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3 years ago

Consider the line =−8x6y−4.

Mathematics

1 answer:

Kaylis [27]3 years ago

5 0

Answer:

The slope of the line perpendicular to 8x - 6y = -4 = -3/4

All lines parallel to y = 4x/ 3 - 2/3 have thesame slope of 4/3

Step-by-step explanation:

To find the slope of a line Parallel or perpendicular to another, we should bear in mind that:

When two lines are parallel, they have an equal slope.

Also, when two lines are perpendicular, they have opposite signs and they are reciprocals of each other.

From the question:

8x - 6y = -4

Let's rearrange the equation to have in the form of:

y = mx + c.

Where m= slope

C = intercept.

Therefore, for PERPENDICULAR

6y = 8x - 4.

y = 8x/6 - 4/6

y = 4x/3 - 2/3

SLOPE = 4/3

To get tge slope perpendicular to the line y = 4x/3 - 2/3;

Lets get the reciprocal and the opposite sign.

Slope = 4/3

Perpendicular slope = - 1/ m

= -3/4

Therefore, the slope of the line perpendicular to = -3/4

PARALLEL:

6y = 8x - 4.

y = 8x/ 6 - 4/6

y = 4x/ 3 - 2/3

SLOPE = 4/3.

Therefore, all lines parallel to y = 4x/ 3 - 2/3 have thesame slope of 4/3

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)

zubka84 [21]

$\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 
$

This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

$\frac{ \sqrt{-49}}{7-2i-4-9i}$

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:

$\frac{ \sqrt{-49} }{3-11i}$

Now, the $\sqrt{-49}$ must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to $\sqrt{49} \sqrt{-1}$
This means that we get the result 7i for the numerator.

$\frac{7i}{3-11i}$

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: $x^2 - y^2 =(x+y)(x-y)$
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

$\frac{7i (3+11i)}{(3-11i)(3+11i)}$

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how $(3-11i)(3+11i)= 3^2 -(11i)^2$ therefore, we can finally write:

$\frac{7i(3+11i)}{3^2 - (11i)^2 }$

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product $7i(3+11i) = 21i+77i^2$ .
You should know from your classes that i^2 = -1, thefore the numerator simplifies to $-77+21i$
You can do it as a curious thing, but simplifying yields the result:
$\frac{-77+21i}{130}$

7 0

3 years ago

How do you answer this

Elanso [62]

Okay so you take the 12 feet I'm pretty sure you multiply 12 and 30 and then that's one of your answers and then the 12 and a 75 you must put those to together and that's an answer and you subtract your 12 x 30 and you're 12 x 75 and that's how you get your answer I am pretty sure that's how you and that's how you get your answer I am pretty sure that's how you do it

5 0

3 years ago

NEED THIS DONE SOON

Sati [7]

65Answer:

we can use sin to find the missing length

Step-by-step explanation:

The ratio states that sin of an angle=opposite/hypotenuse

sin(65)=x/6 since we know the angle and the hypotenuse we need to figure out the opposite side

sin(65)=0.906307...

0.906307=x/6

Multiply 6 on both sides to isolate x

The answer is 5.4378...

Rounded to the hundredth is 5.44

5 0

2 years ago

a gym teacher has a large canvas bag that contains 8 tennis balls, 2 volleyballs, 1 basketball, 3 baseballs, and 5 footballs. if

Serga [27]

Answer:

Step-by-step explanation:

5+1+3+8+2=19

3/19 = 16%

6 0

2 years ago

123456789101112131415161718

lesya692 [45]

Answer:

the third one is the correct answer

Step-by-step explanation:

hope that helps

7 0

3 years ago