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iren [92.7K]
3 years ago
7

A rectangular yard is X feet wide. The yard is 4 feet longer than it is wide. The perimeter P of yard is given by the equation P

= 4x + 8. If the perimeter of the yard is 84 feet how long is the yard?
A. 19 feet
B. 23 feet
C. 24 feet
D. 28 feet
Mathematics
1 answer:
vladimir2022 [97]3 years ago
6 0

Given:

Width of the rectangular yard = x feet

Length of the rectangular yard = x+4 feet

Perimeter of the rectangular yard is:

P=4x+8

Perimeter of the yard = 84 feet

To find:

The length of the rectangular yard.

Solution:

Perimeter of the yard is 84 feet.

4x+8=84

4x=84-8

4x=76

Divide both sides by 4.

x=\dfrac{76}{4}

x=19

So, the width of the rectangular yard is 19 feet.

Length = 19+4

Length = 23

The length of the rectangular field is 23 feet.

Therefore, the correct option is B.

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In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta
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Answer:

See explanation

Step-by-step explanation:

Let x,\ x\ge 0 be the number of students and y,\ y\ge 0 be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

The charity show is conducted in order to raise at least $3,750, thus

15x+25y\ge 3,750

2. The auditorium can accommodate up to 180 spectators, hence

x+y\le 180

3. We get the system of inequalities:

\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise \$(15\cdot 50+25\cdot 125)=\$3,875

8 0
3 years ago
I really need help with this ?
quester [9]

Answer:

Answer=44

Step-by-step explanation:

Rectangle: 6x4=24.

Triangle: 4x4=16, and 16/2=8.

Semicircle: Pi x radius squared, so pi x 2 squared is 16.something, and since it's a semicircle, we divide by 2, so it's 8 again.

Overall: 24+8+8=44 cm squared.

3 0
3 years ago
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3 years ago
What number could replace kkk below? \dfrac{k}{100} = \dfrac{1}{10} 100 k ​ = 10 1 ​ start fraction, k, divided by, 100, end fra
Ivanshal [37]

Answer:

<h3>k = 10</h3>

Step-by-step explanation:

Given the equation;

\dfrac{k}{100} = \dfrac{1}{10}

We are to find the value of k.

Cross multiply;

\dfrac{k}{100} = \dfrac{1}{10} \\10 \times k = 100 \times 1\\10k = 100\\

Divide both sides by 10

10k/10 = 100/10\\k = 10

Hence the value of k is 10

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2 years ago
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