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ss7ja [257]
3 years ago
15

The area of a rectangle is represented with the expression (18x-12) inches squared. The width of the rectangle is 6 inches. Writ

e an expression that represents the length of the rectangle.
Mathematics
1 answer:
Rudik [331]3 years ago
5 0
Are equation for a rectangle is area = (width x length)

(18x - 12) = 6 x length
length = (18x - 12) / 6
length = 3x - 2
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Volume of a rectangular prism is length * width * height. 

The figure can be broken into 3 different prisms. Left to right, I'd label them 1st tower, connecting base, 2nd tower. 

I'll do the 2nd tower first since it has the most measurements. 5 * 5 * 12 = 25 * 12 = 300

The first and second towers are congruent so they have the same measurements; we just do 300 + 300 to find their volumes. It's 600. 

Now, to find the connecting piece. The whole bottom length of this "U" shaped figure is 18 but the two towers have lengths of 5. To find the base of the portion we're looking for, we do 18 - 2(5) = 18 - 10 = 8. To find the height, we take away the top part of the second tower (7 m) from the whole height (12 m). 12 - 7 = 5. The width is given by the towers so we have what we need to solve. 

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4 years ago
North shore community college reimburses faculty members $.298 cents per mile to go to a workshop. professor wells submitted her
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3 years ago
what will be the total paid on an amortized loan of $15,000 for 5 years at 2 3/4% compounded monthly?
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the loan is being amortized, so that doesn't matter for its future value, the simple case that the borrower is paying it in bits monthly.

so, we're really just looking for the future value of the Principal $15000, let's convert theat mixed fraction to improper fraction, and then to a percent format firstly.


\bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}\implies \stackrel{decimal}{2.75} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt}


\bf \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$15000\\ r=rate\to 2.75\%\to \frac{2.75}{100}\dotfill &0.0275\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0275}{12}\right)^{12\cdot 5}\implies A=15000\left( \frac{4811}{4800} \right)^{60}\implies A\approx 17208.318305


how did we get 4811/4800?   well, is really just the 1+(0.0275/12), which gives us about 1.0022917 but is a repeating decimal, so 4811/4800 is just the fraction version of it.

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i can't tell you the answer, but i will teach you how to get it!!

first you convert it to a fraction, then you make it a decimal divide the top number by the bottom number, then you move the decimal two places to the right --> and add a percent symbol %

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