Answers
Answer:
For a function y = f(x), the domain is the set of the possible values of x that we can input, while the range is the set of the possible outputs of the function.
In this case we gave y = f(x) = (1/3)^x
A) Domain
To see the domain we always start assuming that the domain is the set of all real numbers, and then see if there is a real number that causes any problem.
(for example if we had a denominator like "x - 2", the point x = 2 would cause problems because it would make the denominator equal to zero, and we can not divide by zero)
Particularly because x is the exponent, we do not have any problem here, so the domain is the set of all real numbers:
D: = R
B) Range.
To find the range we usually need to find the smallest value of the function.
Here we have:
y = (1/3)^x
Is really easy to see that as x increases, the denominator increases but the numerator remains the same, then as x increases, the value of y decreases.
For example for x = 100 we will have:
y = 1/3^100 ≈ 0
(you also can see that y will never be a negative value, and as x increases the value of y tends to zero)
then:
0 < y
And if we have x negative, like x = -3 for example.
y = (1/3)^-3 = (3/1)^3 = 3^3 = 27
So if x decreases (or increases in the negative value) then the value of y increases, so we do not have any upper limit.
Then the range is only defined by
0 < y.
We can write the rane as:
R: (0, ∞)
C) The y-intercept is the value of y when x= 0
y = (1/3)^0 = 1
(for any number different than zero N, we have that N^0 = 1)
the y-intercept is 1
D) The asymptote is a tendency to a given value, such that the function never does reach that value.
Here we have two asymptotes.
y tends to infinity as x tends to negative infinity.
y tends to zero as x tends to infinity.
Related Questions
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Answers
Answer:
Anderess?
Step-by-step explanation:
Shanti is making a patchwork quilt. Each piece of fabric has a black star on it. She uses the grid shown to plan the locations of the different fabric squares.
a. What transformation maps square 1 onto square 2?
b. What transformation maps square 2 onto square 3?
c. What transformation maps square 1 onto square 5?
Answers
Answer:
A) Translation
B) Reflection
C) Rotation
Step-by-step explanation:
The transformation types in mathematics are;
Reflection, translation, rotation and dilation.
We can see that the squares are all the same size, it's just the position of the stars that will aid us in knowing the specific transformation.
A) We can see that square 2 is the exact same thing as square 1. Just that it was shifted to the right of square 1. Thus, it was translated and the transformation is translation.
B) We can see that the star in square 3 is the exact mirror copy and location from square 2. Thus, this is a reflection.
C) We can see that the position of the star in square 5 is top while that in square 1 is at the left corner. This can only be achieved by rotation.
1. Write a similarity statement if the triangles are similar
2. If the traingles are similar, state the triangle similarity postulate (shortcut) you used to prove similarity.
U
36
73
30
15
D
E
Answers
Answer:
The triangles are not similar
Step-by-step explanation:
The sides are not proportional
36/73 does not equal to 15/30
help me please aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
-2 - 2 = v/4
-4 = v/4
-4•4 = v
v = -16
Answer:
v=-16
Step-by-step explanation:
-2=2+v/4
(we know that 2+-4=-2 so we can see if that works)
(4*-4=-16)
2+-16/4=-2
(-16/4=-4)
2+-4=-2
What is the Surface Area of the figure below?
A. 268 square inches
B. 134 square inches
C. 21 square inches
D. 240 square inches
Answers
Answer:
34.98 yds²
Step-by-step explanation:
To find surface area, we add together the area of each side. We have six sides, but there are three sets of identical sides, so it's easier to calculate.
We begin with the sides with dimensions 2.40 and 2.50. Multiply these together.
2.40 · 2.50 = 6
Since there are two of these sides, we can already say that the combined area of them is 12. So, we start the equation with 12.
Next, the two sides with dimensions 2.34 and 2.50. Multiply these together as well, to get 5.85. Multiply this by two to find the area of both sides, 11.7.
Add to our equation, for 12 + 11.7.
For the final two sides, we have the dimensions 2.34 and 2.40. Multiply to get 5.64. Multiply this again by two to find the area of both sides. We get 11.28. Add this to the equation as well, for 12 + 11.7 + 11.28= 34.98.
The answer is 34.98 yds². Good luck :)
At a recent charity event there was a range of admission charges:
Family (2 Adults + 2 Children)
Adult
Senior
Child (5 to 16 years)
Child under-5
$44
$14
$12
$10
Free
In addition it was possible to buy Family tickets before the event at the reduced cost of $40 per
family.
At the gate tickets to the value of $40 000 were purchased, and prepaid tickets added a further
$10000 to the total income. For every Family ticket sold on the day, 1 Adult, 1 Senior, and 3 Child
tickets were sold and 2 under-5 children were admitted free of charge.
How many people attended?
A
B
c
4400
4600
4650
5400
Answers
Answer:
5400
Step-by-step explanation:
Given data
Family (2 Adults + 2 Children) = $44
Adult = $14
Senior = $12
Child (5 to 16 years) = $10
Child under-5 = Free
At reduced price family buys ticket at = $40
Total prepaid ticket sold = $10,000
Value of ticket sold at the gate = $40,000
Determine how many people attended
first step : determine number of family that purchased the prepaid tickets
= 10,000 / 40 = 250 families
∴ number people who booked prepaid tickets = 250 * 4 = 1000 people
Next step : Determine the number of families that booked the ticket at the gate
let the number of families = y
40,000 = 44 y + 12y + 3y * 10 + 14y + 2y *0
40,000 = y ( 100 ) hence y = 40,000 / 100 = 400
∴ number of people = 400 * ( 4 + 1 + 1 + 3 + 2 ) = 400 * 11 = 4400
Number of people whom attended = 4400 + 1000 = 5,400
(2r^2t ^3)^2
4t^2
explain what you would do first to simplify the expression below.
Answers
Answer:
first expand the brackets
4-
2-
р
911) =
-1 – 3+ 4
0
-4
- 2
2
4
-2-
On which interval are both functions increasing?
O
1-2
3
4
0
-
c)
Answers
Answer:
Step-by-step explanation:
To get the correct answer, you can count the total number of shaded tenths and the total number of shaded hundredths and then regroup.
There are 9 shaded tenths and 18 shaded hundredths. Regroup 10 hundredths into 1 tenth to get 10 tenths and 8 hundredths. Then regroup the 10 tenths in one whole, giving you 1 whole and 8 hundredths. The product is 1.08.
Another way to get the answer is to count the total number of shaded hundredths. There are 108 hundredths. Regroup 100 of them as one whole, giving you 1 whole and 8 hundredths.
Brainliest to answer this math question<33
Answers
Answer:
the . ans 15, 20
Can someone please answer with explanation
Answers
Answer:
This percent is a decrease
11 people quit
Step-by-step explanation:
PLEASE HELP DUE TODAY GIVING BRAINLIEST
Answers
Answer:
(3, 3)
Step-by-step explanation:
AYUDAAAAA!!!
Partes de una cantidad
Es para hoy en la tarde porfis:-|
Answers
Answer:
I don't speak Spanish sorry༼ つ ◕_◕ ༽つ/_ \
Solve for x and show your work! For each equation choose if there are:
• zero solutions for x • exactly one solution for x • or an infinite number of solutions for x.
2(3x + 9) = 18 + 6x
Answers
Answer:
Infinite number of solutions
Step-by-step explanation:
Use the distributive property
2 x 3x = 6x
2 x 9 = 18
6x +18 = 18 + 6x
Answer: infinite solution
PLZS ANSWER BY TODAY!
Answers
Step-by-step explanation:
Buh fr buh
There are eight boys and six girls who are members of the trumpet section in the band. From the members of the trumpet section, a quintet is being formed. If the quintet must consist of three boys and two girls, how many quintets are possible?
Answers
Answer:
8 c 3 * 6 c 2 = 56 * 15 = 840 ways
Step-by-step explanation:
First, we consider how many ways there are to choose three boys from eight. There are 8 choices for the first boy, 7 for the second, and 6 for the third. However, because the boys are indistinct from one another, we have overcounted, and must divide by 3*2. Similarly, there are 6*5 ways to choose the two girls, divided by 2 for overcounting. Thus, there are (8*7*6*6*5)/(3*2*2)=840 possible quintets.
hey please help me with this ty
Answers
Answer:
3d
Step-by-step explanation:
3 miles per day
if he runs for two days he runs 6 miles 3(2)
etc etc
Greg bought a jacket for $35.23, a flag for $10.75, and a baseball cap for $17.25. He paid $50 and
the rest he borrowed from his friend. If Greg got $6.77 in change from the cashier, how much did he
borrow from his friend to pay for all the items?
Answers
Answer:
His friend gave Greg a 20$ bill.
Step-by-step explanation:
35.23+10.75+17.25=63.23
63.23-50= 13.23
13.23+6.77= 20
Answer:
He borrowed $6.46
Step-by-step explanation:
Add the totals up together. 35.23 + 10.75 + 17.25 to get 63.23
Subtract 50 from 63.23 (63.23 - 50.00) to get 13.23.
Subtract 6.77 from 13.23 (13.23 - 6.77) to get 6.46.
He borrowed $6.46 from his friend!
Hope this helps! Pls make brainliest
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Answers
Answer:
Steps To Find The Distance Between Two Planes
Write equations in standard format for both planes.
Learn if the two planes are parallel.
Identify the coefficients a, b, c, and d from one plane equation.
Find a point (x1, y1, z1) in the other plane.
Substitute for a, b, c, d, x1, y1 and z1 into the distance formula.
Step-by-step explanation:
What is the greatest common factor of 36x^3-
9x² +18zy^2??
Answers
Answer:
9.
Step-by-step explanation:
The GCF of 36, 9 and 18 = 9
The GCF of x^3, x^2 and zy^2 = 1
So the answer is 9 * 1.
Answer:
9
Step-by-step explanation:
i
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.(Quadratic Word Problems (Profit/Gravity)
y=-16x^2+121x+83
Answers
Answer:
The rocket will hit the ground after about 8.20 seconds.
Step-by-step explanation:
The height of the rocket y, in feet, x seconds after launch is modeled by the equation:
[tex]y=-16x^2+121x+83[/tex]
We want to find the time at which the rocket will hit the ground.
If it hits the ground, the height of the rocket y will be 0. Thus:
[tex]0=-16x^2+121x+83[/tex]
We can solve for x. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 121, and c = 83. Substitute:
[tex]\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}[/tex]
Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:
[tex]\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}[/tex]
Therefore, our two solutions are:
[tex]\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63[/tex]
Since time cannot be negative, we can ignore the second solution.
Therefore, the rocket will hit the ground after about 8.20 seconds.
What value of x makes the equation true?
3 - 14x = 17
A-1
B-1
C-28
D-2
Answers
Answer:
3 -14x =17
-14x = 17 - 3
-14x = 14
x = 14/-14 = 1/-1 = -1
∴ answer = -1
hope this answer helps you.....
please mark as brainliest... thank you!
Here is an expression. Evaluate the expression: *
3.4 + 4
Answers
Answer:
the answer would be 3.4 + 4 = 7.4 .
Answer:
the answer would be 3.4 + 4 = 7.4 .
Step-by-step explanation:
PLEASE HELP FAST 15 POINTS ANDWER IF YOU ONLY KNOW!
Answers
Answer:
i can see the question in ascending order
PLEASE HELP!!!!! WORTH 40 POINTS
Answers
Answer:
B : 3/2
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
answer is B. i think so...
[tex] \frac{54}{36} = \frac{3}{2} [/tex]
have a nice day
What’s the answer????
Answers
Answer:
X = 9
Step-by-step explanation:
find the value of x and y
Answers
Answer:
It's hard to make out which is x and y, if x is lower right and y is at the top, then:
x = 55°
y = 70°
Step-by-step explanation:
x = 55° because it is an isosceles triangle
y = 180° - 55° - 55° = 70°
HELP PLS ASAP PLS PLS DUE SOON
Answers
Answer:
blank 1: 63 degrees
heart if it helped!
Based on the sample results, about what percent of
the population prefers reading a hard copy?
about 21%
SAMPLE RESULTS
about 16%
DO YOU PREFER TO READ A
HARD COPY OR A DIGITAL
COPY WHEN READING BOOKS,
MAGAZINES, AND/OR
NEWSPAPERS?
about 84%
digital copy: 4
hard copy: 21
n = 25
about 50%
0
-
su come
000
115 Complete
1:11 PM
Answers
Answer:
84%
Step-by-step explanation:
Given that :
Number that prefers digital copy = 4
Number who prefers hard copy = 21
Total number of samples =
(digital + hard copy) = 25
Percentage who prefers hard copy :
(Number who prefer hard copy / total number of samples) * 100%
(21 / 25) * 100%
0.84 * 100%
= 84 %
Please help me it’s due soon!!
Answers
Answer:
12√2
Step-by-step explanation:
It's 12√2 because the hypotenuse of the triangle is 12. that means for a^2 + b^2 = c^2, we get c^2 = 144. a and b are equal so the answer is 6√2.
Also, don't any links you see on this site, they are hackers
HELP ME PLZZ: Francesca is making a scale drawing of the mural on a wall in her school's hallway. The mural is 12 ft high and 135 ft long. She is using a sale of 3 cm for every 4 ft. What are the dimensions of her scale drawing?
Answers
Answer:
i think ur supposed to do 135 divided by 3?
Step-by-step explanation:
tell me if im right or wrong so then i can help
The height of the mural drawing is 9 inches while the length is 101.25 inches.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Hight of the mural = is 12 feet
⇒ 12 × 12 = 144 inches.
Length of mural = 135 feet
⇒ 1620 inches.
Now,
She is using 3 cm for every 4 feet(4×12 = 48 inches)
Scale factor = 3/48 = 1 : 16
Now,
Length of mural drawing = 144/16 = 9 inches.
Height of mural drawing = 1620/16 = 101.25 inches.
Hence "The height of the mural drawing is 9 inches while the length is 101.25 inches".
To learn more about scale factors,
brainly.com/question/22312172
#SPJ2