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docker41 [41]
3 years ago
10

A pack of cinnamon scented pencils sells for $4.00. What is the sales tax rate of the total cost of the pencils is $4.32

Mathematics
1 answer:
Naddika [18.5K]3 years ago
4 0
To get the answer we can use proportion. We know that 4$ its 100% and 4.32 its 100% + taxes.
4$ ---------- 100%
4.32 -------- x
crossmultiply now
4x=4.32*100%
4x=432%     /:4
x=108%
We know that 4.32 its 100% + taxes=108% so to get taxes we have to subtract 108-100.
108%-100%=8% - its the answer.
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What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?​
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Answer:

The roots are

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Step-by-step explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

<h3>x =  \frac{ - b\pm \sqrt{ {b}^{2}  - 4ac} }{2a}</h3>

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

<h3>x =  \frac{ - 54\pm \sqrt{ {54}^{2}  - 4(9)(82)} }{2(9)}  \\ x =  \frac{ - 54\pm \sqrt{2916 - 2952} }{18}  \\ x =  \frac{ - 54\pm \sqrt{ - 36} }{18}  \\ x =  \frac{ - 54\pm 6i}{18}</h3>

Separate the real and imaginary parts

That's

<h3>x =  -  \frac{54}{18} \pm \frac{6}{18}  \: i \\ x =  - 3\pm \frac{1}{3} i</h3>

We have the final answer as

<h3>x =  - 3 +  \frac{1}{3}  i \:  \:  \: or \:  \:  \: x =  - 3 -  \frac{1}{3} i \\</h3>

Hope this helps you

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