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4 years ago

A 275 inch pipe is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.

Mathematics

1 answer:

Darina [25.2K]4 years ago

3 0

Since one piece is four time the length x, 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.

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Step-by-step explanation:

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3 years ago

If a > b > c > d, then which is larger, a+c or b+d ? Can we tell from a > b > c > d which of a+d and b+c is la

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Answer:

1. a+c is larger than b+d

2. No way to tell whether a+d or b+c is larger.

Step-by-step explanation:

1. Which is larger, a+c or b+d?

Let a, b, c, and d be any numbers such that $a > b > c > d$ .

Specifically, note that $a > b$ , and subtracting b from both sides of the inequality, observe that $a-b > 0$ .

Similarly, $c > d$ , and subtracting d from both sides of the inequality, observe that $c-d > 0$ .

From this, add "a-b" (a positive number, as proven above) to both sides of the inequality.

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Addition by zero (the additive identity) doesn't change anything, so the right side remains "a-b"...

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... and "a-b" is positive...

$(a-b)+(c-d) > a-b > 0$

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Recall that subtraction is addition by a negative number...
$a+(-b)+c+(-d) > 0$

...and that addition is associative and commutative, so things can be added in any order, so the middle two terms on the left side can be rearranged...

$a+c+(-b)+(-d) > 0$

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2. Which is larger, a+d or b+c?

Consider the following two examples:

Example 1

Suppose a=10; b=3; c=2; d=1.

Note that $a > b > c > d$ ( $10 > 3 > 2 > 1$ ) and, also observe that $a+d=(10)+(1)=11$ , and $b+c=(3)+(2)=5$ , so a+d is larger than b+c.

Example 2

However, suppose a=10; b=9; c=8; d=1.

Note that $a > b > c > d$ ( $10 > 9 > 8 > 1$ ) but that $a+d=(10)+(1)=11$ , and $b+c=(9)+(8)=17$ , so a+d is smaller than b+c.

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Answer:

Step-by-step explanation:

just think about it :

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which is

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in the same way

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