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KatRina [158]
3 years ago
7

Evaluate the expression for h=-54. |h| + 30=

Mathematics
1 answer:
insens350 [35]3 years ago
3 0

1. Observe problem

2. Plug in values

|-54|+30=

54+30=

84

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<h3>Answer: C) ASA Theorem</h3>

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Explanation:

Let's go through the answer choices one at a time.

  • A) The AA postulate is only used for similar triangles, and not congruent triangles. We need information about at least one pair of sides. Using the angles only isn't enough. We can rule out choice A.
  • B) The HL postulate only applies to right triangles. These triangles are acute triangles, so we can rule out choice B.
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3 years ago
Sara invests $1,200 each year in an IRA ( 12 years in an account that earned 5%
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A)

\bf \qquad \qquad \textit{Future Value of an ordinary annuity}&#10;\\\\&#10;A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]&#10;\\\\

\bf \begin{cases}&#10;A=&#10;\begin{array}{llll}&#10;\textit{original amount}\\&#10;\textit{already compounded}&#10;\end{array}&#10;\begin{array}{llll}&#10;&#10;\end{array}\\&#10;pymnt=\textit{periodic deposits}\to &1200\\&#10;r=rate\to 5\%\to \frac{5}{100}\to &0.05\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{each year, once}&#10;\end{array}\to &1\\&#10;&#10;t=years\to &12&#10;\end{cases}

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let's say after 12years, she ended up with a value of say "P"
so.. now she's just sitting on P, making no more deposits to it
just taking whatever the compound 5% interest will give, thus

\bf \qquad \textit{Compound Interest Earned Amount}&#10;\\\\&#10;A=P\left(1+\frac{r}{n}\right)^{nt}&#10;\qquad &#10;\begin{cases}&#10;A=\textit{compounded amount}\\&#10;P=\textit{original amount deposited}\to &\boxed{P}\\&#10;r=rate\to 5\%\to \frac{5}{100}\to &0.05\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{again, is only once}&#10;\end{array}\to &1\\&#10;&#10;t=years\to &11&#10;\end{cases}


C)

from A) she made 1,200 every year, for 12 years that's 1200*12, that's how much she put out of pocket, if you got an amount P from A), then the interest is just the difference, or P - (1200*12)

from B), she started with an original amount of P, and ended up with a compounded amount of A after 11years, so the interest is just also the difference, or A - P

add those two folks together, and that's the total interest she got for the 23  years



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Answer:

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\sqrt{16}  = 4

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