting x = 52 in the solution of Part B

⇒ Money after 52 weeks =

⇒ Money after 52 weeks =

⇒ Money after 52 weeks = 2,700

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The length of the area is 8 feet.

What is the shape of outdoor space?

Step-by-step explanation:

Given :

Distance between the furthest corners(Length)= 4 feet

Width(breadth) = 2 feet

Area of rectangle = Length * Breadth

                              = 4 * 2

                              =8 feet

Hence, The length of the area is 8 feet.

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Answer:

T = 52

Step-by-step explanation:

Answer:

x = 82°

Step-by-step explanation:

The three angles of the triangle add up to 180°

x + 40° + 58° = 180°

x + 98° = 180°

subtract 98°

x = 82°

Answer:

x = 82°

Step-by-step explanation:

The sum of the internal angles of a triangle = 180°

58° + 40° + x° = 180°

98° + x° = 180°

x° = 180° - 98°

x° = 82°

The original price of the shirt before the discount will be $25.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

You're looking for another shirt and find one that is discounted to $16.25. According to the sign, it is a 35% markdown.

Then the original price of the shirt before the discount will be given as,

⇒ $16.25 / (1 - 0.35)

⇒ $16.25 / 0.65

⇒ $25

The original price of the shirt before the discount will be $25.

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The inequality shown is -4 ≤ x ≤ 3.

We are given a diagram of the number line. The diagram shows the range of the inequality. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. Let the variable "x" represent all the values contained in the inequality. The minimum value contained in the inequality is -4. The maximum value contained in the inequality is 3. All the values between the minimum and maximum limits are included in the inequality. Hence, we can write the following inequalities :

-4 ≤ x

x ≤ 3

We can combine these into a single inequality.

-4 ≤ x ≤ 3

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A prospective research of men and women looked at body mass index, waist circumference, and the risk of coronary heart disease.

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Answer:

x = 20

Step-by-step explanation:

Comment

If you follow the angles down, you discover 2 things

There are only 2 answers

One is the supplement of the other.

In this case, both angles can be shown to be the same. The process is accomplished by two vertically opposite angles and 2 supplements. I can't show you how this is done because there are no letters on the lines.

It turns out that 3x + 10 = 4x - 10

Solution

3x + 10 = 4x - 10                         Add 10 to both sides

3x + 10  + 10 = 4x - 10 + 10          Combine

3x  + 20 = 4x                               Subtract 3x from both sides.

3x-3x + 20 = 4x-3x                      Combine

20 = x

Answer:

375

Step-by-step explanation:

h + c = 680

c = h - 70

h + h - 70 = 680

2h = 680 + 70

2h = 750

2/2 h = 750/2

h = 375