Find the slope of the line passing through each of the following pairs of points.

1 answer:

5 0

Look carefully at the first pair: (−3, 9), (−3, −5) Note that x does not change, tho' y does. This is how we recognize a vertical line (whose slope is undefined). The equation of this vertical line is x = -3.

Looking at the second pair: from (3,4) to (5,6), x increases by 2 and y by 2; thus, the slope is m = rise/run = 2/2 = 1.

Third pair: as was the case with the first pair, x does not change here, and thus the equation of this (vertical) line is x=0 (which is the y-axis). The slope is undefined.

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Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2

guajiro [1.7K]

F(x) = ln(x² - 12x)
The derivative is
$f'(x)= \frac{2x-12}{x^{2}-12x}$

f(x) is undefined when x² - 12x = x(x - 12) = 0
That is, when x = 0 or x = 12.
Therefore the domain is (-∞, 0)∪(0,12)∪(12, ∞)

Answer:
The derivative is
$f'(x) = \frac{2x-12}{x^{2}-12x}$
The domain is
(-∞, 0)∪(0, 12)∪(12,∞)

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A money bag contains ten 5-dollar notes and thirty 10-dollar notes. If a note is randomly selected from the bag, what is the pro

lapo4ka [179]

Not a 5 dollar just means a 10 dollar

probblity=desired outcomes/total possible outcomes

desired=number of 10 dollar notes or 30

total possible=10+30 or 40

the probablity is 30/40 or 3/4 or 75% that you do not select a 5 dollar note

4 0

3 years ago

Vhat is the equation of the line with a slope of 2 through (-4, 6) in point-slope form?

Harlamova29_29 [7]

Answer:

y=2x+14

Step-by-step explanation:

y-y=m(x-x1)

y-6=2(x-(-4))

y-6=2x+8

+6 +6

y=2x+14

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Write an equation in standard form of the line that contains the point (-1,2) amd is perpendicular to y = 3x - 1

Strike441 [17]

Since it is perpendicular to y=3x-1, the slope must be a negative reciprocal.
there the slope of the perpendicular line is $-\frac{1}{3} x$

So now we have,
$y=- \frac{1}{3} x+b$

To find b, we use the point that the line passes through and substitute it to the y and x values.

$2=- \frac{1}{3} (-1)+b$

which would give us b=5/3

Therefore, the equation of the line is
$y=- \frac{1}{3} x+ \frac{5}{3}$

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3 years ago

The perimeter of an isosceles trapezoid is 28 in and the ratio of lengths of its bases is 5:3. Find the lengths of the sides of

Natalka [10]

The measurements are:
b₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂ = 2.8 inches

Let x = length of base and leg

The formula for perimeter of isosceles trapezoid is P = b₁ + b₂ + 2(leg)
Where: b = base

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   28 = 8x + 2x
28/10 = 10x/10
2.8 = x

Now, substitute the values:
     P = b₁ + b₂ + 2(leg)
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Hence the measurements are:
b₁ = 8.4 inches; b₂ = 14 inches; leg₁ = 2.8 inches; leg₂ = 2.8 inches

8 0

3 years ago