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3 years ago

What is the slope of a line that passes through the points (-1, 1) and (1, -15)?

Mathematics

1 answer:

Alex Ar [27]3 years ago

6 0

Answer:

-8

Step-by-step explanation:

y2 - y1 / x2 - x1

-15 - 1 / 1 - (-1)

= -16 / 2

= -8

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Given the functions f (x)=\x] and g(x)= 2 x + 31 – 4 a. Determine the

Arisa [49]

Functions can be transformed through translation, dilation, etc.

The changes are horizontal translations and vertical compression.
The domain of f(x) is $(-\infty,\infty)$ , while its range is $(0,\infty)$
The domain of g(x) is $(-\infty,\infty)$ , while its range is $(-4,\infty)$

We have:

$f(x) = |x|$

$g(x) = 2|x - 3| - 4$

(a) The changes from f(x) to g(x)

First, f(x) was translated to the left by 3 units.

The rule is:

$(x,y) \to (x-3.y)$

So, we have:

$f'(x) = |x - 3|$

Next, the function is compressed vertically by 2

The rule is:

$(x,y) \to (x,2y)$

So, we have:

$f"(x) = 2|x - 3|$

Lastly, the function is translated down by 4 units.

The rule is:

$(x,y) \to (x, y - 4)$

So, we have:

$g(x) = 2|x - 3| - 4$

Hence, the changes are horizontal translations and vertical compression.

(b) Analyze f(x) and g(x)

f(x)

It spans across the x-axis; so, its domain is $(-\infty,\infty)$

The y values start from 0 and opens upward; so, its range is $(0,\infty)$

It crosses the x and y axes at 0; so its intercepts are 0.

g(x)

It spans across the x-axis; so, its domain is $(-\infty,\infty)$

The y values start from -4 and opens upward; so, its range is $(-4,\infty)$

It crosses the x-axis at -1 and -5; so its y-intercepts are -1 and -5

It crosses the y-axis at 2; so its x-intercept is 2

Read more about function transformation at:

brainly.com/question/13810353

4 0

3 years ago

HELP NEEDED PLEASE!!!

postnew [5]

Using vector concepts, it is found that:

The component form is of approximately (-9.58, 7,22). It means that the ship is about 9.58 miles to the west and about 7.22 miles to the north of where the ship left the port.

<h3>How can a vector be represented in component notation?</h3>

Given a magnitude M and angle $\theta$ , then a vector V can be represented as follows in component notation:

$V = (M\cos{\theta}, M\sin{\theta})$

In this problem, the magnitude and the angle are given, respectively, by:

$M = 12, \theta = 143^\circ$

Hence:

V = [12cos(143º), 12sin(143º)] = (-9.58, 7,22).

Which means a displacement of 9.58 miles to the west(negative x = west) and 7.22 miles to the north(positive y = north).

The component form is of approximately (-9.58, 7,22). It means that the ship is about 9.58 miles to the west and about 7.22 miles to the north of where the ship left the port.

More can be learned about vectors at brainly.com/question/24606590

#SPJ1

8 0

3 years ago

I have a friend in need. Her name is Sienna and she has cancer along with co.vid. Please pray for her well being because she rea

Rzqust [24]

Answer:

I will

Step-by-step explanation:

7 0

3 years ago

Find the inverse of the function f(x)= 4x-2

Tju [1.3M]

Answer:

f⁻¹(x) = x/4 + 1/2

Step-by-step explanation:

To find the inverse of a function, switch the x and y variables, then isolate y.

f(x) replaced y, so you can replace it back.

y = 4x - 2

x = 4y - 2 Switched x and y

x + 2 = 4y Added 2 to both sides

y = x/4 + 2/4 Divided both sides by 4

y = x/4 + 1/2 Simplified

f⁻¹(x) = x/4 + 1/2 Use function notation

4 0

4 years ago

The weight of 10 identical samples of a substance is 0.01 pounds what is the weight of 100 samples

valentina_108 [34]

Hola!!

If 10 = 0.01
then you could divide 100 by 10 which is 10
So then you multiply 0.01 by 10 which is 0.1

So the answer is 0.1

Get another answer to be sure. c:

5 0

3 years ago

Read 2 more answers