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1 year ago

What is the slope of a line perpendicular to the line whose equation is 6x+2y=−32. Fully simplify your answer.

Mathematics

1 answer:

Reika [66]1 year ago

5 0

The slope of the line that is perpendicular to 6x + 2y = -32 is: 1/3.

<h3>What is the Slope of Perpendicular Lines?</h3>

The slope of two lines that are perpendicular to each other will always have a product that is equal to -1, which means that their slopes are negative reciprocals to each other.

Rewrite 6x + 2y = -32 in slope-intercept form:

2y = -6x - 32

2y/2 = -6x/2 - 32/2

y = -3x - 16

The slope is -3. Negative reciprocal of -3 is 1/3.

Therefore, the slope of the perpendicular line would be: 1/3.

Learn more about the slope of perpendicular lines on:

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1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

7 0

3 years ago

From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade,

natulia [17]

Answer:

1222 billion dollars.

Step-by-step explanation:

To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:

In the period 1960-1970, we have x = 1, and the growth is:

$y(1) = 43e(1/2) = 70.895$

In the period 1970-1980, we have x = 2, and the growth is:

$y(2) = 43e(2/2) = 116.8861$

The growth in the following 3 periods are:

$y(3) = 43e(3/2) =192.7126$

$y(4) = 43e(4/2) = 317.7294$

$y(5) = 43e(5/2) =523.8472$

So the total growth in the period 1960 - 2010 is:

$Total = y(1) + y(2) + y(3) + y(4) + y(5)$

$Total = 70.895 + 116.8861+192.726+317.7294+523.8472$

$Total = 1222.08\ billion\ dollars$

Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.

6 0

2 years ago

Lol again another math solver help pls! LOL

gladu [14]

Answer:

b = 4

Step-by-step explanation:

5-1=5b-4b

4=b

4 0

2 years ago

Read 2 more answers

What is the range of the function f(x)=(x-4)^2-5

uranmaximum [27]

f(x) = (x - 4)^2 - 5

Vertex (4 , -5)

This function opens upward and has min. value = -5

So range y >= - 5

So answer is A. -5 <= f(x) < ∞

4 0

2 years ago

Read 2 more answers

PLEASE HELP ME WITH THIS PROBLEM IVE BEEN ON IT FOR 3 DAYS NOW!

Len [333]

85 x 3 = 255
first 2 test grades were 81 and 86:
81 + 86 = 167

Need to find the 3rd to have exact average 85:
255 - 167 = 88

So her 3rd test needs to make 88 to make average of 85

Double check: 81 + 86 + 88 = 255 = 85 + 85 + 85

3 0

3 years ago