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Feliz [49]
2 years ago
15

suppose you have $55 in your bank account. You start saving $10 each week. Your friend has $20 in her account and is saving $15

each week. When will you and your friend have the same amount of money in your accounts?
Mathematics
1 answer:
zhenek [66]2 years ago
7 0
The equation is:
55 + 10 x = 20 + 15 x, where x is number of the weeks.
55 - 20 = 15 x - 5 x
35 = 5 x
x = 35 : 5
x = 7
Answer:
The same amount of money in both accounts will be after 7 weeks.
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How would I find a? What formula would I use?
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Answer:

  You can use either of the following to find "a":

  • Pythagorean theorem
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Step-by-step explanation:

It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.

I find it reasonably convenient to find the length of x using the sine of the 70° angle:

  x = (15 ft)/sin(70°)

  x ≈ 15.96 ft

That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.

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Consider the diagram below. The relation between DE and AE can be written as ...

  DE/AE = tan(70°)

  AE = DE/tan(70°) = DE·tan(20°)

  AE = 15·tan(20°) ≈ 5.459554

Then the length EC is ...

  EC = AC - AE

  EC = 6.3 - DE·tan(20°) ≈ 0.840446

Now, we can find DC using the Pythagorean theorem:

  DC² = DE² + EC²

  DC = √(15² +0.840446²) ≈ 15.023527

  a ≈ 15.02 ft

_____

You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)

  DC² = AD² + AC² - 2·AD·AC·cos(A)

  a² = x² +6.3² -2·6.3x·cos(70°) ≈ 225.70635

  a = √225.70635 ≈ 15.0235 . . . feet

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3 years ago
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guajiro [1.7K]

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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