Complete the table of values for the function f(x) = (1/3)x for a, b, and c. x : -2, -1, 0, 1, 2. f(x) : a, b, c, 1/3, 1/9
Answers
Given:
The function is
[tex]f(x)=\left(\dfrac{1}{3}\right)^x[/tex]
To find:
The missing values for a, b, and c in the given table.
Solution:
We have,
[tex]f(x)=\left(\dfrac{1}{3}\right)^x[/tex]
At x=-2,
[tex]f(-2)=\left(\dfrac{1}{3}\right)^{-2}[/tex]
[tex]a=\left(3\right)^{2}[/tex] [tex]\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right][/tex]
[tex]a=9[/tex]
At x=-1,
[tex]f(-1)=\left(\dfrac{1}{3}\right)^{-1}[/tex]
[tex]b=\left(3\right)^{1}[/tex] [tex]\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right][/tex]
[tex]b=3[/tex]
At x=0,
[tex]f(0)=\left(\dfrac{1}{3}\right)^{0}[/tex]
[tex]c=1[/tex] [tex]\left[\because a^0=1, a\neq 0\right][/tex]
Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.
Answer: below
Step-by-step explanation:
Related Questions
This is due today, please help!!! I will give brainliest.
Answers
Answer:
Step 1, all the exponents are increased by 4
Step-by-step explanation:
The first incorrect step occurred in Step 1, where all the exponents were increased by 4.
This is mathematically incorrect due to exponential rules. When distributing exponents inside parentheses, we have to multiply the existing exponents inside the parentheses by the exponent outside the parentheses.
For example, (x²)³ is not x²⁺³, but rather, x⁽²⁾⁽³⁾.
We multiply the exponents instead of adding them together.
Therefore, the correct Step 1 should multiply all the variables' exponents by 4.
Steps 2 and 3 are correct since we do add the exponents when multiplying exponents with the same base, and we do subtract exponents with the same base when dividing.
2 times what gives you 7
Answers
Answer:
You cannot do 2 times whatever number because 7 is an odd number, whilst numbers getting multiplied by 2 are always even
Step-by-step explanation:
Hope this helps!!!!!
(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
Answer:
nothing!
unless you mean 1 x 7 or 7 x 1
Step-by-step explanation:
Write an equation of the line that passes through the given points.
(2,6) (-4,-2)
Answers
Answer:
y = 8/6x + 10/3
Step-by-step explanation:
You find the slope (m) first which is
Change of y over change of x
(6) - (-2) over (2)- (-4)
8/6 = m
Then you plug it into the equation y = mx + b
y = (8/6)x + b
Now you pick any of the set of points to plug in for x and y to solve for b
(6) = (8/6)(2) + b
6 = 8/3 + b
b = 10/3
Then plug into the equation for just m and b to get the equation of the line that passes thru both sets of points.
y = 8/6x + 10/3
Write an equation of a line in slope-intercept form with the given slope and y-intercept. slope: 2/3, y-intercept: −5
Answers
What is the value of p2 + r3 , when p=2 and r=3
Answers
Answer:
13
Step-by-step explanation:
(2)2 + (3)3 = 4 + 9 = 13
Answer: 31
Step-by-step explanation:
(4) 4 + (3) 3
P2 - 2 x 2
= 4
R3 - 3 x 3 x 3
= 27
27 + 4
= 31
Hope it helps!
Ava's family has completed 40% of their road trip. They have traveled 72 miles. How many miles is the trip?
Answers
Answer:
180 miles
Step-by-step explanation:
if you divide 72 by 4 you can see what 1/10 of the trip is, which is 18. 18 times 10 (since 18 is one tenth of it) equals 180. hope this helps!
Using addition, subtraction, multiplication, division, exponents, grouping symbols, and at least one positive and negative number, make an expression equal to 10 (no repeating numbers)
Answers
Answer:
2 + 3 (1) + (10 / 5)^2 + 7 - 6 = 10
Step-by-step explanation:
2 + 3 (1) + (10 / 5)^2 + 7 - 6
= 2 + 3 + (2)^2 + 7 - 6
= 2 + 3 + 4 + 7 - 6
= 10
what is the area of 4 1/2 feet wide and 6 1/2 feet long
Answers
Answer: 29 1/4
Step-by-step explanation:
Multiply and simplify to 29 1/4
Item 6 A rectangular prism has a length of 8 meters, a width of 4 meters, and a height of 5 meters. Which equations could be used to determine the volume, V, of the prism? Select each correct answer. V = 12 × 5 V = 5 × 4 × 4 V = 8 × 4 × 5 V = 32 × 5
Answers
Answer:
I am 100% sure that the answer is 240.
Step-by-step explanation:
The volume of the prism is 160 m³ and the correct equation is V = 8 × 4 × 5.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
The length, width and height of the rectangular prism are given as 8m, 4m and 5m respectively.
Since, the volume of the prism is given as the product of its length, width and sides.
For the given prism the volume can be obtained as,
V = 8 × 4 × 5
⇒ V = 160 m³
Hence, the correct equation is given as V = 8 × 4 × 5.
To know more about linear equation click on,
https://brainly.com/question/11897796
#SPJ5
A manufacture of spark plugs how's it going producing less than 2% affective ones. Of the last 8000 spark plugs, 13 were defective. a. What is the experimental probability that the next sparkplug will be defective? b. Did the manufacture reach his goal? Explain.
Answers
Answer:
P = 0.001625
yes, it did
Step-by-step explanation:
given data
affective ones = 2%
spark plugs = 8000
defective = 13
to find out
experimental probability that the next sparkplug will be defective and Did the mannufacturer reach its goal
solution
we know that there are 13 are defective out of 8000
so P = 13 ÷ 8000
P = 0.001625
so that P( the next sparkplug will be defective) is = 0.001625
and
yes, we mannufacturer to reach goal
because 0.001625 < .02
So, the goal is reached as the experimental probability is less than 2%
A new app charges an annual fee plus an additional fee per new game downloaded. The table shows the linear relationship between the number of new games downloaded and the total cost including the annual fee. Which statement is true?
A.
The additional fee per game is $10.
B.
The additional fee per game is $1.99.
C.
The annual fee is $1.99.
D.
The annual fee is $19.99.
Answers
The correct answer is below:
16-2k=14. what is the value of k
Answers
Answer:
k = 1
Step-by-step explanation:
16 - 2k = 14
- 16 - 16
-2k = -2
-2 -2
k = 1
Divide -2 on both sides. k = 1
Write an equation of the line that passes through (0,5) and (4,5).
plssss
Answers
A 4-ounce serving of yogurt has 8 grams of protein. How many grams of protein are in a 16-ounce serving container of yogurt? *
Answers
Answer:
16/4 = 4
4 * 8 = 32
32 grams in a 16 ounce serving
Answer:
32 grams of protein
Step-by-step explanation:
We know that 8 is double of 4, which means that if you have 16 ounces you are going to multiply by 2 to double it, which gives you 32.
a car uses 8 gallons of gas to travel 290 miles. how much gasoline will the car use to travel 490 miles
Answers
Answer:
11.03
Step-by-step explanation:
To find this answer, you would need to find how many miles 1 gallon of gas will take them. To find this, you would do 290÷8=36.25. So with this information, you will be able to find out how much gas it would take to travel 400 miles. You would do 400÷36.25=11.03. 11.03 would be how many gallons of gas is used to travel 400 miles.
Can someone help me solve all of these problems for brainliest and a heart? please and thank you!
Answers
Answer:
Top Right Problem: PACKAGE #2 and $0.80
Bottom left: BAND and $0.05
Bottom Right: PEPSI and $0.05
What is the absolute value of -3?
A. -3
B. 3
Answers
Answer:
B. 3Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&if&a\geq0\\-a&if&a<0\end{array}\right[/tex]
Examples:
[tex]|3|=3\ because\ 3\geq0\\\\|-10|=-(-10)=10\ because\ -10<-\\\\|0|=0\ because\ 0\geq0\\\\|-0.5|=-(-0.5)=0.5\ because\ -0.5<0\\\\|-1,000|=1,000\ because\ -1,000<0[/tex]
Your question:
[tex]|-3|=-(-3)=3\\\\|-3|=3[/tex]
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 7. If there were 6936 total votes, how many no votes were there?
Answers
Answer:
4046
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
What are four ways to represent functions?
Answers
A function can be represented algebraically. For example, 3x+6 3 x + 6 .
A function can be represented numerically.
A function can be represented graphically.
A function shows the relationship between at least two variables. There are several ways to represent a function; some of them are:
Using tablesUsing equationsUsing graphsBy verbal expressionsTables
The following table shows the relationship between two variables x and y
[tex]\left[\begin{array}{cccccc}x&1&2&3&4&5\\y&2&4&6&8&10\end{array}\right][/tex]
Equations
Notice that the y values of the above table are twice the corresponding x-values.
So, the equation can be represented as:
[tex]y = 2x[/tex]
Graphs
See attachment for the graph of [tex]y = 2x[/tex]
Verbal
As stated above, the value of y is twice the value of x.
The above statement is a verbal representation of a function
Hence, a function can be represented with a table, graph, equation and verbally.
Read more about functions at:
https://brainly.com/question/6241820
what is 3a + 2b - 6c
Answers
Answer:
Step-by-step explanation:
a = 3
b = 2
c = 12
3a+2b-6c
3(3)+2(2)-6(12)
-59?
A_______consists of an infinite number of points which form a flat surface that extends in all
directions forever.
A) Line
B) Plane
C) Point
D) Line segment
Answers
Answer:
that is the definition of a PLANE
Step-by-step explanation:
FUNCTION LOVERS?? Can u send a pic with all this pla
Answers
Answer:
uhhh
Step-by-step explanation:
GIVING OUT BRAINLEST
WY is the perpendicular
bisector of XZ.
What is X= ?
Answers
Answer:
x = 8
Step-by-step explanation:
Since the statement is true, then XY and ZY are the same length. You can set them to equal each other.
[tex]XY = ZY[/tex]
[tex]2x + 3 = 3x - 5[/tex]
[tex]3 = x - 5[/tex]
[tex]8 = x[/tex]
[tex]x = 8[/tex]
Hope this helps!
Figure A is a scale image of Figure B.
16
10
Figure A
12.5
Figure B
What is the value of x?
Answers
Answer:
20
Step-by-step explanation:
I got it correct on khan
Opposites
"Problem #1:
a. How would the frog hop to meet the following requirements?
• From 6, make one hop and land on 8.
• From 8, make one hop and land on the opposite of 8.
• From the opposite of 8, make one hop to land on the opposite of the
opposite of 8.
Answer:
How could you write the opposite of the opposite of 8" using math symbols?
Answer:
Answers
Answer:
opposite of 8 is -8 and the opposite of -8 is 8 :D
A customer paid 9x + 11y dollars for a bag that contains x pounds of chocolate and y pounds of almonds.
Which statements about the expression are true?
Select the three statements that are true.
The amount the customer paid, in dollars, for the chocolate in the bag is 9x.
O The amount the customer paid, in dollars, for the chocolate in the bag is 11y.
The total weight of the bag of chocolate and almonds is 9x + 11y.
The total weight of the bag of chocolate and almonds is x + y.
The cost per pound of the chocolate is $11.
The cost per pound of the almonds is $11.
Answers
Answer:
*The amount the customer paid, in dollars, for the chocolate in the bag is 9x.
*The total weight of the bag of chocolate and almonds is x + y.
*The cost per pound of the almonds is $11.
Step-by-step explanation:
A customer paid 9x + 11y dollars for a bag that contains x pounds of chocolate and y pounds of almonds.
From the above questions, we know that:
The weight of Chocolate = x pounds
The weight of Almonds = y pounds
The cost per Chocolate = $9
The cost per Almonds = $11
Therefore, the three statements that are true are:
* The amount the customer paid, in dollars, for the chocolate in the bag is 9x.
* The total weight of the bag of chocolate and almonds is x + y.
*The cost per pound of the almonds is $11.
HELP PLZZZZZ AS SOON AS POSSIBLE GEOMETRY WITH EXPLANATION
Answers
Answer:
34.06°
Step-by-step explanation:
25 is the length of the hypotenuse side and 14 is the length of the opposite side.
Therefore, you will need to use sine to work out the missing angle.
sinx = opp / hyp
sinx = 14 / 25
x = sin ^ -1 (14 / 25)
= 34.06°
A company rents out 16 food booths and 23 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The fee for a game booth is $95 plus $5 per dat. The fair lasts for d days, and all the booths are rented for the entire time. What is the simplified expression for the amount, in dollars, that the company is paid.
Answers
Answer:
3785 + 259d
Step-by-step explanation:
cost of food booths = 16 * (100 + 9d) = 1600 + 144d
cost of game booths = 23 * (95 + 5d) = 2185 + 115d
total = 1600 + 2185 + 144d + 115d = 3785 + 259d
Someone please answer this for me ASAP
Answers
Answer:
m=-1/2
Step-by-step explanation:
8. Over a period of 3 hours, the outside temperature changed an average of -2.25 Fahrenheit per hour. Which statement correctly describes the change in the temperature from the beginning to the end of the 3 hour period?
a. The temperature decreased by 0.75 degrees Fahrenheit.
a. The temperature decreased by 0.75 degrees Fahrenheit.
b. The temperature increased by 0.75 degrees Fahrenheit.
b. The temperature increased by 0.75 degrees Fahrenheit.
c. The temperature decreased by 6.75 degrees Fahrenheit.
c. The temperature decreased by 6.75 degrees Fahrenheit.
d. The temperature increased by 6.75 degrees Fahrenheit.
Answers
Answer:
c
Step-by-step explanation:
-2.25*3 = 6.75 decreased (since negative)