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
serg [7]
3 years ago
13

This table shows the input and output values for an exponential function f(x) .

Mathematics
2 answers:
Gre4nikov [31]3 years ago
8 0
The correct answer is:  [B]:  "4 " .
______________________________________
Explanation: 
______________________________________
Refer to the table (provided within the actual question).

Note that the "inputs" ; or "x-values" ; are all listed in "chronological order" ; and are all "one (1) unit apart. and range from:  "x = -3"  to "x = 3" .

When "x = 0" ; the "output" ; or "f(x)"  is "1/4" . 
When "x = 1"  ; the "output" ; or "f(x)" is:  "1" .
_________________________________________________
So; the ratio of these two "outputs"  is:  "¼ : 1"  ; or, write as:
  " (¼) / 1 " ;   and note that:  " (¼) / 1 =  (¼) ÷ 1 = ¼.

However; note that: "1/4" ; or  "1:4" is NOT among the [answer choices given].

However, the ratio of the 2 (two) corresponding "outputs"; chronologically,
going from when "x = 1" ; to "x = 0" ;  is:  "1 : ¼" ; or;  write as:  "1 / (¼)" ; 

And note that:  "1 / (¼)"  =  " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" .

This corresponds to:  Answer choice: [B]:  "4<span>" .
</span>_________________________________________________
Let us further confirm that this answer is correct:
_________________________________________________
When x = 3;  the "output" is:  "16" .

When x = 2;  the "output" is:  "4" .

The ratio:  "16/4 = ?  4 ? " ;    →  Yes!
_________________________________________________
When x = 2;  the "output" is:  "4" .

When x = 1;   the "output" is:  "1" .

The ratio:  "4/1  = ?  4 ? " ;    →  Yes!
_________________________________________________
When x = 1;  the "output" is:  "1" .

When x = 0; the "output" is:  "(¼)" .

The ratio:  "1 / (¼)  = ?  4 ? " ;  

   →  "1 / (¼)"  =  " 1 ÷ (¼) " = 1 * (4/1) = 1 * 4 = "4" . YES!
________________________________________________
When  x = 0; the "output" is:  "(¼)" .

When  x = -1; the "output" is:  "(¹/₁₆)" .

The ratio:  "(¼) / (¹/₁₆)  = ?  4 " ? ;  
  
   →  "(¼) / (¹/₁₆) = "(¼) ÷ (¹/₁₆) " =  "(¼) * (¹⁶/₁) = (1*16) / (4*1) = 16/4 = "4" .  Yes!
________________________________________________________
When  x = -1; the "output" is:  "(¹/₁₆)" .

When  x = -2; the "output" is:  "(¹/₆₄)" .

The ratio:  "(¹/₁₆) / (¹/₆₄)  = ?  4 " ? ;  
  
   →  "(¹/₁₆) / (¹/₆₄)  = "(¹/₁₆) ÷ (¹/₆₄)" = "(¹/₁₆) * (⁶⁴/₁)" = (1*64) / (16*1) = 64/16 = "4" . Yes!
__________________________________________________________
When  x = -2; the "output" is:  "(¹/₆₄)" .

When  x = -3; the "output" is:  "(¹/₂₅₆)" ,

The ratio:  "(¹/₆₄)/(¹/₂₅₆)  = ?  4 " ? ;  
  
 → "(¹/₆₄) / (¹/₂₅₆)"  ;
 
       =   " (¹/₆₄) ÷ (¹/₂₅₆)" = " (¹/₆₄) * (²⁵⁶/₁) " = (1*256) / (64*1) = 256/164  =  "4 " . Yes!
__________________________________________________________
  → So; as calculated; the ratio is:  "4" ;  which is:
__________________________________________________________
  →  Answer choice:  [B]:  "4" .
__________________________________________________________
Otrada [13]3 years ago
8 0

The correct answer is:  [B]:  "4 " .


You might be interested in
What is the solution to this equation 1/2n^2+18=0
ololo11 [35]

Answer:

n = ±6 .

Step-by-step explanation:

A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,

\rm\implies -\dfrac{1}{2}n^2+18=0

Subtracting 18 both sides ,

\rm\implies -\dfrac{1}{2}n^2 = -18

Multiplying both sides by -2 ,

\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18

On simplyfing , we get ,

\rm\implies n^2= 36

Putting squareroot both sides ,

\rm\implies n= \sqrt{36}

This equals to ,

\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }}

<u>Hence</u><u> the</u><u> </u><u>value</u><u> of</u><u> </u><u>n </u><u>is </u><u>±</u><u>6</u><u> </u><u>.</u>

6 0
3 years ago
During 30 minutes on the treadmill, LaToya burned 20 calories per minute. What is the rate of change of the function that repres
Genrish500 [490]
The answer I believe is 10 calories per minute because 20 x30 =600 I did that because she burned 20 calories per minute so with that being said there’s 60 minutes is the maximum minutes any time can go to so you do 600 divided by 60 which equals 10 which means she burns 10 calories per minute hope this is right
3 0
3 years ago
Does this graph represent a function? What is the domain and range of the graph
Daniel [21]
Yes it is a function. It passes the vertical line test. In other words, it is impossible to draw a single vertical line through more than one point on the V shaped graph. Any input leads to exactly one output.

The domain is the set of all real numbers. This is because we can plug in any x value leading to some specific y value. There are no holes or gaps or jumps to indicate we must restrict any given x value. The domain would not be the set of whole numbers only because values between the whole numbers (eg: decimal values like x = 2.75) work just fine. 

The range is the set of y values such that y is either 0 or larger than 0. In short, the range is y \ge 0. Notice how any point on the V shaped graph has a y coordinate that is either 0 or larger than 0. It is impossible to get a y value that is negative.

--------------------------------------------------------------------

In summary,
Yes it is a function
Domain: all real numbers
Range: y \ge 0
So the answer is choice B
6 0
3 years ago
60 z+ 50 - 97z = - 37z + 49<br> How many solutions does this equation have ?
ExtremeBDS [4]

Answer:

no solutions

Step-by-step explanation:

6 0
3 years ago
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Ivahew [28]
Check the picture below.

\bf \textit{Law of Cosines}\\ \quad \\&#10;c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies &#10;c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}&#10;\\\\\\&#10;\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;d=10\\&#10;e=18\\&#10;f=22&#10;\end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D

\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D

7 0
3 years ago
Other questions:
  • Which side of the dilation corresponds to side AC of the original figure?
    15·1 answer
  • Carol needs for lb of nuts for her granola she has 26 oz of walnuts and 28 oz of cashews how many ounces of peanuts should she b
    10·1 answer
  • Complete the expression below to create an expression equal to 72 + 45<br> (8 + 5)
    6·1 answer
  • 3/4 + 5/8= ?<br><br><br> ignore this it told me to do atleast 20 words in order to ask a question.
    12·2 answers
  • What is the value of -2/5 / 3/4?
    7·1 answer
  • Ella used 3 fourths of lemons to make one half liters of lemonade. If Ella's recipe is for 1 liter of lemonade, how many lemons
    14·1 answer
  • Table 1 contains outputs of the function f(x)=b^x for some x values and Tables 2 contains outputs of the function g(x)=logb (x)
    5·1 answer
  • Slove.<br> -5 3/4 - 3 1/2 =<br> A. -9 1/4 <br> B. -2 1/4 <br> C. -8 2/3<br> D. 2 1/4
    6·2 answers
  • -1-2•[(-1)+5)} I am so lost on these math problems
    7·2 answers
  • HELP ASAP!!!!!!!!!!!!!! ITS AN EMERGENCY!!!!!!!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!