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GaryK [48]
3 years ago
6

A store is having a sale in which all items are discounted 20%. Including tax , Jennifer paid $21 for a picture. if the sales ta

x rate is 5% what is the original price for the picture?
Mathematics
1 answer:
hammer [34]3 years ago
5 0
Original price is $25. Hope this helps :D
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20 points and brainliest <br> I’m in quiz in need it asap <br> Number 4
iren [92.7K]

Answer and step-by-step explanation:

The polar form of a complex number a+ib is the number re^{i\theta} where r = \sqrt{a^2+b^2} is called the modulus and \theta = tan^-^1 (\frac ba) is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.

(a) let's first calculate moduli and arguments

r_1 = \sqrt{(-2\sqrt3)^2+2^2}=\sqrt{12+4} = 4\\ \theta_1 = tan^-^1(\frac{2}{-2\sqrt3}) =-\pi/6\\r_2=\sqrt{1^2+1^2}=\sqrt2\\ \theta_2 = tan^-^1(\frac 11)= \pi/4

now we can write the two numbers as

z_1=4e^{-i\frac \pi6}; z_2=e^{i\frac\pi4}

(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:

Arg(z_1\cdot z_2) = Arg(z_1)+Arg(z_2) = -\frac \pi6 + \frac \pi4 = \frac\pi{12}

(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.

(z_1)^1^2=[4e^{-i\frac \pi6}]^1^2=4^1^2\cdot (e^{-i\frac \pi6})^1^2=2^2^4\cdot e^{-i(12)\frac\pi6}\\=2^2^4 e^{-i\cdot2\pi}=2^2^4

Now, in the last step I've used the fact that e^{i(2k\pi+x)} = e^i^x ; k\in \mathbb Z, or in other words, the complex exponential is periodic with 2\pi as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.

7 0
2 years ago
10p-2(3p-6)=4(3p-6)-8p
lisabon 2012 [21]

Answer:

undefined / no solution

Step-by-step explanation:

10p - 2(3p-6) = 4(3p-6) - 8p

10p - 6p - 12 = 12p - 24 - 8p

4p - 12 = 4p - 24

0 = -12

0 cannot equal -12

4 0
2 years ago
Which interval notation represents the set of all numbers less than or equal to -6 or greater than or equal to -2
Alik [6]

Answer: 1≤x<12

Step-by-step explanation:

The values that are greater than or equal 1 but less than 12 are values ranging from 1 to 11 i.e {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Note that 1 is included because the number is greater than or equal to 1 (1 included) and less than 12(12 not included).

x≥1 and x< 12

if x≥1, it means 1≤x

combining both inequality

1≤x and x<12

1≤x<12

The interval notation that represent the set S =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} will be given as S = {x: 1≤x<12}

5 0
2 years ago
The table shows values of a function. What is the average rate of change of over the interval from x = 5 to x = 9? Show your wor
Allushta [10]

\frac{f(9) - f(5)}{9 - 5}  \\  =  \frac{14 - ( - 2)}{4}  \\  =  \frac{16}{4}  \\  = 4

Hope this helps. - M
3 0
3 years ago
Please help me on this
Marizza181 [45]

Answer:    m=2.8

Step-by-step explanation:

You can reverse the equation and instead solve...

4-1.2 which equals 2.8.

  • m=2.4  
8 0
3 years ago
Read 2 more answers
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