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3 years ago

If 5y + 3 = 2y + 9 then find 2y=

Mathematics

1 answer:

Serhud [2]3 years ago

5 0

If you were to solve for y, it would be 2. Therefore 2y would be 4.

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A market researcher conducts a survey of residents in three neighborhoods. The residents are asked whether they prefer ice cream

Naya [18.7K]

Answer: what’s the answer

Step-by-step explanation:

3 0

3 years ago

Merry Soy, married, earns a weekly salary of $830 and claims one withholding allowance. By the percentage method, how much incom

xxMikexx [17]

You need to find the amount subject to withholding, subtracting from the weekly salary the amount for one withholding allowance for weekly salaries, which is 77.90$:

830 - 77.90 = 752.1 $.

Then, look in the Fed Tax tables (
http://www.opers.ok.gov/Websites/opers/images/pdfs/2016-Fed-Tax-Tables.pdf ) for a married person with a weekly payroll.

You previously found an amount of 752.1 which is greater than 521 but less than 1613$: therefore the income tax to withhold is 35.70$ + 15% of excess over $521.

Therefore, calculate the income tax due: 35.70 + (752.1 - 521) × 15 ÷ 100 = 70.37$

The total amount of income tax that will be withheld is 70.37$

4 0

2 years ago

If you drive three cars from a regular deck of 52 cards for keeping each card out of the deck after you drive what are the chanc

Andreyy89

Chance to draw 7: 4 out of 52
chance to draw 1st queen: 4 out of 51
chance to draw 2nd queen: 3 out of 50
total chance = multiplication of
$\frac{4}{52}$ times $\frac{4}{51}$ times $\frac{3}{50}$

$\frac{2}{5525}$

pretty miserable change... apox 1 out of 2762, but still much better than any lottery ticket

6 0

2 years ago

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

Which point lies on the graph of Y= 4x-4<br> 1.(0,4)<br> 2.(0,-4)<br> 3.(-4,0)<br> 4.(4,0)

statuscvo [17]

Answer:

Step-by-step explanation:

$y=4x-4\\\\\text{Substitute the coordinates of each points to the equation}\\\text{and check the equality.}\\\\1.\ (0,\ 4)\to x=0,\ y=4\\\\4=4(0)-4\\4=0-4\\4=-4\qquad\bold{FALSE}\\\\2.\ (0,\ -4)\to x=0,\ y=-4\\\\-4=4(0)-4\\-4=0-4\\-4=-4\qquad\bold{TRUE}\\\\3.\ (-4,\ 0)\to x=-4,\ y=0\\\\0=4(-4)-4\\0=-16-4\\0=-20\qquad\bold{FALSE}\\\\4.\ (4,\ 0)\to x=4,\ y=0\\\\0=4(4)-4\\0=16-4\\0=12\qquad\bold{FALSE}$

5 0

3 years ago