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3 years ago

You earn $49 for washing 7 cars. How much do you earn for washing 4 cars?

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

4 0

Answer:

Step-by-step explanation:

We can use the rule of three!

We know we have the following relationship:

$\frac{49}{7} = \frac{x}{4}$

From here, we can solve this like any other equation:

$4(\frac{49}{7}) = x\\x = 28$

Therefore, you would earn $28 after washing 4 cars.

Good luck!

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The slope of a line can be stated many ways if not put into simplest form.

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3 years ago

today reza ate 20 grapes which is 400% as many grapes as he ate yesterday. explain how to use equal ratios to find the number of

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Answer:

Write 400% as the ratio 400/100. To find an equivalent ratio, you know that 400 divided by 20 is 20, so 100 divided by 20 will give you the answer. 100 ÷ 20 = 5. Reza ate 5 grapes yesterday.

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7 0

3 years ago

Read 2 more answers

Need answer 25 and answer 27

UNO [17]

$\\ \bull\tt\dashrightarrow \dfrac{-3}{8}x-20+2x>6$

$\\ \bull\tt\dashrightarrow \dfrac{-3}{8}x+2x=6+20=26$

$\\ \bull\tt\dashrightarrow \dfrac{-3+16}{8}x=26$

$\\ \bull\tt\dashrightarrow \dfrac{13}{8}x=26$

$\\ \bull\tt\dashrightarrow x=26\times \dfrac{8}{13}$

$\\ \bull\tt\dashrightarrow x=8(2)=16$

#27

$\\ \bull\tt\dashrightarrow 0.5x-4-2x\leqslant 2$

$\\ \bull\tt\dashrightarrow 0.5x-2x\leqslant=2+4=6$

$\\ \bull\tt\dashrightarrow -1.5x\leqslant 6$

$\\ \bull\tt\dashrightarrow x\leqslant\dfrac{6}{-1.5}$

$\\ \bull\tt\dashrightarrow x\leqslant 4$

8 0

3 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