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Triss [41]
3 years ago
5

In ΔSTU, the measure of ∠U=90°, the measure of ∠S=84°, and ST = 87 feet. Find the length of TU to the nearest tenth of a foot.

Mathematics
1 answer:
Amanda [17]3 years ago
3 0

Answer:

TU=86.5 feet

Step-by-step explanation:

We are given with <U is 90 degrees. It means it is a right triangle.

So, we can use trigonometric ratio to solve.

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A business was valued at £80000 at the start of 2013. In 5 years the value of this business raised to £95000. this is equivalent
Yuri [45]

the yearly increase of x% assumes is compounding yearly, so let's use that.

~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\£95000\\ P=\textit{original amount deposited}\dotfill &\£80000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}

95000=80000\left(1+\frac{~~ \frac{r}{100}~~}{1}\right)^{1\cdot 5}\implies \cfrac{95000}{80000}=\left( 1+\cfrac{r}{100} \right)^5 \\\\\\ \cfrac{19}{16}=\left( 1+\cfrac{r}{100} \right)^5\implies \sqrt[5]{\cfrac{19}{16}}=1+\cfrac{r}{100}\implies \sqrt[5]{\cfrac{19}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[5]{\cfrac{19}{16}}=100+r\implies 100\sqrt[5]{\cfrac{19}{16}}-100=r\implies 3.5\approx r

4 0
2 years ago
Add 350 pounds to 4 tons.<br><br> 4,350 lb.<br> 8,350 lb.<br> 4.5 tons<br> 5 tons
levacccp [35]
8,350 lb.

1 ton = 2000 lbs, 2000 x 4 = 8000 + 350 lbs = 8,350 lbs
7 0
2 years ago
Write the sum of the numbers as the product of their GCF and another sum 64+28 PLEASE ANSWER QUICKLY
zepelin [54]

64 and 28 have a GCF of 4, since 64 = 4 x 16, 28 = 4 x 7, and 7 and 16 have no factors other than 1 in common. Knowing that, we can rewrite 64 + 28 as

4 x 16 + 4 x 7

and then use the distributive property to rewrite it again as

4 x (16 + 7)

5 0
3 years ago
Read 2 more answers
Explain the error in the work and how you might prevent it
Law Incorporation [45]

Answer:

The error is  -12x² - 14x = - 26x² because 12x² and 14x are unlike terms, so we can not add them

To prevent it the dividend must be written as 6x³ + 0x² - 14x + 1

Step-by-step explanation:

<em>In the division, you must arrange the dividend according to the greatest power of the variable, and put 0 as a coefficient of the missing term to avoid adding, unlike terms.</em>

<u>Example:</u>

If the dividend is 3x³ - 2x + 5, then you must write it as 3x³ + 0x² - 2x + 5

Let us solve our question

∵ The dividend is 6x³ + 1 - 14x

→ You must arrange it from the greatest power of x

∴ The dividend is 6x³ - 14x + 1

∵ The term of x² is missing

→ Write it in the dividend with a coefficient of 0

∴ The dividend is 6x³ + 0x² - 14x + 1

The error is the adding of unlike terms

∵ 6x³ - 14x + 1 ÷ 3x + 6 = 2x² and [6x³ - 14x + 1 - 6x³ - (6x³ + 12x²)]

∵ [6x³ - 14x + 1 - 6x³ - (6x³ + 12x²)] = 6x³ - 14x + 1 - 6x³ - 12x²

∵ 6x³ - 14x + 1 - 6x³ - 12x² = 0 - 12x² - 14x + 1

∵ 0 - 12x² - 14x + 1 = -26x² + 1 ⇒ error

∴ The error is  -12x² - 14x = - 26x² because 12x² and 14x are unlike terms,

   so we can not add them

→ To prevent it, write 0 as a coefficient of the missing term

∵ The missing term is the term of x²

∴ Add to the dividend the term 0x²

∴ The dividend must be written as 6x³ + 0x² - 14x + 1

4 0
2 years ago
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When evaluating (6x+9)2-5for x=1
hjlf

Answer:

25

Step-by-step explanation:

(6x + 9)2 - 5

x = 1

(6 + 9)2 - 5

(15)2 - 5

30 - 5

25

Hope this helps!

8 0
3 years ago
Read 2 more answers
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