the area of a rectangular place mat is 98 inches its length is seven inches longer than the width. find the length and width of the place mat

A

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

y=5.5x+8

Step-by-step explanation:

Answer:

w or x

Step-by-step explanation:

the square root of 40 is 6.3

Answer:

okay i'll keep this in mind

Step-by-step explanation:

Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.

By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

With regard to the inequality expression

-3m + 5 > 14

5 from each side is subtracted.

-3m + 5 - 5 > 14 - 5

-3m > 9

Subtract -3 from both sides.

-3m/-3 < 9/-3

m < -3

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Answer:

2( 100%) +75%

Step-by-step explanation:

a full box will literally be 100%, so two full boxes will be 2 × a full ie 100%, 'and' a box ie 75% full is addition '+'

Given:

Slope of a line = 3

Line passes through the point = (2,7)

To find:

The equation of the line.

Solution:

The point slope form of a line is:

\(y-y_1=m(x-x_1)\)

Where, m is the slope of the line.

The line passes through the point (2,7) and slope of the line 3. So, the equation of the line is:

\(y-7=3(x-2)\)

\(y-7=3x-6\)

\(y=3x-6+7\)

\(y=3x+1\)

Therefore, the correct option is 3.

Answer:

x = 2

Step-by-step explanation:

hope that helps....

We want to see which of the given polar coordinates are equivalent to the given ones.

The two equivalent pairs are:

(2, -60°) → (2, 300°)

(-2, 240°) → (-2, -120°)

Polar coordinates have a given period, such that:

A polar coordinate (R, θ) is equivalent to (R, θ + n*360°) where n is an integer number.

So if we have the polar coordinate:

(2, -60°), an equivalent polar coordinate can be (2, -60° + n*360°)

if we get n = 1 then we have:

(2, -60° + 360°) = (2, 300°)

So the equivalent polar coordinate is (2, 300°).

For the other polar coordinate we have (-2, 240°) is equivalent to something like (-2, 240° + n*360°)

For example, with n = -1 we have:

(-2, 240° - 360°) = (-2, -120°)

Then the two equivalent pairs are:

(2, -60°) → (2, 300°)

(-2, 240°) → (-2, -120°)

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Answer:

D

Step-by-step explanation:

The scale factor is the ratio of the corresponding sides, image to original, that is

scale factor = \(\frac{P'S'}{PS}\) = \(\frac{6}{3}\) = 2 → D

Answer:

the missing measure is 129° all around is 360° half of 360° is 180°, 180° is one line so if you subtract 51° from 180° you get 129° im not so good at explaining but i hope you understand

Answer:-2

Step-by-step explanation:y=500+250x

Answer:

lake Ontario =240m lake Erie =60m

Step-by-step explanation:

5x=300

x=60

Answer:

The correct answer is coconuts

Step-by-step explanation:

Answer:

the correct answer is 64°

Step-by-step explanation:

Answer:

3x + 1

Step-by-step explanation:

let the unknown number be x

x * 3 + 1  ...........here we multiplied by 3 and added 1

3x + 1

Answer:

\(x(3)+1\)

Step-by-step explanation:

As we don't know what we are multiplying, simply use x to replace that factor. we'll receive the equation  x(3)+1.

Albert

Compound interest formula:

where:

A: final amount

P: principal

r: annual interest rate, as a decimal

t: time in years

n: number of times interest applied per year

Substituting with P = $1000, r = 0.012 (= 1.2/100), n = 12 (interest is compounded monthly), t = 10 years, we get:

If $500 lost 2%, then it keeps 98% of its original value, that is,

$500x98% = $490

Continuous compound formula:

where the variables have the same meaning as before.

Substituting with P = $500, r = 0.008 ( = 0.8/100), and t = 10 years, we get:

The balance of Albert’s $2000 after 10 years is:

$1127.43 + $490 + $541.64 = $2159.07

Marie

Substituting in the compound interest formula with P = $1500, r = 0.014 (= 1.4/100), n = 4 (interest is compounded quartely), t = 10 years, we get:

Answer:

Cube Root Calculator

Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

It will help you alot.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A for loop basically relies on repeating the same code for a pre-set number of times. During which you can make any code repeat inside of it, including indexing through a type of list. Many times a for-loop will use the indexes in a list to calculate the number of times that the loop has to repeat. This is usually done in order to search or apply changes in an array of other types of data structures that have countless values stored in it.

Answer:

Step-by-step explanation:

1+1=22 SO 10 FEET OF THAT WILL BE UP YOU A

SS

Answer:

Step-by-step explanation:

1+1=22 so 10 feet of that will be up you a

Answer:

The answer is p+q

Step-by-step explanation:

The probability that the marble choose is not green is 9/10

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability is expressed as;

probability = sample space/total outcome

total number of marble = 8+6+2+4 = 20marbles

Probability that it is green = 2/20 = 1/10

therefore probability that Is not green = 1-1/10

= 10-1)/10

= 9/10

therefore the probability that a marble chosen is not green is 9/10.

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Answer:

32,000

Step-by-step explanation:

10% of 320,000 is 32,000

Answer:

240

Hope this Helps

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

\(a_1 = 10, q = -\frac{2}{3}, k = 8\)

The formula for the sum of the first n terms is given as follows:

\(S_n = a_1\frac{1 - r^n}{1 - r}\)

Hence the sum for this problem is given as follows:

\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)

\(S_8 = 5.77\)

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Answer:

The value of both x and y is 5 degree

Step-by-step explanation:

Answer:

Standard deviation is 70

Step-by-step explanation:

square root of 4,900= 70 (solved using standard deviation formula)

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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