At noon, a block of ice was taken

The perimeter of a rectangle is equal to 163 yard. The width is 8 more than twice the length. Find the length and width.

Sedaia [141]

Answer:

l = 29.4 yards

w = 66.8 yards

General Formulas and Concepts:

Order of Operations: BPEMDAS
Perimeter of a Rectangle: P = 2w + 2l

Step-by-step explanation:

Step 1: Define

P = 163 yards

w = 2l + 8

l = l

Step 2: Set up equation

P = 2w + 2l

163 = 2(2l + 8) + l

Step 3: Solve for l

Distribute 2: 163 = 4l + 16 + l
Combine like terms: 163 = 5l + 16
Subtract 16 on both sides: 147 = 5l
Divide both sides by 5: 147/5 = l
Rewrite: l = 147/5
Evaluate: l = 29.4 yards

Step 4: Find w

Define: w = 2l + 8
Substitute: w = 2(29.4) + 8
Multiply: w = 58.8 + 8
Add: w = 66.8 yards

4 0

3 years ago

Can someone give me the answers and step by step instructions please??

professor190 [17]

Answer:

$-1,4,-7,10,...$ neither

$192,24,3,\frac{3}{8},...$ geometric progression

$-25,-18,-11,-4,...$ arithmetic progression

Step-by-step explanation:

Given:

sequences: $-1,4,-7,10,...$

$192,24,3,\frac{3}{8},...$

$-25,-18,-11,-4,...$

To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For $-1,4,-7,10,...$ :

$4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)$

Hence,the given sequence does not form an arithmetic progression.

$\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}$

Hence,the given sequence does not form a geometric progression.

So, $-1,4,-7,10,...$ is neither an arithmetic progression nor a geometric progression.

For $192,24,3,\frac{3}{8},...$ :

$\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}$

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For $-25,-18,-11,-4,...$ :

$-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)$

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

3 0

3 years ago

If the side of a square is 3/4 feet, what is the area of the square

yuradex [85]

$\text{Area of square}=~ \text{Side}^2\\\\~~~~~~~~~~~~~~~~~~~~~=\left(\dfrac 34 \right)^2\\\\~~~~~~~~~~~~~~~~~~~~~=\dfrac{9}{16}~ \text{ft}^2$

6 0

2 years ago

Read 2 more answers

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 3x-2y=7 equati

svetlana [45]

Answer:

x = 31/9 and y = 5/3

Step-by-step explanation:

It is given that,

3x - 2y = 7 -----(1)

3x + 4y = 17 ----(2)

To find the solution by elimination method

Step 1: Subtract eq(2) from eq(1)

3x - 2y = 7 -----(1)

3x + 4y = 17 ----(2)

0 - 6y = -10

6y = 10

y = 10/6 = 5/3

Step 2: Substitute the value of y in eq (1)

3x - 2y = 7 -----(1)

3x - 2*(5/3) = 7

3x = 7 + 10/3

3x = 31/3

x = 31/9

Therefore x = 31/9 and y = 5/3

5 0

3 years ago

Read 2 more answers

At the local pet store, zebra fish cost $2.00 each and neon tetras cost $2.15 each. If Ernesto bought 15 fish for a total cost o

bezimeni [28]

So first create and define your variables:
Z = amount of zebra fish
N = amount of neon tetras

Now create your equations:
2z+2.15n=31.20
z+n=15
This is your system. There are multiple methods to use but in this problem I’ll use the substitution method by simplifying the bottom equation.
2z+2.15n=31.20
z=15-n
Now I’ll plug the bottom equation into the top one.
2(15-n)+2.15n=31.20
And just solve from here.
30-2n+2.15n=31.20
0.15n=1.20
n=8
So he bout 8 neon tetras, and 15-8= 7, so he bought 7 zebra fish

6 0

2 years ago

Read 2 more answers