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3 years ago

What is the equation of the line that passes through (–2, –3) and is perpendicular to 2x – 3y = 6?

Mathematics

1 answer:

lyudmila [28]3 years ago

6 0

An equation that would be perpendicular is opposite the reciprocal.

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Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parenthe

AlekseyPX

The answer is
$\frac{-6i-3}{5}$ .

Before we rationalize the denominator, we must simplify the numerator and denominator. We evaluate the square root on the top, and combine like terms on the bottom:
$\frac{\sqrt{-9}}{(4-7i)-(6-6i)}
\\
\\=\frac{\sqrt{9i^2}}{4-6-7i--6i}
\\
\\=\frac{3i}{-2-i}$

To rationalize the denominator, we multiply by the conjugate. The conjugate is found by making the imaginary term of the complex number, the i part, the opposite sign. The conjugate of -2-i is -2+i:

$\frac{3i}{-2-i}\times \frac{-2+i}{-2+i}
\\
\\=\frac{3i(-2+i)}{(-2-i)(-2+i)}
\\
\\=\frac{3i\times -2 + 3i\times i}{-2\times -2 + -2\times i + -2\times -i + -i\times i}
\\
\\=\frac{-6i+3i^2}{4-2i+2i-i^2}
\\
\\=\frac{-6i+3(-1)}{4-i^2}=\frac{-6i-3}{4-(-1)}=\frac{-6i-3}{5}$

7 0

3 years ago

3. Sam and Tim each have savings accounts. Every month they each put in some of their

Setler [38]

Answer:

$y = 30x +50$ --- Sam

$y = 20x +80$ --- Tim

Step-by-step explanation:

Given

Sam Tim

х --- f(x) --------------- g(x)

1 --- 80 --------------- 100

2 --- 110 --------------- 120

3 --- 140 --------------- 140

4 --- 170 -------------- 160

Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,80)$

$(x_2,y_2) = (4,170)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{170 - 80}{4 - 1}$

$m = \frac{90}{3}$

$m = 30$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 80 = 30(x - 1)$

$y - 80 = 30x - 30$

Make y the subject

$y = 30x - 30 + 80$

$y = 30x +50$

Calculating the equation of Tim

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,100)$

$(x_2,y_2) = (4,160)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{160 - 100}{4 - 1}$

$m = \frac{60}{3}$

$m = 20$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 100 = 20(x - 1)$

$y - 100 = 20x - 20$

Make y the subject

$y = 20x - 20+100$

$y = 20x +80$

7 0

3 years ago

Identify the property used in the first five steps to solve the equation 2(x – 5) - 6x= -22

USPshnik [31]

To answer this question, you need to multiply the number inside the bracket first. Then you can move the number to the right side of the equal sign and keep the x on the left side of the equal sign. The step would be like this

2(x – 5) - 6x= -22
(2x - 10) - 6x = -22
2x - 6x = -22 +10
-4x= -12
x= -12/-4
x=3

4 0

3 years ago

If you flipped the graph y=x^2+2x-2 vertically, you would get the graph y=-(x^2 +2x-2). true or false

Mars2501 [29]

If you flipped the graph y=x^2+2x-2 vertically, you would get the graph y=-(x^2+2x-2) this is True.

5 0

3 years ago

PLEASE HELP solve the following: two and two thirds − one and one third

alina1380 [7]

Answer:

we know that and means adding so.

from the question

2+2/3-1+1/3

=1+2/3+1/3

=(3+2+1)/3

=6/3

6 0

2 years ago