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3 years ago

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>Solution:</h3>

a. The points (-4,1) and (2,4) both lie on the line

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,

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

b.) m= -1 and the point (2, -1) lies on the line

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

c. )It has the same slope as y = 5 and passes through (1, 1)

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

d. ) m= -3 and it has a y-intercept of (0, 8)

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

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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!

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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: