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ahrayia [7]
3 years ago
8

The dimensions of a square are altered so that 8inches is added to one side while 3 inches is subtracted from the other. The are

a of the resulting rectangle is 126in^2 .What was the original side length of the square?
Mathematics
1 answer:
OlgaM077 [116]3 years ago
7 0
Let s original sides, l length, w width:

s+8=l

s-3=w

lw= 126in²

substitute:

(s+8)(s-3)=126

s²+5s-24=126

s²+5x-150=0

(s-10)(s+15)

s=10

each side is 10 inches


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Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8
vredina [299]

Question:

Consider the sequence of numbers: \frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + \frac{3}{8}  .

Explanation:

A sequence of numbers are

\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}

Let us first change mixed fraction into improper fraction.

\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}

\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}

\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}

\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding \frac{3}{8} to the previous term.

Hence, the sequence is recursive and can be represented by the function f(n + 1) = f(n) + \frac{3}{8}  .

3 0
3 years ago
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