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sveticcg [70]
3 years ago
8

A water tank holds 944 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,180 gallons but is le

aking at a rate of 9 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Mathematics
1 answer:
podryga [215]3 years ago
8 0

Answer:

59

Step-by-step explanation:

The equation is

944 - 5x = 1180 - 9x

Notice what is being said. You start with 944 gallons and take off 5 per week

You also start with 1180 gallons and take on 9 per week.

You want to know when the two are equal. The second tank is larger, but it leaks more. That's what's going to bring about equality.

Add 9x to both sides

944 - 5x + 9x = 1180

944 + 4x = 1180                

Subtract 944 from both sides.

4x = 1180 - 944

4x = 236      

Divide by 4

x = 236/4

x = 59 weeks

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How many triangles can be constructed with side lengths of 9.6 cm, 11.6 cm, and 21.2 cm?
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Answer:  A) 0 triangles

============================================================

Explanation:

Adding up the two smaller sides gets us 9.6+11.6 = 21.2, but this result is not larger than the third side of 21.2

For a triangle to be possible, we need to be able to add any two sides and have the sum be larger than the third remaining side. This is the triangle inequality theorem.

I recommend you cutting out slips of paper with these side lengths and trying it out yourself. You'll find that a triangle cannot be formed. The 9.6 cm and the 11.6 cm sides will combine to form a straight line that is 21.2 cm, but a triangle won't form.

As another example of a triangle that can't be formed is a triangle with sides of 3 cm, 5 cm, and 8 cm. The 3 and 5 cm sides add to 3+5 = 8 cm, but this does not exceed the third side. The best we can do is form a straight line but that's not a triangle.

In short, zero triangles can be formed with the given side lengths of 9.6 cm, 11.6 cm, and 21.2 cm

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