To determine if the function t : R^2 → R^2, given by t(x, y) = (4x, y), is one-to-one and/or onto, we need to consider the properties of injectivity (one-to-one) and surjectivity (onto). Answer : the function t(x, y) = (4x, y) is both one-to-one and onto.
(a) One-to-one: A function is one-to-one if each element in the domain maps to a unique element in the codomain. In other words, if t(x1, y1) = t(x2, y2), then (x1, y1) = (x2, y2).
For the given function t(x, y) = (4x, y), we can see that if (x1, y1) = (x2, y2), then (4x1, y1) = (4x2, y2). From this, we can conclude that x1 = x2 and y1 = y2, which means that the function is one-to-one. Thus, option (a) is correct.
(b) Onto: A function is onto if every element in the codomain has a pre-image in the domain. In other words, for every (a, b) in the codomain, there exists an element (x, y) in the domain such that t(x, y) = (a, b).
For the given function t(x, y) = (4x, y), we can see that for any (a, b) in the codomain, we can choose x = a/4 and y = b, and we will have t(x, y) = (4(a/4), b) = (a, b). This shows that every element in the codomain has a pre-image in the domain, and thus the function is onto. Therefore, option (b) is also correct.
In summary, the function t(x, y) = (4x, y) is both one-to-one and onto.
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Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?
Answer:
3 times as many pounds
Step-by-step explanation:
7.2 / 2.4 = 3 times as many pounds
Hope that helps!
Daniel wants to know the volume of his cube. He notices that the cube 1/5 centimeters side lengths. What is the volume of the cube?
Answer:
1/125 cm^3
Step-by-step explanation:
Given data
Length of one side = 1/5cm
Required
The volume of the cube
We know that
V= l^3
substitute
V= (1/5)^3
V= 1/125cm^3
Hence the volume is 1/125 cm^3
Solve this equation
12y = 30
Answer:
hI!!
Y = 5/2
Step-by-step explanation:
Let's solve your equation step-by-step.
12y=30
Step 1: Divide both sides by 12.
12y/12 30/12
Your garden has 9 pots that use 2 1/3 bag of soil. How much soil does each pot hold?
Answer:
2 6/7
Step-by-step explanation:
i divided
Kiran's family took a road trip to Niagara Falls. Kiran slept through the last 62% of the trip. If the total length of the trip was 1000 miles, how many miles had they traveled when Kiran fell asleep?
Answer:
380 miles
Step-by-step explanation:
First, find 62% of 1,000:
1,000 • .62 = 620 miles
Next, subtract 620 from 1,000:
1,000 - 620 = 380 miles
The family had traveled 380 miles before Kiran fell asleep
A company has 200 employees there are 150 female employees. 40 employees are under the age of 20. The probability of randomly selecting an employee who is female or is under the age of 30 is 85%. What is the probability of randomly selecting an employee who is female and under the age of 30?
Answer and explanation:
Probability= number of favorable outcomes/ total number of outcomes
Probability of selecting an employee who is female= number of female employees/ total number of employees
Probability of selecting an employee who is female= 150/200
Probability of selecting an employee who is under 30= number of employees under 20/ total number of employees
Probability of selecting an employee who is under 30 = 40/200
Probability of randomly selecting an employee who is female and under the age of 30= Probability of selecting an employee who is female × Probability of selecting an employee who is under 30
Probability of randomly selecting an employee who is female and under the age of 30= 150/200×40/200=15/20×4/20=3/20= 0.15
Therefore there's a 15% chance of selecting an employee who is female and under the age of 30
Which equations are correct?
Select each correct answer.
−4b3(5b2+3)=−20b6−12b3
−6y4(4y2+2)=−24y8−12y4
−5a4(2a2+4)=−10a6−20a4
−4x2(2x2+5)=−8x4−20x2
All movies until 4:00 PM require a discount tiket, and all the movies after 4:00 Pm require a regular -price ticket. Each theater at the movieplex seats 98 people. What is the least number of showings the theater could have shown after 4:00 PM last saturday?
Answer:
4 shows
Step-by-step explanation:
The theater has 7 cinemas and all of them has capacity of 98 seating. The theater offers discount before 4.00 and there it runs 3 shows before 4 pm in each cinema, after 4.00 pm the theater has capacity of running 4 more shows in each cinema without discount on the tickets.
In ΔRST, the measure of ∠T=90°, TS = 65, SR = 97, and RT = 72. What ratio represents the cotangent of ∠S?
Answer:
65/72
Step-by-step explanation:
Given that ∠T=90° then the triangle ΔRST is a right angled triangle. Considering ∠S, RT is the opposite side, TS is the adjacent side and RS is the hypotenuse side. Using the notation
SOH CAH TOA
Tan ∠S = 72/65
Hence the cotangent of ∠S which is the inverse of the tangent will be
= 65/72
Tonya and Mario are asked to use a pan balance to find the mass of the same rock. Tonya finds the rock's mass to be 680 grams. Mario finds the rock's mass to be 672 grams. Which is the best explanation for the difference in their measurements?
A. Either Mario or Tonya measured the mass of the rock incorrectly on the pan balance.
B. The rock was cold when Tonya measured its mass and hot when Mario measured in mass.
C. The rock changed in size between the time Tonya measured it and the time Mario measured it.
D. The rock broke before Mario measured it. So the mass of the two pieces together was less than when Tonya measured it. PLEASEEEE HELPPP
the base of a rectangular prism has an area of 1 over 8 ft2 and the height of the prism is 2 over 3 ft. what is the volume of the prism?
Answer: the volume is 1/12 ft³
Step-by-step explanation:
Multiply the area of the base times the height:
1/8 × 2/3 = 2/24 or 1/12
the ft² times ft becomes ft³
So the volume is 1/12 ft³
3/11 as a decimal equivalent
Answer:
The decimal form for this is 0.27 (With a line on top of it.)
Step-by-step explanation:
See this image:
The right triangle below has legs of length and.
The hypotenuse has length.
Four copies of this triangle are arranged as follows.
The hypotenuses form a square of side length and area.
Answer the questions below to find how, and are related.
Part 1: Compute the total combined area of the four triangles:
Part 2: Compute the area of the large (outer) square:
Part 3: Using your answers in Parts 1 and 2, find the area of the small (inner) square.
Part 4: We are given the side lengths and. Compute.
Part 5: Use, or complete the statement below.
Answer + explanation:
Part 1: First, find the area of one triangle using the formula base * height / 2. You have base = 10 and height = 7, so area = 7 * 10 /2 = 70/2 = 35. Since you're finding the combined area of 4, you have to do 35 * 4 = 140.
Part 2: To do this, find the side length of the square. Looking at the picture, you see that all you have to do is 10 + 7 = 17 to find one side. Then, to find the area do 17 * 17 = 289.
Part 3: To find the area of the small square, all you do is area of the large square - combined area of 4 small triangles, so 289 - 140 = 149.
Part 4: a^2 = 7 * 7 = 49. Then, b^2 = 10 * 10 = 100. Adding them together, you get 100 + 49 = 149.
Part 5: Since you already have the a^2 + b^2 part, all you need to do is find what c^2 is. You can see in the picture that c^2 equals the area of the small square, which you found in part 3. c^2 = 149. Then, you have 149 and 149, which are equal so the answer is =.
PLEASE HELP FAST ANSWER ONLY 1 through 3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. 13n+15
2. 12n+18
3. 18n+12
aye anyone please help me with my math its really easy 9th grade I just figure out part of this question !!! please help
Answer:
hope this helps!
Step-by-step explanation:
Find the length of AD if AB = 24, DE = 8, and DC = 12.
a.8
b.12
c.14
d.10
HELP PLS
Answer:
AD = 12
Step-by-step explanation:
Find the diagram attached
From the given diagram, it can be inferred that;
AB = AD+DB and AD = DB
AB = AD + AD
AB = 2AD
AD = AB/2
Given that AB = 24
AD = 24/2
AD = 12
Hence the length of AD is 12
Answer: 10
Step-by-step explanation:
I got it right after trying the answer of 12 on CAOLA
which equation has a solution x= -3
A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x + 8 = 10
D) 1/2(2x - 6) = -6
Answer:
D
Step-by-step explanation:
1/2 ( 2x - 6) = -6
1/2 = 0.5
0.5(2x-6) = -6
1x-3=-6
1x=-6+3
x=-3/1
x=-3
can someone explain how to solve this please my midterms tomorrow! :)
Answer:
Step-by-step explanation:
What’s the volume of this cube?
Answer:
Formula: V = a^3
a = 2in
Input: V = a^3 = 2^3 = 8
Step-by-step explanation:
Convert the decimal below to a fraction in simplest form. 0.689
Answer:
689 / 1000 is the answer
Step-by-step explanation:
zzzzzzzzzzzzz
Help Please........
Answer:
4
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
(4 x 2)/2 + (4 x (6-2))/2 = 12
I NEED HELP WITH THESE ASAP!
Answer:
I can not see it
Step-by-step explanation:
If two quantities x and y are in direct proportion, then ----------.
Answer:
x/ y = k
Step-by-step explanation:
It can also be written in forms like-
x= ky
y= x/ k
-------------------
x/y = k
(here k is constant )
help me please I need help
Answer:
D) 6 in x 4 in
Step-by-step explanation:
3" x 2" scaled up to 1:20 would be 60" x 40"
60" x 40" scaled back to 1:10 would be 6" x 4"
also the scale factor 1:20 is double the scale factor of 1:10
Transform to slope-intercept form. 1+2y=6x-3
Answer: Y=3X-2
Step-by-step explanation:
First you are gonna need to combine all like factors.
1+2y=6x-3 (subtract 1 from both sides)
2y=6x-4
Then you need to get the y by itself.
2y=6x-4 (divide all terms by 2)
y=3x-2
now you are in slope intercept form (y=mx+b)
Please help due today
Answer:
It's gotta be either A or B because C and D don't even make up a square.
I believe that it's one of those ( A or B).
Step-by-step explanation:
Sorry I couldn't help you all the way through to the answer. Hope this helps though! :)
You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. What floor do you get off the elevator?
Answer: (B) 6 floors
Step-by-step explanation: Use the equation -3 + 9 to get the amount of floors above ground level.
-3 + 9 = 6
6 floors.
If this helps may I please have a brainliest.
Answer:
you would get off at the 9th floor because in order to reach ground level again your would already go up 3 of the 12 floors. leaving 9 floors left to go up.
Step-by-step explanation:
-3+12=9
Which polynomial represents the difference below?
2x +7X+6
(3x? – X
A. - x + 6x + 6
B. 2x2 + 4x + 6
c. 2x2 + 5x + 6
D. - x2 + 3x + 6
Answer:
-x²-8x+6
Step-by-step explanation:
Given the polynomial expression
2x²+7x+ 6 and 3x² – X
Taking their difference
2x²+7x+ 6 - (3x² – X)
2x²-3x²+7x+x+6
-x²-8x+6
Hence the required difference is -x²-8x+6
Answer:
-x²+8x+6
Step-by-step explanation:
Ape-x
which one pls help me i’ll give extra points
Answer:
C
Step-by-step explanation:
Answer:
A. The doctors will give Charlie an operation
Step-by-step explanation:
A baseball player earns $3 million in 2015. During the next 15 years, the earnings increase 4% each year.
a. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal.
An exponential growth model is y=
b. In which year will the player's earnings first exceed $5,000,000?
Answer:
[tex]y=3*1.04^{t}[/tex]
in 2029
Step-by-step explanation:
[tex]y=3*1.04^{t}[/tex]
[tex]when y=5\\t=\frac{ln(5/3)}{ln(1.04)} =13.02 ..[/tex]
have to round it up to 14 to exceed