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Elis [28]
3 years ago
6

A box of nails weighs 130 pounds when it is 2/3 full. It weighs 74 pounds when it is 3/8 full. What is the weight of the box?

Mathematics
1 answer:
NeTakaya3 years ago
7 0
Let the weight of the full Volume of nails in the box be W.
Let the weight of the box be B.

2/3 W  + B =  130 ........i          From the first statement.
3/8 W  + B =      74 ......ii         From the second statement.

Equation (i)  Minus (ii)

2/3 W  - 3/8 W + B  - B =  130 - 74
(16W  - 9W) / 24                 = 56

7W / 24  =  56.
W        =  56 * 24 / 7
W        =    192  Pounds.

Substituting V = 64 in equation (i)
2/3 W  + B =  130
2/3 * 192  + B =  130
2 * 64  + B =  130
128  + B =  130
B =  130 -128 = 2.

Therefore, weight of box, B = 2 pounds.

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a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side m
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Answer:

The measure of the shortest side is 851 miles

Step-by-step explanation:

Let

x ----> the measure of the shortest side

y ---> the measure of the middle side

z ---> the measure of the longest side

we know that

The perimeter of triangle is equal to

P=x+y+z

P=3,067\ mi

so

3,067=x+y+z ----> equation A

the shortest side measures 71 mi less than the middle side

so

x=y-71 ----> equation B

the longest side measures 372 mi more the the middle side

so

z=y+372 ----> equation C

substitute equation B and equation C in equation A

3,067=(y-71)+y+(y+372)

solve for y

3,067=3y+301\\3y=2,766\\y=922

Find the value of x

x=y-71\\x=922-71\\x=851

therefore

The measure of the shortest side is 851 miles

6 0
3 years ago
What does 2 3/5 divided by 1 1/25 equal
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2 x 5 = 10 + 3 = 13

So 13/5 / 11/25.

Keep, change, flip rule: 13/5 x 25/11.

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Y_Kistochka [10]
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Solving Rational Inequalities and use sign diagram to sketch the graph. Image attached for better understanding.
Digiron [165]

Answer:

x ∈ (-∞, -1) ∪ (1, ∞)

Step-by-step explanation:

To solve this problem we must factor the expression that is shown in the denominator of the inequality.

So, we have:

x ^ 2-1 = 0\\x ^ 2 = 1

So the roots are:

x = 1\\x = -1

Therefore we can write the expression in the following way:

x ^ 2-1 = (x-1)(x + 1)

Now the expression is as follows:

\frac{(x-2) ^ 2}{(x-1) (x + 1)}\geq0

Now we use the study of signs to solve this inequality.

We have 3 roots for the polynomials that make up the expression:

x = 1\\x = -1\\x = 2

We know that the first two are not allowed because they make the denominator zero.

Observe the attached image.

Note that:

(x-1)\geq0 when x\geq-1

(x + 1)\geq0 when x\geq1

and

(x-2) ^ 2 is always \geq0

Finally after the study of signs we can reach the conclusion that:

x ∈ (-∞, -1) ∪ (1, 2] ∪ [2, ∞)

This is the same as

x ∈ (-∞, -1) ∪ (1, ∞)

6 0
3 years ago
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