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4 years ago

What is the solution off the inequality shown below? 7+y>0

Mathematics

2 answers:

FinnZ [79.3K]4 years ago

8 0

Answer:

y > -7

Step-by-step explanation:

Isolate the variable, y. Treat the > as a equal sign, what you do to one side, you do to the other. Subtract 7 from both sides:

y + 7 (-7) > 0 (-7)

y > 0 - 7

y > -7

y > -7 is your answer.

Brrunno [24]4 years ago

7 0

Answer:

$\huge \boxed{y>-7}$

Step-by-step explanation:

Switch sides.

$\displaystyle y+7>0$

Subtract by 7 from both sides of equation.

$\displaystyle y+7-7>0-7$

Simplify, to find the answer.

$\displaystyle 0-7=-7$

$\huge \boxed{y>-7}$ , which is our answer.

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Find the cube roots of 27(cos 330° + i sin 330°)

Aleksandr-060686 [28]

Answer:

See below for all the cube roots

Step-by-step explanation:

DeMoivre's Theorem

Let $z=r(cos\theta+isin\theta)$ be a complex number in polar form, where $n$ is an integer and $n\geq1$ . If $z^n=r^n(cos\theta+isin\theta)^n$ , then $z^n=r^n(cos(n\theta)+isin(n\theta))$ .

Nth Root of a Complex Number

If $n$ is any positive integer, the nth roots of $z=rcis\theta$ are given by $\sqrt[n]{rcis\theta}=(rcis\theta)^{\frac{1}{n}}$ where the nth roots are found with the formulas:

$\sqrt[n]{r}\biggr[cis(\frac{\theta+360^\circ k}{n})\biggr]$ for degrees (the one applicable to this problem)
$\sqrt[n]{r}\biggr[cis(\frac{\theta+2\pi k}{n})\biggr]$ for radians

for $k=0,1,2,...\:,n-1$

Calculation

$z=27(cos330^\circ+isin330^\circ)\\\\\sqrt[3]{z} =\sqrt[3]{27(cos330^\circ+isin330^\circ)}\\\\z^{\frac{1}{3}} =(27(cos330^\circ+isin330^\circ))^{\frac{1}{3}}\\\\z^{\frac{1}{3}} =27^{\frac{1}{3}}(cos(\frac{1}{3}\cdot330^\circ)+isin(\frac{1}{3}\cdot330^\circ))\\\\z^{\frac{1}{3}} =3(cos110^\circ+isin110^\circ)$

First cube root where k=2

$\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(2)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+720^\circ}{3})\biggr]\\3\biggr[cis(\frac{1050^\circ}{3})\biggr]\\3\biggr[cis(350^\circ)\biggr]\\3\biggr[cos(350^\circ)+isin(350^\circ)\biggr]$

Second cube root where k=1

$\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(1)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ+360^\circ}{3})\biggr]\\3\biggr[cis(\frac{690^\circ}{3})\biggr]\\3\biggr[cis(230^\circ)\biggr]\\3\biggr[cos(230^\circ)+isin(230^\circ)\biggr]$

Third cube root where k=0

$\sqrt[3]{27}\biggr[cis(\frac{330^\circ+360^\circ(0)}{3})\biggr]\\3\biggr[cis(\frac{330^\circ}{3})\biggr]\\3\biggr[cis(110^\circ)\biggr]\\3\biggr[cos(110^\circ)+isin(110^\circ)\biggr]$

4 0

3 years ago

Hello! this is function or no?

Sergeeva-Olga [200]

Yes, they are both functions.

8 0

4 years ago

Read 2 more answers

Im given a XY line, the midpoint is (3.-5) and the Y end is (0,2) how do I find the X ending of the line

romanna [79]

Using the midpoint formula, the coordinates of the endpoint X, are calculated as: X(6, -12).

<h3>How to Apply the Midpoint Formula?</h3>

The midpoint formula is expressed as: M(x, y) = [(x_1 + x_2)/2, (y_1 + y_2)/2].

We are given the following:

Line XY has a midpoint with the coordinates: (3, -5)

It has one endpoint: Y(0, 2)

To find the coordinates of the other endpoint, X, let:

X(?, ?) = (x_1, y_1)

Y(0, 2) = (x_2, y_2)

M (x, y) = (3, -5)

Plug in the values into the midpoint formula

M(3, -5) = [(x_1 + 0)/2, (y_1 + 2)/2]

Isolate and solve each variable

3 = (x_1 + 0)/2

6 = x_1

x_1 = 6

-5 = (y_1 + 2)/2

-10 = y_1 + 2

-10 - 2 = y_1

y_1 = -12

Therefore, the coordinates of the endpoint X, are: X(6, -12).

Learn more about the midpoint formula on:

brainly.com/question/13115533

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2 years ago

The domain and range of all linear functions, with the exception of vertical and horizontal lines, is

Ede4ka [16]

Answer:

All real numbers

Step-by-step explanation:

Linear functions have a domain and range of all real numbers because they reach from -∞ to ∞ on the x-axis and y-axis.

An example is given below. The domain and range of the function are all real numbers.

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

What is the solution off the inequality shown below? 7+y>0​

What is the solution off the inequality shown below? 7+y>0