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-Dominant- [34]
3 years ago
5

If 5 potatoes together have a mass of 1 kilometer and 8 pears together have a mass of 1,200 grams, which has the greater mass a

potato or a pear? Explain.
Mathematics
1 answer:
saul85 [17]3 years ago
3 0

____________________________________________________

Answer:

The Potato has a greater mass.

____________________________________________________

Step-by-step explanation:

In order to see which one of them has the greater mass, we're going to need to figure out how much one of them weigh.

Lets get the key information from the question:

5 potatoes = 1 kilograms (kg)

8 pears = 1,200 grams (g)

With the information above, we can solve the problem.

1 Kilogram = 1000 grams

With that information, we know that 5 potatoes would equal 1000 grams, now we would need to divide 1000 by 5 to get the grams for one potato in order to find the mass of it.

1000 \div 5=200

<u>1 Potato = 200 grams</u>

Now, we would need to divide 1,200 by 8 to find the mass of 1 pear.

1200 \div 8=150

<u>1 Pear = 150 grams</u>

With the information we have now, we would know that the Potato has the greater mass than the pear.

A potato has a greater mass.

____________________________________________________

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Note that it is impossible to have:

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A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is
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Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

∵ The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

∴ The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

∴ 4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

∴ x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

∴ (x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

∴ x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

∴ The width of the is 4 inches

7 0
2 years ago
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