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Levart [38]
3 years ago
7

Find the slope of the line through the given points. d (3, 7) and (3, −8)

Mathematics
1 answer:
Romashka [77]3 years ago
6 0

Answer:

Undefined

Step-by-step explanation:

Use rise over run (y2 - y1) / (x2 - x1), where (x1, y1) and (y1, y2) are points on the line

Plug in the given points:

(y2 - y1) / (x2 - x1)

(-8 - 7) / (3 - 3)

-15/0

= undefined

The slope is undefined, because you cannot divide by 0.

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NO LINKS!!! What is the transformation f(x)= x^3:
Mama L [17]

Answer:

4.  Horizontal shrink by a factor of ¹/₅

5.  Left 5, Up 5

6.  Right 5, Down 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

<u>Transformations</u>

For a > 0

f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}

f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}

f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}

f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}

y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a

y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}

y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}

y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}

Identify the transformations that take the parent function to the given function.

<u>Question 4</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(5x)^3

Comparing the parent function with the given function, we can see that the <u>x-value of the parent function</u> has been <u>multiplied</u> by 5.

Therefore, the transformation is:

y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}

As a > 1, the transformation visually is a compression in the x-direction, so we can also say:  Horizontal shrink by a factor of ¹/₅

<u>Question 5</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(x+5)^3+5

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>added to the x-value</u> of the parent function.

f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}

<u>Step 2</u>

5 has then been <u>added to function</u>.

f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}

<u>Transformation</u>:  Left 5, Up 5

<u>Question 6</u>

\textsf{Parent function}: \quad f(x)=x^3

\textsf{Given function}: \quad f(x)=(x-5)^3-5

Comparing the parent function with the given function, we can see that there are a series of transformations:

<u>Step 1</u>

5 has been <u>subtracted from the x-value</u> of the parent function.

f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}

<u>Step 2</u>

5 has then been <u>subtracted from function</u>.

f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}

<u>Transformation</u>:  Right 5, Down 5

Learn more about graph transformations here:

brainly.com/question/27845947

6 0
2 years ago
Read 2 more answers
Which expression is equivalent to -6(3x- 2/3)?
Anestetic [448]

Answer: −18x+4

Step-by-step explanation:  

=(−6)(3x+ −2/3)

=(−6)(3x)+(−6)(

−2/3)

5 0
3 years ago
A mountain has a 20 degree slope, and is 1 mile tall. How far do you need to hike to reach the summit?
netineya [11]

Answer:21

Step-by-step explanation:

3 0
3 years ago
Using the diagram below, translate the figure 3 units to the left and 2 units up. Graph the translated figure and provide the tr
aleksandrvk [35]
Bah ahaha because i’m trying to get answers to m
8 0
3 years ago
The first term of a geometric series is -3, the common ratio is 6, and the sum of the series is -4,665. Using a table of values,
tamaranim1 [39]

Answer:

Option A. 5

Step-by-step explanation:

From the question given above, the following data were obtained:

First term (a) = –3

Common ratio (r) = 6

Sum of series (Sₙ) = –4665

Number of term (n) =?

The number of terms in the series can be obtained as follow:

Sₙ = a[rⁿ – 1] / r – 1

–4665 = –3[6ⁿ – 1] / 6 – 1

–4665 = –3[6ⁿ – 1] / 5

Cross multiply

–4665 × 5 = –3[6ⁿ – 1]

–23325 = –3[6ⁿ – 1]

Divide both side by –3

–23325 / –3 = 6ⁿ – 1

7775 = 6ⁿ – 1

Collect like terms

7775 + 1 = 6ⁿ

7776 = 6ⁿ

Express 7776 in index form with 6 as the base

6⁵ = 6ⁿ

n = 5

Thus, the number of terms in the geometric series is 5.

8 0
3 years ago
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