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3 years ago

A rectangular pen is to contain 108 ft^2 of area. if the width is 3 feet less than the length, find the dimensions of the pen.

Mathematics

1 answer:

velikii [3]3 years ago

6 0

Answer:width is 9ft

Length is 12 ft

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The area of a triangle is expressed as length, L × Width, W.

Area of the rectangular pen is 108 ft^2. Therefore,

LW = 108 - - - - - - - 1

if the width is 3 feet less than the length, it means that

W = L - 3

Substituting W = L - 3 into equation 1, it becomes

L(L - 3) = 108

L^2 - 3L = 108

L^2 - 3L- 108 = 0

L^2 + 9L- 12L - 108 = 0

L(L + 9) - 12(L + 9) = 0

L - 12 = 0 or L + 9= 0

L = 12 or L = - 9

The length cannot be negative,

so Length = 12ft

W = 108/L = 108/12 = 9 ft

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ser-zykov [4K]

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6 0

3 years ago

Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12

KIM [24]

Answer:

Rate of slower bus; 90 km/h

Rate of faster bus; 102 km/b

Step-by-step explanation:

We know that formula do distance is;

Distance = speed/time

We are told that One bus travels 12h slower than the other.

Let speed of slower bus be x.

Thus;

Speed of faster bus = x + 12

Speed of slower bus = x

After 3 hours, distance by faster bus = 3(x + 12)

Speed of slower bus = 3x

Since the towns are 576 km apart, then;

3(x + 12) + 3x = 576

Divide through by 3 to get;

x + 12 + x = 192

2x + 12 = 192

2x = 192 - 12

2x = 180

x = 180/2

x = 90 km/h

Faster bus speed = 90 + 12 = 102 km/h

8 0

3 years ago

AB = 3 + x

strojnjashka [21]

Answer:

Option A) 4, 2

Step-by-step explanation:

We are given that quadrilateral ABCD is a parallelogram with sides:

$AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y$

Since the opposite sides of a parallelogram are equal, we can write:

$AB = DC\\AD=BC$

Equating the sides we get,

$\Rightarrow 3+x = 4x\\4x-x = 3\\3x = 3\\x = 1\\\Rightarrow y + 1 = 2y\\y = 1$

Putting the values of x and y, we get:

$AB = 3 + x =4\\DC = 4x =4\\AD = y + 1=2\\BC = 2y=2$

Thus, the lengths of the opposite side pairs is 4,2.

4 0

3 years ago

You are tasked with helping plan a school dance. You expect 110 people to attend the dance and need to provide seating for each

galben [10]

Answer:

2x + 4y = 110

Step-by-step explanation:

Let

The quantity of small tables = x

The quantity of large tables = y

The smaller tables can fit 2 people, the larger tables can seat 4 people.

Equation that describes the relationship between the quantity of small tables and the quantity of large tables, assuming exactly 110 people need seats.

Number of people×quantity (small table) + number of people×quantity (large table) = 110

2x + 4y = 110

5 0

3 years ago

15 less than 2 times a number is represented by the algebraic expression of 2h - 15. True or false

Advocard [28]

False here are extra words tho make 20 words

8 0

3 years ago