1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ehidna [41]
2 years ago
14

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. 3 1/3 -1/3 −3

Mathematics
1 answer:
Irina-Kira [14]2 years ago
3 0

This is about interpretation of graphs.

Option C is correct.

From the graph, we can see the 2 lines representing function f(x) and function g(x).

Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

For f(x), when x = -3, y = 1

For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

You might be interested in
Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5
zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}} or \displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}

Therefore, the solution is 31.

__________________________________________________________

Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as \displaystyle \large{a_{n-1} \cdot r = a_n} meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

7 0
2 years ago
A recipe that makes 4 servings calls for 2/3 cup of flour. Isadora uses a large container of flour to make 20 servings of the re
Luden [163]
2/3 x 5 = 3
the ratio from 4 to 20 is 5, then you multiply it by the original amount
so it's 3 
3 0
3 years ago
1 ) $45, the markup is 20%. <br> 2) 1.25 the markup is 80%<br> 3) 150. the markdown is 40%
baherus [9]
Hi there! I can help you with these! For these types of questions, all you have to do is that if there is a markup, multiply by one hundred something to get the new price, because you're including the original price and the markup. For example, if there is a 75% markup on something, you multiply by 175% (1.75). Or, if there is a markdown, basically multiply by the remaining percentage. For example, if the markdown is 35%, you multiply the original price by 65% (0.65), because that is the amount of the price that it's on sale for. With that being said, if you do this correctly, here are the answers:

1. $54
2. $2.25
3. $90

Hopefully if you're talking about the markup or markdown from these prices, those are your answers.
8 0
3 years ago
Harry owns a car dealership. During a sale one week, he sold 8 small cars out of every 11 cars he sold. Harry sold a total of 33
Cerrena [4.2K]

Answer:

24

Step-by-step explanation:

6 0
3 years ago
Someone plssss help me I’m in the middle of a test and imma fail this class if I don’t get an a or b
Firdavs [7]

Answer:

It's A. 4 units

Step-by-step explanation:

Literally, you just have to count the number of units (those gaps) between W and Z

7 0
2 years ago
Other questions:
  • Anitais making curtain to surround a table.she bought 3/1/4 yards of fabric ,her total was $13, what was the cost per yard
    13·1 answer
  • Which statement illustrates the identity property of addition?
    10·2 answers
  • I Need The Answer Plz!!! Geometry Is Hard!!!
    6·1 answer
  • the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family include
    10·1 answer
  • A survey is targeted at 12-year-old children. Which questions are appropriate for the population?
    11·1 answer
  • Jennifer buys a 2-liter bottle of apple juice and a 3-liter bottle of orange juice at the market. How many deciliters of juice d
    10·1 answer
  • If a linear regression has a correlation coefficient of 0.85, which of the following statements is true?
    9·2 answers
  • Madelyn has x nickels and y dimes, having a maximum of 15 coins worth no
    8·1 answer
  • What are the intercepts of 7x+2y-14z=56
    12·1 answer
  • B is the midpoint of ac. ab equals 4x-1 and bc equals 5x-5. what is the length of bc?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!