whats the area of sector and length of arc

Answer: Let's start by using algebra to solve the problem.

Let's call the width of the rectangle "w". Then we know that the length of the rectangle is twice the width, or "2w".

The formula for the perimeter of a rectangle is:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

We know that the perimeter is 18 inches, so we can substitute the values we have:

18 = 2(2w) + 2w

Simplifying:

18 = 4w + 2w

18 = 6w

Dividing both sides by 6:

w = 3

So the width of the rectangle is 3 inches.

To find the length, we can use the fact that it is twice the width:

l = 2w = 2(3) = 6

So the length of the rectangle is 6 inches.

Therefore, the rectangle is 6 inches long and 3 inches wide.

enjoy!

i. The points of intesection of the common chords of the curve x² + y² = 4 and y² = 3x are

ii. The points of intesection of the common chords of the curve x² + y² = 4 and x² - 4y + 1 = 0 are

The common chords of circles are the chords that pass through the points of intersection of the curves.

i. Given the curve x² + y² = 4 and y² = 3x. We desire to find their points of intesection of the common chords. We proceeds as follows.

Since  x² + y² = 4 and y² = 3x. Substituting the second equation into the first, we have

x² + y² = 4 and y² = 3x.

x² + 3x = 4

Re-arranging, we have

x² + 3x - 4 = 0

Factorizing the quadratic equation, we have

x² - x + 4x - 4 = 0

x(x - 1) + 4(x - 1) = 0

(x + 4)(x - 1) = 0

⇒ x + 4 = 0 and x - 1 = 0

⇒ x = - 4 and x = 1

Now, y² = 3x.

⇒ y = ±√3x

So.substituting x = -4 into the equation, we have

y = ±√3x

y = ±√(3 × -4)

= ±√(-12)

Since the square root is negative, this answer is invalid.

Substituting x = 1 into y, we have

y = ±√3x

y = ±√3(1)

y = ±√3

So, the points of intersection are (1, √3) and (1,-√3)

ii. Given the curve x² + y² = 4 and x² - 4y + 1 = 0. We desire to find their points of intesection of the common chords. We proceeds as follows.

Since  x² + y² = 4 and x² - 4y + 1 = 0. From the second equation, we have

x² = 4y - 1

Substituting this equation into the first, we have

x² + y² = 4 and x² = 4y - 1

y² + 4y - 1 = 4

Re-arranging, we have

y² + 4y - 1 - 4 = 0

y² + 4y - 5 = 0

Factorizing the quadratic equation, we have

y² - y + 5x - 5 = 0

y(y - 1) + 5(y - 1) = 0

(y + 5)(y - 1) = 0

⇒ y + 5 = 0 and y - 1 = 0

⇒ y = - 5 and y = 1

Now, x² = 4y - 1

⇒ x = ±√(4y - 1)

So, substituting y = -5 into the equation, we have

x = ±√(4y - 1)

x = ±√[(4 × -5) - 1)]

= ±√(- 20 - 1)

= ±√-21

Since the square root is negative, this answer is invalid.

Substituting y = 1 into x, we have

x = ±√(4y - 1)

x = ±√(4(1) - 1)

x = ±√(4 - 1)

x = ±√3

So, the points of intersection are (√3, 1) and (-√3, 1)

Learn more about point of intersection of common chords here:

https://brainly.com/question/27251228

#SPJ1

Answer:

Length - 12 m, width - 8m, height - 4 m

--------------------------------------

The relation between dimensions of the box:

Use volume equation and find the value of l:

Find the width and height:

The price of an item that is normally £120 after a 20% discount is £96.

To find the price of an item that is normally £120 after a 20% discount,

Calculate the discount amount: To find the discount amount, multiply the original price (£120) by the discount rate ( 20% ) in decimal form:

Discount amount = Original price x Discount rate

= £120 x 0.2

= £24

Calculate the sale price: To find the sale price, subtract the discount amount from the original price:

Sale price = Original price - Discount amount

= £120 - £24

= £96

Therefore, the sale price is £96

Learn more about discount rate here

brainly.com/question/25925899

#SPJ4

Answer:

Hello, your answer is 10

Step-by-step explanation:

Have a good day UwU

The given facts about power sets: Statement 1: False, Statement 2: True, Statement 3: True.

Statement 1: The power set of X is a subset of X. False. The power set of X, denoted by P(X), is a set containing all subsets of X. However, X is not a subset of P(X).

Statement 2: The cardinality of P(X) is greater than the cardinality of X. True. Since the power set of X contains all subsets of X, it has a higher cardinality than X. This can be proven with the equation |P(X)| = 2^|X|.

Statement 3: The cardinality of the power set of the empty set is 1. True. The empty set, denoted by Ø, has no elements, and therefore the power set of the empty set, P(Ø), has one element, which is the empty set itself. Therefore, |P(Ø)| = 1.

In conclusion, each statement is either true or false depending on the given information.

Know more about power sets here:

https://brainly.com/question/80705

#SPJ11

Answer:

70%

Step-by-step explanation:

3 out of the 10 marbles are not orange, so 7/10 chance you don't, and then you can multiply by 10, and then you have 70 percent

The value of m, n and w are 92, 48 and 88 respectively

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon( 3sided polygon). The sum of angles In a polygon is 180. i.e A+B +C = 180

In the triangle above, The triangle is divided into two.

42+36+w = 180

88+w = 180

w = 180 - 88

w = 92°

From the law of the law of exterior angle of a triangle which states that; The exterior angle of a triangle is equal to the sum of opposite angles.

Therefore;

92 = n + 44

n = 92-44

n = 48°

w = 180-92( angles on a straight line)

w = 88°

Therefore the value of m, n, w are 92, 48 and 88 respectively

learn more about sum of angle In a triangle from

https://brainly.com/question/28164102

#SPJ1

Therefore , the solution of the given problem of fraction comes out to be Y is therefore equivalent to 26/5.

Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.

Here,

We can begin by isolating the variable with one side of the solution in order to solve for y. The reciprocal of fraction on the left side of the equation can be used to add both sides of the equation to achieve this:

=> 2/5 = (y - 4)/3

=> 3 * 2/5 = y - 4 [add 3 to both ends]

=> 6/5 = y - 4 [simplify]

=> y = 6/5 + 4 [Adjust both ends by 4]

=> y = 6/5 + 20/5 Using the denominator 5 as the corresponding fraction, write 4.

=> y = 26/5

Y is therefore equivalent to 26/5.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

In conclusion, we need to identify the set of values of x for which either f(x)=-1/4 or f(-x)=-1/4 in order to solve to the equation f(|x|)=-1/4.

The expression f(|x|)=-1/4 indicates that the absolute value of x's function f is equal to 1/4. Any x values that satisfy this equation are what we are trying to find. We can rewrite the equation as f(x)=-1/4 when x is positive and f(-x)=-1/4 when x is negative because the absolute value of x is always positive.

We must search for values of x such that f(x)=-1/4 or f(-x)=-1/4 in order to identify the answers. Without knowing more about the function, f may be anything, hence we cannot know the precise solutions.

Therefore, we can state that x or -x is a solution to the equation if there is a value of x such that f(x)=-1/4 or f(-x)=-1/4.

As a result, we must identify the range of x values for which either f(x) or f(-x) = 1/4.

Learn more about linear equation here:

brainly.com/question/11897796

#SPJ1

There is no one definite answer.

Given information: If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must also be roots?To find out the other roots of P(x), we have to make use of the Fundamental theorem of algebra which states that every polynomial of degree n has n roots, both real and complex.In order to find out the other roots, we have to divide the polynomial P(x) by its given roots i.e (x-(3-2√5))(x-(6+????)) = 0Let's begin by solving the first root:Since, If 3 −2√5 is the root, thus we can write, x - (3 - 2√5) = 0Or, x - 3 + 2√5 = 0Or, x = 3 - 2√5Similarly, for the second root, 6 + ???? ,

we can write: x - (6 + ???? ) = 0Or, x = 6 + ????Now, Let's combine these two roots and write the polynomial in factored form. Using these two roots, we can write the equation as below: Thus, P(x) = (x - 3 + 2√5)(x - 6 - ???? ) = 0We have found the other roots to be: Other roots = (x - 3 + 2√5)(x - 6 - ???? ) = 0Where ???? can be any value. Therefore, there is no one definite answer.

Learn more about Roots

brainly.com/question/16932620

#SPJ11

The set of ordered pairs in option C does not represent a function.

What is a function?

A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable.

We know that in a function each input has only one output.

So, on evaluating the options, we get

Option A

This represents a function as each input has only one output.

Option B

This represents a function as each input has only one output.

Option C

This does not represent a function as input 2 has two different outputs which are 2 and 7.

Option D

This represents a function as each input has only one output.

Option E

This represents a function as each input has only one output.

Hence, the set of ordered pairs in option C does not represent a function.

Learn more about function from the given link

https://brainly.com/question/11624077

#SPJ1

Question: Which set of ordered pairs does NOT represent a function?

A. (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)

B. (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)

C. (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)

D. (1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)

E. (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)

Answer:

Plot the point on 1

Step-by-step explanation:

Answer: 1

Step-by-step explanation: There are 10 space on the number line between the two pts. Since we are finding a 1:4 ratio we will need to divide these 10 space by 5.

[tex]10/5=2[/tex]

Which means that the point is two spaces away from T. Which is point 1 on the number line.

Answer:

y = 0

Step-by-step explanation:

the 2 points (- 1, 0 ) and (0, 0 ) both have the same y- coordinate.

this indicates the line is horizontal with equation

y = c ( c is the value of the y- coordinates the line passes through )

both points have a y- coordinate of 0 , then

y = 0 ← equation of line

The given expressiοn is equivalent tο -19.5b - 6.9.

A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. Unknοwn variables, integers, and arithmetic οperatοrs are the cοmpοnents οf an algebraic expressiοn.

Here, we have

Given: 3(-4.5b-2.1)-(6b+0.6)

We have tο find the expressiοn that is equivalent tο the given expressiοn.

= 3(-4.5b-2.1)-(6b+0.6)

= -13.5b - 6.3 - 6b - 0.6

= -19.5b - 6.9

Hence, the given expressiοn is equivalent tο -19.5b - 6.9.

Tο learn mοre abοut the expressiοn frοm the given link

https://brainly.com/question/28998898

#SPJ1

Answer:  A^2 + B^2 = C^2

Step-by-step explanation:

please check for more knowledge,

https://brainly.in/question/55669292

Answer: go to your profile and you'll see the account or profile I

think,  and you go to settings and it it will probably say something like delete the account or give you the choice to.

Step-by-step explanation:

Answer:

I think that you click on your profile picture, then go to your settings from there, and then you eventually find the cancel account or delete account choice.

Step-by-step explanation:

you do the above

The ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.

An inequality is a mathematical statement that compares two values and shows the relationship between them using symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

For the given ordered pairs:

(6, 38): The y-coordinate (38) is greater than 0, this ordered pair is a solution to the inequality y > 0.

(-4, -13): The y-coordinate (-13) is not greater than 0, this ordered pair is not a solution to the inequality y > 0.

(-1, 8): The y-coordinate (8) is greater than 0, this ordered pair is a solution to the inequality y > 0.

(3, 26): The y-coordinate (26) is greater than 0, this ordered pair is a solution to the inequality y > 0.

Therefore, the ordered pairs (6, 38), (-1, 8), and (3, 26) are solutions to the inequality y > 0, while (-4, -13) is not a solution.

To know more about inequality, visit:

https://brainly.com/question/30238989

#SPJ1

Answer:

6.75 in

Analysis:

[tex]\text{The average heights of gymnasts is 60 in, the other is 75 in.}[/tex]

[tex](60+75)\div2=6.75 \ \text{in}[/tex]

Answer:

2 and 6

Step-by-step explanation:

2 and 6 is the correct option

Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.

To calculate the volume of the rectangular prism planter box, we need to multiply the length, width, and height of the box.

Volume = length x width x height

V = 4.5 ft x 2 ft x 1.5 ft

V = 13.5 cubic feet

Therefore, Mr. Moore needs 13.5 cubic feet of soil to fill the planter box.

It is important to note that the volume of the box represents the amount of space inside the box and does not take into account any obstructions or irregularities that may be present inside the box.

Thus, the actual amount of soil required may be slightly different from the calculated value. Additionally, it is always a good idea to add some extra soil to account for settling and to ensure that the planter box is completely filled.

To learn more about planter box

https://brainly.com/question/11911669

#SPJ4

Answer:

-77

Step-by-step explanation:

What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, nth root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.

(Taken from Online)

Answer:

13 dollars and 12 cents

Step-by-step explanation:

I added all of the ingredient prices in parenthesis then multiplies it by 4. :)

In a case whereby Filipe bought a classic car, originally valued at $60,000, in 2012. whee  the value of the car depreciates exponentially at a rate of 4% the expected value of Filipe's car after 6 years is $46970

Based on the given information, the future value when there is a depreciation can be calculated using the formular below:

FV =[ P (1 - r)^n]

where the

R  represent the rate of depreciation =4%  = 0.04

N represent the number of years =  6 years

FV represent the Future value

P represent the Present value

From the formula we can input the values as :

$60,000 x ( 1 - 0.04)^6 = $42,890

=$46965.5

=$46970 (rounded up)

Learn more about depreciates at:

https://brainly.com/question/11560012

#SPJ1

Answer:

290 feet/minute

Step-by-step explanation:

2320/9 = 290

4350/15 = 290

Answer: x=9

Step-by-step explanation:

Simplify the expression

Add 777 to both sides

Simplify the expression

Divide both sides by the same factor

Simplify the expression