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e-lub [12.9K]
4 years ago
7

14. A rectangle has a width described by the expression (x2 + 2x – 15)/x and a length described by the expression

Mathematics
1 answer:
tensa zangetsu [6.8K]4 years ago
8 0

Answer:

The answer to your question is Perimeter = [4x³ + 14x² + 50x - 150] / x(5 + x)

Step-by-step explanation:

Data

Width = (x² + 2x - 15)/x

Length = (3x² + 4x)/ (5 + x)

Process

1.- Write the formula for the perimeter of a rectangle

Perimeter = 2W + 2L

2.- Substitution

Perimeter = 2(x² + 2x - 15)/x + 2(3x² + 4x)/(5 + x)

3.- Simplification

Perimeter = (2x² + 4x - 30)/x + (6x² + 8x)/(5 + x)

4.- Sum the fractions

Least common factor = x(5 + x)

Perimeter = [(2x² + 4x - 30)(5 + x) + (x(6x² + 8x)] / x(5 + x)

-Simplification

Perimeter = [10x² + 20x - 150 - 2x³ - 4x² + 30x + 6x³ + 8x²] / x(5 + x)

Perimeter = [4x³ + 14x² + 50x - 150] / x(5 + x)

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A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If fie
balu736 [363]

Answer:

20,000m²

Step-by-step explanation:

If they jog 12 km/h for half an hour, they have covered.

12 X 0.5 = 6km in 10 circuits. Making 1 perimeter

6 / 10 =0.6 km (600 m).

To determine area we need to convert this perimeter to length and width. We know that it is a rectangle, with 2 equal widths and 2 equal lengths, and the length is twice the width.

So L = 2W

Perimeter = 2W + 2L

600 m = 2W + 2(2W)

600 m = 6W

W = 100 m

L = 200 m

Area = 100 X 200 = 20,000 m²

4 0
3 years ago
A certain school district has specified 5 different novels and 4 different non-fiction books from which teachers can choose to a
shutvik [7]

Answer:

There are 60 different summer reading lists possible.

Step-by-step explanation:

A certain school district has specified 5 different novels and 4 different non-fiction.

Each summer reading list must have exactly 3 novels and 2 non-fiction books.

So, the number of different summer reading lists that are possible is given by:

5C3\times 4C2

= \frac{5!}{3!2!} \times\frac{4!}{2!2!}

= 10\times6=60

Hence, there are 60 different summer reading lists possible.

5 0
4 years ago
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. Which customer wil
Gala2k [10]
Find the multiples of 25 and 60

25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300
60: 60, 120, 180, 240, 300
The 300th customer will recieve both gift cards
5 0
4 years ago
Please solve this question
777dan777 [17]
The first figure, on left, is the composition of two areas, the area of a 7cm circle and the area of a 7 cm square so:

A=7^2+7^2π/4

A=49+49π/4

A=49(1+π/4) cm^2

A≈87.48 cm^2  (to nearest hundredth of a square centimeter)

...

The second figure is the area of a 15cm by 8cm rectangle minus the area of a 3cm circle so:

A=15(8)-3^2π/4

A=120-9π/4

A=120-2.25π cm^2

A≈112.93 cm^2  (to nearest hundredth of a square centimeter)

4 0
4 years ago
Use the unit circle to find the value of tan 30
Harlamova29_29 [7]

Answer:

\frac{\sqrt{3}}{3}

Explanation:

\sin(30^{\circ}) = \frac{1 }{2 }

\cos(30^{\circ}) = \frac{\sqrt{3} }{2 }

\tan(30^{\circ}) = \frac{\text{opposite} }{\text{adjacent} }

\tan(30^{\circ}) = \frac{\frac{1 }{2 }} {\frac{\sqrt{3} }{ 2}}

\tan(30^{\circ}) = \frac{1 }{2 } \times{\frac{2}{\sqrt{3} }}

\tan(30^{\circ}) = \frac{1}{\sqrt{3}}

\tan(30^{\circ}) = \frac{\sqrt{3}}{3}

7 0
3 years ago
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