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3 years ago

the perimeter of a rectangular campsite is 64m and its area is 207m^2. find the length and breadth of the campsite

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

4 0

Answer:

The length is $23\ m$ and the breadth is $9\ m$

Step-by-step explanation:

Let

x ----> the length of a rectangular campsite

y ----> the breadth of a rectangular campsite

we know that

The perimeter of a rectangle is equal to

$P=2(x+y)$

$P=64\ m$

$64=2(x+y)$

$32=(x+y)$

$y=32-x$ ------> equation A

The area of a rectangle is equal to

$A=xy$

$A=207\ m^{2}$

$207=xy$ -----> equation B

substitute equation A in equation B

$207=x(32-x)\\\\207=32x-x^{2}\\\\x^{2}-32x+207=0$

Solve the quadratic equation by graphing

The solution is $x=23\ m$ ( I assume that the length is greater than the breadth)

see the attached figure

Find the value of y

$y=32-23=9\ m$

therefore

The length is $23\ m$ and the breadth is $9\ m$

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3 years ago

Find the distance between the complex numbers. z1 = 9 - 9i z2 = 10 - 9i

steposvetlana [31]

Answer:

The distance between the two given complex numbers = 9

Step-by-step explanation:

Explanation:-

Step(i):-

Given Z₁ = 9 - 9 i and Z₂ = 10 -9 i

Let A and B represent complex numbers Z₁ and Z₂ respectively on the argand plane

⇒ A = Z₁ = x₁ +i y₁ = 9 - 9 i and

B = Z₂ = x₂+ i y₂ = 10 -9 i

Let (x₁ , y₁) = ( 9, -9)

(x₂, y₂) = (10, -9)

Step(ii):-

The distance between the two points are

A B = $\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }$

A B = $\sqrt{(10 - 1)^{2}+(-9 - (-9))^{2} }$

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3 years ago

This system of equations has an infinite number of solutions. Define the solutions algebraically, and allow z to represent all r

Soloha48 [4]

Answer:

x = 12z + 1 and y = 10z - 1

Step-by-step explanation:

To solve the system of equations, we can use the substitution method

If we call

3x - 4y + 4z = 7 I

x - y - 2z = 2 II

2x - 3y + 6z = 5 III

Clearing II x = 2 + y + 2z

Now, replacing II in III

2(2 + y + 2z) - 3y +6z = 5

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Finally, replacing y in I

3x - 4(10z - 1) + 4z = 7

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Done

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3 years ago

Within a computer service company, 20 percent of the male employees and 30 percent of the female employees attend night school.

Maksim231197 [3]

26% of all the employees attend night school

Step-by-step explanation:

The given is:

Within a computer service company, 20 percent of the male employees and 30 percent of the female employees attend night school

40 percent of all employees are male

We need to find what percent of all the employees attend night school

Assume that the number of all employees is x

∵ The company has x employees

∵ 40 percent of all employees are male

- Find 40% of x

∵ 40% × x = $\frac{40}{100}$ × x = 0.4 x

∴ The number of the male employees is 0.4 x

- Subtract 0.4 x from x to find the number of the female employees

∵ The number of female employees = x - 0.4 x = 0.6 x

∴ The number of the female employees is 0.6 x

∵ 20 percent of the male employees attend night school

- Multiply 20% by 0.4 x to find the number of male employees

who attend night school

∴ The number of male who attend night school = 20% × 0.4 x

∴ The number of male who attend night school = $\frac{20}{100}$ × 0.4 x

∴ The number of male who attend night school = 0.08 x

∵ 30 percent of the female employees attend night school

- Multiply 30% by 0.6 x to find the number of female employees

who attend night school

∴ The number of female who attend night school = 30% × 0.6 x

∴ The number of male who attend night school = $\frac{30}{100}$ × 0.6 x

∴ The number of male who attend night school = 0.18 x

Add the number of male and female who attend night school

∵ 0.08 x + 0.18 x = 0.26 x

∴ The number of male and female who attend night school is 0.26 x

- Find the percentage of 0.26 x of x

∵ $\frac{0.26x}{x}$ × 100% = 26%

∴ 26% of all the employees attend night school

26% of all the employees attend night school

Learn more:

You can learn more about the percentage in brainly.com/question/6871421

#LearnwithBrainly

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3 years ago

Do all ratios compare a part to a whole number? Explain

STALIN [3.7K]

Yes and no...

A ratio can be defined in a new ways. Let's say I have a party with twelve people, four of whom are male and eight of whom are female. The ratio of male to female guests would be written as 4:8, neither of which is the whole number (12) but which instead relate parts of the whole. I could alternatively write the ratio of male guests to total guests as 4/12. This does compare it to the whole. A ratio relates two quantities by showing how many times one quantity is contained within or contains another quantity.

By the phrasing of your question, I'm not sure if you maybe mean whole number as an integer. If that's the case, then yes, ratios are almost always written as integers. If I had something like 8.5:7, I would multiply it by two to get 17:14, which is a correct ratio.

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3 years ago