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schepotkina [342]
3 years ago
14

Type in expanded form. Use parentheses to indicate multiplication. (3x)²

Mathematics
1 answer:
Brrunno [24]3 years ago
3 0
Hint:  \bf (abc)^z\implies a^zb^zc^z\impliedby \textit{apply the exponent to "all" factors}
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Write the equation of each line using the given information.
Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3><u>Solution:</u></h3>

<em><u>a. The points (-4,1) and (2,4) both lie on the line</u></em>

The general line equation on which (a, b) and (c, d) lies is:

y-\mathrm{b}=\frac{d-b}{c-a}(x - a)

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

y-1=\frac{4-1}{2-(-4)}(x-(-4))

On solving we get,

\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}

<em><u>b.) m= -1 and the point (2, -1) lies on the line</u></em>

The equation of line in point slope form is y – b = m(x – a)  

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)  

y + 1 = -x + 2  

y = -x + 2 -1  

y = -x + 1

<em><u>c. )It has the same slope as y = 5 and passes through (1, 1)</u></em>

our line has same slope with y = 5, then our equation would be y = k  and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1  

Then our equation will be y = k

y = 1

<em><u> d. ) m= -3 and it has a y-intercept of (0, 8)</u></em>

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

6 0
3 years ago
ASAP PLS!!!!!! LOGISTICS MODEL STUDY GUIDE!!!! 40 POINTS
Monica [59]

This all depends on the content you are studying, and what learning style works for you. One thing that works for most people is repetition. Although it sucks, it works because that’s how our brains are wired. Tell yourself, “I will not stop studying until I understand this concept or calculation,” for example. Then take a break once you are comfortable with it. Repeat again as needed. Start studying early and only study what you don't know. Try to be as consistent as possible. Good luck!

3 0
2 years ago
What is the square root of -2i?
Studentka2010 [4]

Answer:

1-i and -1+i

Step-by-step explanation:

We are to find the square roots of z=0-2i. First, convert from Cartesian to polar form:

r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2

\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}

z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})

Next, use the formula \displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr] where \displaystyle k=0,1,2,...\:,n-1 to find the square roots:

<u>When k=1</u>

<u />\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr]

\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr]

\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)

\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i

<u>When k=0</u>

<u />\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr]

\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)

\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i

Thus, the square roots of -2i are 1-i and -1+i

4 0
1 year ago
Prove cos a = 5/13 pls solve it and no link pls..........​
Scorpion4ik [409]

<u>Answer</u> : The demonstration is below :)

Step-by-step explanation :

<u>We use Pythagoras' </u><u>theorem </u><u>:</u>

  • In the triangle ABC we have :

AB² = AC² - BC² = 15² - 9² = 144 = 12²

  • In the triangle ABD we have :

DB² = AD² - AB² = 13² - 12² = 5²

cos(a) = BD/AD = 5/13

3 0
2 years ago
A menu has five choices of appetizers
Vinil7 [7]

The number of the meals possible is 350.

The complete question is given below:-

A menu has 5 choices of appetizers, ten main courses, and seven desserts. How many meals are possible?

<h3 /><h3>What is the combination?</h3>

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

  • A menu has 5 choices of appetizers, ten main courses, and seven desserts.

The number of the combination of the meals will be calculated as:-

N = 5 x 10 x 7

N = 350

Therefore the number of the meals possible is 350.

To know more about combinations follow

brainly.com/question/11732255

#SPJ1

3 0
1 year ago
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