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goblinko [34]
3 years ago
7

Last year alvina contributed 85$ per month toward her 401k account if her employer matched 20% of her contributions, what was th

e total amount contributed to the 401 k at the end of the year?
Mathematics
1 answer:
julsineya [31]3 years ago
3 0
So, first let's solve for the total amount that Alvina contributed to her 401k account, by multiplying the amount contributed per month ($85) times the number of months (12):
85*12=1020
So, Alvina contributed $1020 to her 401k account.

Her employer contributed 20% of that, which we can find by multiplying the amount Alvina contributed by .2:
1020*.2=204
So we know that Alvina's employer contributed $204 to her 401k account.

We can add these two numbers to get the total:
1020+204=1224
And that's our final answer of $1224 total contributed to the account!

Hope I helped, and let me know if you have any questions! :)
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Explanation:

Let the height of the tree be x. The tree casts a shadow of x-49 meters and the distance from the top of the tree to the end of the shadow is x+1 meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

x^{2}+(x-49)^{2}=(x+1)^{2}

Expanding, we get,

2 x^{2}-98 x+2401=x^{2}+2 x+1

2 x^{2}-98 x+2400=x^{2}+2 x

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x^{2}-100 x+2400=0

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x=\frac{100\pm\sqrt{10000-9600}}{2}

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Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

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