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Fofino [41]
3 years ago
13

Rectangle with a length of 96 inches and width of 60 inches. A rug maker wants to increase each dimension by a different amount.

Let e and w be increases in inch of length and width. Write a simplified expression
Mathematics
1 answer:
mr Goodwill [35]3 years ago
7 0

Answer:

The perimeter of the new rectangle in simplified expression can be given as:

2l+2w+312

Step-by-step explanation:

The question is incomplete.

The actual question should be:

A rug maker is using a patter that is a rectangle with a length of 96 inches and a width of 60 inches. The rug maker wants to increase each dimension by a different amount. Let l and w be the increases in inches of the length and width. write and simplify an expression for the perimeter of the new pattern.

Solution:

Original length of the rectangular pattern = 96 inches

Original width of the rectangular pattern = 60 inches

Let increase in length be = l inches

New length of rectangle = (96+l) inches

Let increase in width be = w inches

New width of rectangle = (60+w) inches

The perimeter of a rectangle is given by :

⇒ 2(length+width)

Substituting the new length and width of the triangle.

⇒ 2(96+l+60+w)

Simplifying.

⇒ 2(l+w+156)

Using distribution.

⇒ 2l+2w+312

Thus, the perimeter of the new rectangle in simplified expression can be given as:

2l+2w+312

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Find the value of x such that 365 based seven + 43 based x = 217 based 10.
Pepsi [2]

We need to find the base x in the following equation:

365_7+43_x=217_{10}

First, lets convert 365 from base 7 to base 10. This is given by

365_7=3\times7^2+6\times7^1+5\times7^0

where the upperindex denotes the position of eah number. This gives

\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}

that is, 365 based 7 is equal to 194 bases 10.

Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

43_x=4\times x^1+3\times x^0

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

43_x=(4x+3)_{10}

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

194_{10}+(4x+3)_{10}=217_{10}

For simplicity, we can omit the 10 and get

194+4x+3=217

so, we can solve this equation for x. By combining similar terms. we have

197+4x=217

and by moving 197 to the right hand side, we obtain

\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}

Finally, we get

\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}

Therefore, the solution is x=5

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