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The perimeter of the rectangle is 60 yards

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the length of the rectangle be = a

Let the width of the rectangle be = b

The length of the rectangle is twice the width

So ,

a = 2b

The area of the rectangle is A = 200 yards²

The area of the rectangle is given by

Area of Rectangle = Length x Width

And , substituting the values for length and width , we get

Area of Rectangle = 2b x b

2b² = 200

Divide by 2 on both sides , we get

b² = 100

Taking square root on both sides , we get

b = 10

a = 2b

a = 20

Therefore , the length of the rectangle is 20 yards and width of the rectangle is 10 yards

Now , the perimeter of the rectangle is P = 2 ( length + width )

Perimeter of the rectangle P = 2 ( 10 + 20 )

                                                = 2 x 30

                                                = 60 yards

Hence , the perimeter of the rectangle is 60 yards

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Answer:

c

Step-by-step explanation:

Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.

To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.

(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i

You may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.

Final answer:

To solve a complex number, understand it as a sum of a real number and an imaginary number and use operations like conjugation. For division, multiply by the conjugate to simplify. Complex numbers ensure all polynomial equations have solutions.

Explanation:

To solve a complex number, one must understand that a complex number z is the sum of a real number and an imaginary number, which is written as z = a + ib. The terms a and b represent the real and imaginary parts respectively, often notated as Re(z) and Im(z).

To divide by a complex number, you multiply the numerator and the denominator by the conjugate of the denominator, simplifying to a form without imaginary numbers in the denominator. This can be expressed as z/z' = (aa' + bb')/(a'² +b'²) + i(ba' - ab')/(a'² + b'²). The conjugate of a complex number z is written as z* or z*.

Complex numbers are crucial in solving polynomial equations as they ensure that every polynomial equation has a solution. This is shown by the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. For instance, the equation x² - 2x + 5 = 0 has no real solutions but two complex solutions, x = 1±2i.

look where the line is on the y axis at x =2

 answer is y=-3

value is -3

Jane studied a total of 5 11/12 hours for her history final and math exam.

To find the total number of hours Jane studied for the two tests, we add together the number of hours she studied for each test. Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.

To add these fractions, we need to have a common denominator. The least common multiple of 3 and 4 is 12. We can convert 2/3 to 8/12 and 1/4 to 3/12.

Now we can add the fractions: 4 8/12 + 4 3/12 = 5 11/12.

Therefore, Jane studied a total of 5 11/12 hours for the two tests.

Final answer:

Jane studied a total of 7 3/4 hours for her history and math exams.

Explanation:

To find out how many hours Jane studied for the two tests, we simply need to add the hours she studied for each test together.

Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.

We can add these two fractions by finding a common denominator and then adding the numerators.

In this case, the common denominator is 12. So, we have (4 * 4 + 2) / 3 = 18/3 and (4 * 3 + 1) / 4 = 13/4.

Adding these fractions together, we get (18/3) + (13/4) = 54/12 + 39/12 = 93/12. Simplifying this fraction, we get 7 3/4 hours.

Therefore, Jane studied a total of  7 3/4 hours for the two tests.

Answer:

25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Non-foliated metamorphic rocks are those which don't have a rough texture, like foliated ones, their composition gives them this characteristics: not having layers or banded appearance.

To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.

To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.

First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).

Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.

To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.

This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.

Answer:

c: 18

Step-by-step explanation:

ASA

Is the answer i got on my work

8.2% = 0.082

50 * 0.082 = 4.1

the answer is 4.1

300/6 = 50 mph

250/5 =50mph

 so they drove 50 miles per hour

 so 50 *3 = 150 miles in 3 hours

25 * 2.5 = 62.5 *2 = 125

8x5 = 40

125 +40 = 165 square feet

>First jump = 4.25 m

>Best jump = 1.12 * First jump

Best jump = 1.12 * (4.25 m)

Best jump = 4.76 m

>Best jump = 0.85 * Winning jump

Hence,

Winning jump = Best jump / 0.85

Winning jump = 4.76 m / 0.85

Winning jump = 5.6 m

Answer:

[tex]P(n)=66n-1200[/tex]

Step-by-step explanation:

Let x be the revenue collected from selling each ticket.

We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.

Since we know that net profit is the difference between total revenue and total cost.

[tex]\text{Net profit}=\text{Total revenue- Cost}[/tex]

We can represent our given information in an equation to find the revenue collected from each ticket:

[tex]12000=200x-1200[/tex]

Let us solve for x by adding 1200 to both sides of equation.

[tex]12000+1200=200x[/tex]

[tex]13200=200x[/tex]

[tex]x=\frac{13200}{200}[/tex]

[tex]x=66[/tex]

Therefore, the revenue collected from selling each ticket is $66.

Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.

The revenue from selling n tickets will be 66n.

Production costs = 1200

[tex]P(n)=66n-1200[/tex]

Therefore, our desired function will be: [tex]P(n)=66n-1200[/tex].

Answer:

[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following integration:

[tex] \displaystyle \int \frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]

in order to do so we can consider using u-substitution

let our

[tex] \displaystyle u = {x}^{ \frac{1}{2} } \quad \text{and} \quad du = \frac{ {x}^{ - \frac{1}{2} } }{2} [/tex]

to apply substitution we need a little bit arrangement

multiply both Integral and integrand by 2 and ½

[tex]\displaystyle 2\int \frac{1}{2} \cdot\frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]

factor out [tex]x^{\frac{1}{2}}[/tex]:

[tex]\displaystyle 2\int \frac{1}{2 {x}^{ \frac{1}{2} } } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]

recall law of exponent:

[tex]\displaystyle 2\int \frac{ {x}^{ - \frac{1}{2} } }{2 } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]

apply substitution:

[tex]\displaystyle 2\int \frac{5}{ 1+ {x}^{ } } du[/tex]

rewrite x as [tex]\big(x^{\frac{1}{2}}\big)^{2}[/tex]:

[tex]\displaystyle 2\int \frac{5}{ 1+ ( {x ^{ \frac{1}{2} } })^{ 2 } } du[/tex]

substitute:

[tex]\displaystyle 2\int \frac{5}{ 1+ ( u)^{ 2 } } du[/tex]

recall integration rule of inverse trig:

[tex] \displaystyle 2 \times 5 \tan^{-1}(u)[/tex]

simplify multiplication:

[tex] \displaystyle10 \tan^{-1}(u)[/tex]

substitute back:

[tex] \displaystyle10 \tan^{-1}( {x}^{ \frac{1}{2} } )[/tex]

simplify if needed:

[tex] \displaystyle10 \tan^{-1}( \sqrt{x} )[/tex]

finally we of course have to add constant of integration:

[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]

and we are done!