Write an equation in slope intercept form thag passes through (4,-4) and is parallel to 3+4x=2y-9

Mathematics

2 answers:

uysha [10]3 years ago

7 0

The original line is

4x - 2y = -12

The parallel lines will all be

4x - 2y = constant

and the constant is given by the point directly:

4x - 2y = 4(4) - 2(-4) = 24

2y = 4x - 24

y = 2x - 12

Answer: y = 2x - 12

sashaice [31]3 years ago

4 0

Let's deal with the slope first: we know that our line is parallel to the given line, and two lines are parallel if and only if their slopes are the same.

So, if we find the slope of the given line, we also have the slope of our line.

When a line is written in the form $y=mx+q$ , the slope is the coefficient $m$ .

So, we can rearrange the expression of the given line as follows:

$3+4x=2y-9 \iff 4x+12 = 2y \iff y = 2x+6$

and so the slope is 2.

Now, when you know the slope $m$ and a point $(x_0,y_0)$ belonging to a line, you can write the equation of the line as

$y-y_0 = m(x-x_0)$

if you substitute your values, you have

$y-(-4) = 2(x-4) \iff y+4 = 2x-8 \iff y = 2x-12$

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What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be def

Misha Larkins [42]

The square root of a a negative integer is imaginary.
It would still be a negative under a square root if you multiplied it by 2, therefor it will still be imaginary, or I’m assuming as your book calls it, undefined.
2•(sqrt-1) = 2sqrt-1

If you add a number to -1 itself, specifically 1 or greater it will become a positive number or 0 assuming you just add 1. In that case it would be defined.
-1 + 1 = 0
-1 + 2 = 1

If you add a number to the entire thing “sqrt-1” it will not be defined.
(sqrt-1) + 1 = 1+ (sqrt-1)

If you subtract a number it will still have a negative under a square root, meaning it would be undefined.
(sqrt-1) + 1 = 1 + (sqrt-1)

however if you subtract a negative number from -1 itself, you end up getting a positive number or zero. (Subtracting a negative number is adding because the negative signs cancel out).
-1 - -1 = 0
-1 - -2 = 1

If you squared it you would get -1, which is defined
sqrt-1 • sqrt-1 = -1

and if you cubed it, you would get a negative under a square root again, therefor it would be undefined.
sqrt-1 • sqrt-1 • sqrt-1 = -1 • sqrt-1 = -1(sqrt-1)

Sorry if this answer is confusing, I don’t have a scientific keyboard, I’ll get one soon.

8 0

3 years ago

Find the surface area of the prism shown (Remember, rectangular prisms have a total of 6 sides)

gregori [183]

Answer:

The answer is 190mm2

Step-by-step explanation:

(3x5)x2 30

(3x10)x2 60

(5x10)x2 100

add them all up to get 190

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