Since one piece is four time the length <em>x, </em>we can represent that as 4x.
Thus making the equation:
4x+x=275
5x=275
x=55
4(55)=220
220+55=275
So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.
Greetings.
The answer is x = -2.
Explanation:
By solving the Absolute-Value Equation. We give them 2 conditions.
<em>When x ≥ 0 and When x < 0</em>
<em>The different is that When x ≥ 0, |x-a| = x-a as defined.</em>
<em>And when x < 0. |x-a| = -x+a as defined.</em>
( 1 ) - When x ≥ 0 for |x-1| and |x+5|
When x ≥ 0, |x-1| = x-1 and |x+5| = x+5
Therefore, x-1 = x+5

Because the equation is false. Therefore, The condition (1) doesn't apply.
( 2 ) - When x ≥ 0 for |x-1| and x < 0 for |x+5|
This time, we try another condition.
When x ≥ 0, |x-1| = x-1 and When x < 0, |x+5| = -x-5.

And we get the answer, |x-1| = |x+5| when x = -2.
But we haven't tried the last condition.
( 3 ) And that is when x < 0 for both terms.
|x-1| = -x+1 (x < 0)
|x+5| = -x-5 (x < 0)

The equation is not true. Therefore, the answer is x = -2.
Complete question is;
Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )
( k )
Answer:
I've been able to prove that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Step-by-step explanation:
I've attached the proof that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Answer:
$466
Step-by-step explanation:
Represent her salary by s. Then the amount spent on rent is s/2.
After spending 168 on her electric and water bills, she had s/2 - 168 dollars left. She spent half of this on her phone bill, leaving her with
s/2 - 168
-------------- dollars.
2
After buying $57 worth of gas, she had
s/2 - 168
-------------- - 57 dollars left, and this came to $92.
2
We must now solve for s.
First, multiply all three terms by 2. We get
s/2 - 168 - 2(57) = 2(92), or
s/2 - 168 - 114 = 184
Simplifying this, we get s/2 = 168 + 114 + 184, or s/2 = 466.
She spent half her salary (that is, half of s) on rent. As seen above, this is $466.