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Gnoma [55]
2 years ago
6

The sale tax rate in Brads town is 4.25%. If he buys 3 lamps for 22.49 each and a sofa for 829.99, how much sales tax does he ow

e?
Mathematics
1 answer:
eimsori [14]2 years ago
5 0
Brad should owe $38.16 in taxes, but his total should be $935.96
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Why is ti that when you add two numbers together (5+5,6+6,3+3, etc.) you get an even sum?? I need this for my 8 year-old-brother
astra-53 [7]

Essentially, the rule goes as so: odd + odd = even, even + even = even.

Although that may not be the answer you're looking for, it is a math rule that is never debunked and essentially the premises for why you get an even sum practically always depending on the numbers.

Hope this helps!

3 0
3 years ago
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Find all the complex roots. Write the answer in exponential form.
dezoksy [38]

We have to calculate the fourth roots of this complex number:

z=9+9\sqrt[]{3}i

We start by writing this number in exponential form:

\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}

Then, the exponential form is:

z=18e^{\frac{\pi}{3}i}

The formula for the roots of a complex number can be written (in polar form) as:

z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})

We can now calculate for each value of k:

\begin{gathered} k=0\colon \\ z_0=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{0}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{0}{2}))) \\ z_0=\sqrt[4]{18}\cdot(\cos (\frac{\pi}{8})+i\cdot\sin (\frac{\pi}{8}) \\ z_0=\sqrt[4]{18}\cdot e^{i\frac{\pi}{8}} \end{gathered}\begin{gathered} k=1\colon \\ z_1=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{1}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{1}{2}))) \\ z_1=\sqrt[4]{18}\cdot(\cos (\frac{5\pi}{8})+i\cdot\sin (\frac{5\pi}{8})) \\ z_1=\sqrt[4]{18}e^{i\frac{5\pi}{8}} \end{gathered}\begin{gathered} k=2\colon \\ z_2=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{2}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{2}{2}))) \\ z_2=\sqrt[4]{18}\cdot(\cos (\frac{9\pi}{8})+i\cdot\sin (\frac{9\pi}{8})) \\ z_2=\sqrt[4]{18}e^{i\frac{9\pi}{8}} \end{gathered}\begin{gathered} k=3\colon \\ z_3=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{3}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{3}{2}))) \\ z_3=\sqrt[4]{18}\cdot(\cos (\frac{13\pi}{8})+i\cdot\sin (\frac{13\pi}{8})) \\ z_3=\sqrt[4]{18}e^{i\frac{13\pi}{8}} \end{gathered}

Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

5 0
1 year ago
64 POINTS AWARDED, PLEASE ANSWER ASAP!!!!!
antoniya [11.8K]

Answer:

Area of rectangle = 40 square units

Step-by-step explanation:

<u>Points to remember</u>

<u>Distance formula</u>

Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Area of rectangle = Length * Breadth

<u>To find the length and breadth</u>

Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)

Length1 =  √[(x₂ - x₁)² + (y₂ - y₁)²]

√[(12 - 7)² + (3 - 3)²] = √5² = 5

Length2 =  √[(x₂ - x₁)² + (y₂ - y₁)²]

√[(12 - 12)² + (11 - 3)²] = √8² = 8 units

Therefore Length of rectangle = 8 and  

Breadth of rectangle = 5 units

<u>To find the area of rectangle</u>

Area = Length * Breadth

  = 8 * 5 =  40 square units

8 0
3 years ago
Read 2 more answers
Triangle FGH is similar to triangle IJK. Find the measure of side KI. Round your
erastovalidia [21]

Answer:

5.8

Step-by-step explanation:

Similar shapes also maintain a constant proportion of sides. Therefore, we can set up the following equation:

\frac{31}{43}=\frac{\text{KI}}{8}

Solving, we get:

\text{KI}=\frac{8\cdot 31}{43}\approx \boxed{5.8}

5 0
3 years ago
Can someone help me with this I’m very confused
shepuryov [24]

Answer:

is this a question meant to evaluate you, such as a test, exam, quiz, or assessment?

5 0
3 years ago
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