Answer:
In functions, there can be more than one of the same output, but there cant be more than one of the same input.
Step-by-step explanation:
Let's look at table A.
Input Output
4 3
3 2
3 1
We have two 3's for our input.
Let's take a different approach to this if you don't understand.
Let's imagine we have a vending machine.
If you press the number 2 you get Doritos
If you press the number 4 you get Sprite
Though if you press the number 3 you could either get Cashews or Cheetos. If you paid for the Cheetos and you get Cashews, that wouldn't be good; Its like a guessing game.
So, therefore Table A is NOT correct, as two of our input's are the same number.
Now let's look at Table B
Input Output
1 3
3 5
5 7
All of our input's are different, which is good. Let's imagine the vending machine again.
Pressing number 1 gives us Doritos
Pressing number 3 gives us Barbecue Chips
Pressing number 5 gives us Kettle Chips.
We get what we pay for, which means, in this equation, if you input is number 1, we will have number 3 as our output, ect.
This table IS correct.
I think you can apply this procedure to the other two tables to determine which one is right :)
Hope this helps, reach out if you need any more help!
The moped traveled 78 miles on 1.2 gallons of gas The moped averaged how many miles per gallon
The average miles per gallon is given by the equation A = 65 miles per gallon
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the average miles per gallon be represented as A
Now , the equation will be
The total distance moped = 78 miles
The amount of gallons of gas for 78 miles = 1.2 gallons
Now , average miles per gallon = total distance moped / amount of gallons of gas for 78 miles
Substituting the values in the equation , we get
The average miles per gallon A = 78 / 1.2
The average miles per gallon A = 65 miles per gallon
Therefore , the value of A is 65 miles per gallon
Hence , the equation is A = 65 miles per gallon
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I will be giving massive thanks for whoever answers this right. ^0^
- - - (It will seem hard, but it absolutely is not.) - - -
The equation y = 1.6x represents the number of laps Henry can swim over time, where y is the number of laps and x is time in minutes. This table shows the number of laps Larry can swim over time.
How many laps can each boy complete per minute, and who can swim laps at a faster rate? ;)
2. A skydiver jumps from a plane from an altitude of 6000 ft. An observer on the ground measures the skydiver’s altitude at time t = 0 to be 4500 ft. The linear graph shows the skydiver’s altitude at various times during her descent.
(a) Identify the y-intercept. How does the y-intercept relate to the skydiver’s position relative to the ground? Explain.
(b)Determine the slope of the line. According to the slope, is the skydiver ascending or descending and what is the rate of ascent or descent? Explain. (c) Identify the x-intercept. What does the x-intercept mean in this context? Explain. (d) Write an equation for the line.
a. The y-intercept of the linear graph is (0, 4500).
b. The rate of descent is 1500 ft per minute.
c. The x-intercept of the linear graph is (3, 0).
d. The equation for the line representing the skydiver's altitude during descent is y = 4500 - 1500x.
(a) The y-intercept of the linear graph is (0, 4500). In this context, the y-intercept represents the initial altitude of the skydiver when time [tex]\( t = 0 \)[/tex], which is 4500 ft above the ground. It indicates the starting point of the skydiver's descent relative to the ground.
(b) To determine the slope of the line, we use the formula for slope:
[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]
From the given points, we see that:
- Change in y = 4500 - 0 = 4500 ft
- Change in x = 0 - 3 = -3 minutes
Substituting these values into the slope formula:
[tex]\[ \text{Slope} = \frac{4500}{-3} = -1500 \text{ ft/minute} \][/tex]
Since the slope is negative, it indicates that the skydiver is descending. The rate of descent is 1500 ft per minute.
(c) The x-intercept of the linear graph is (3, 0). In this context, the x-intercept represents the time it takes for the skydiver to reach the ground, which is 3 minutes after jumping from the plane. At the x-intercept, the altitude of the skydiver is 0 ft, indicating that the skydiver has landed on the ground.
(d) The equation for the line can be written using the slope-intercept form:
[tex]\[ y = mx + b \][/tex]
where m is the slope and b is the y-intercept.
From the given information:
- Slope m = -1500 ft/minute
- y-intercept b = 4500 ft
Substituting these values into the slope-intercept form:
y = -1500x + 4500
Therefore, the equation for the line representing the skydiver's altitude during descent is y = 4500 - 1500x.
what is -4 4/5 ÷ 4 equal to
Of 24 students in class 8 said they have at least 2 siblings which ratio is equivalent to 8/24
The equivalent ratio to 8/24 is 1/3, which can be used to calculate that approximately 33.33% of students have at least 2 siblings. This demonstrates how to convert a ratio to a percentage by setting up a proportion with 100 as the denominator.
Explanation:The ratio 8/24 represents the portion of students in a class who have at least 2 siblings. To find an equivalent ratio, one could simplify the given ratio by dividing both the numerator and the denominator by the same number. In this case, both 8 and 24 are divisible by 8, so dividing both by 8 yields the equivalent ratio 1/3. This ratio can also be used to express the percentage of students with at least 2 siblings. The calculation would be (1/3) * 100 to find the percentage, which gives us approximately 33.33%.
To further illustrate calculating percentages using equivalent fractions, we can take the original ratio (8/24) and set up a proportion with 100 as the denominator. The equation would be:
8/24 = X/100
where X represents the percentage of students. To solve for X, cross-multiply and divide:
(8 * 100) / 24 = 33.33%
This confirms that 33.33% is the percentage of students with at least 2 siblings. It is important to note that simplifying ratios and working with equivalent fractions is a useful skill in understanding data representation in statistics and mathematics.
An angle turns through 60 one-degree angles. What is the measure of the angle?
An angle turns through 160 one-degree angles. What is the measure of the angle?
The measure of an angle is equivalent to the number of one-degree angles it turns through. Therefore, an angle that turns through 60 one-degree angles measures 60 degrees. Similarly, an angle that turns through 160 one-degree angles measures 160 degrees.
Explanation:In mathematics, when we say an angle turns through 60 one-degree angles, we mean the angle measure is 60 degrees. This means that counter-clockwise rotation that makes up this angle is equivalent to 60 one-degree angles. Similarly, if an angle turns through 160 one-degree angles, then the angle is 160 degrees.
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An angle turns through 60 one-degree angles, so the measure of the angle is 60 degrees. An angle turns through 160 one-degree angles, so the measure of the angle is 160 degrees.
Explanation:An angle turns through 60 one-degree angles. Since each one-degree angle is a small portion of the whole angle, dividing the whole angle into 60 equal parts gives us the measure of each one-degree angle. Therefore, the measure of the angle is 60 degrees.
An angle turns through 160 one-degree angles. Using the same logic as before, dividing the whole angle into 160 equal parts gives us the measure of each one-degree angle. Hence, the measure of the angle is 160 degrees.
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#3 is the tough one for me I get it but I don't can you help me and tell me how you got that answer as soon as possible.
The pineapple is seven times as heavy as an orange or pineapple also weighs 870 g videos in the orange what is the total weight in grams for the pineapple and orange
Three different ways to make 12
45/55 expressed as a percentage
evaluate 950,000+(4.6×10^7)
What equation is graphed in this figure?
A. y−4=−1/3(x+2)
B. y−3=1/3(x+1)
C. y+2 = −3(x−1)
D. y−5=3(x−1)
Bella is planning to write in her journal some pages will have two journal entries on them and other pages with three journal entries on them if Bello wants to make 18 entries how many different ways can she write them in her Journal
Victoria made some chocolate pudding. For every 2 cups of chocolate, she added 5 cups of milk. The ratio of chocolate to milk in Victoria's chocolate pudding is ____. (1 point)
2:5
because 2 cups of chocolate to 5 cups of milk the ratio would be 2:5 u can't put 5:2 because it's asking the ratio of chocolate milk to chocolate pudding not chocolate pudding to chocolate milk.
~PrinncessAngel~
Happy To Help:D
Answer:2:5
Step-by-step explanation:
3(m+3)=_m+_ write equivalent expressions in the blanks
a slug crawls 5.62 meters in 0.4 hours. what is the slugs speed in meters per hour?
The table shows masses of different types of nuts that Nathan buys. He plans to mix the nuts and then separate them into bags. Each bag will have 1.2 kg of nuts in it.
Write how many bags of mixed nuts Nathan can completely fill.
Nathan can completely fill a bag of mixed nuts by calculating the total weight of the nuts, then dividing that total by 1.2 kg, which is the weight of nuts per bag. Any decimal in the result would be rounded down to give the number of full bags.
Explanation:To determine the number of bags of mixed nuts Nathan can completely fill, you first need to calculate the total weight of all the nuts he bought. This is done by adding up the masses of all the different nuts mentioned in the table.
Let's assume that Nathan's total weight of nuts is 'T'. His plan is to fill each bag with 1.2 kg of nuts, thus the number of full bags he can make, denoted as 'B', is the total weight divided by the weight per bag. In other words, B = T / 1.2.
A key fact here is that this calculation will give a decimal if 'T' is not a multiple of 1.2. However, since he cannot create partial bags, you would round down any decimal to get the number of complete bags.
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use divisio to find all the whole number ratios equivalent to 56:24
Answer:
7:3
Step-by-step explanation:
When dividing 878 by 31 a student finds a quotient of 28 with a remainder of 11 check the students work and use the check to find the error in the solution
A bottle of water costs $1.50. Explain how you would make a graph of four ordered pairs to model the total cost of the water in terms of the number of bottles.
State whether the ratios form a proportion. 1/4 and 2/5 A. yes B. no
the wilsons drove 324 miles in 6 hours. if they drove the same number of miles each hour how many miles did they drive in 1 hour
if a tip of 15% is added to the food bill, what is the total on the food bill of $12.95
$14.89 its a correct answer
Test each set of equivalent ratios to find which set of values describes the proportional relationship of the two quantities.
40.5 ounces of nuts to 48.6 ounces of raisins
A) (5, 7)(60, 84)(47, 65.8)
B) (36, 48.6)(2, 2.7)(12, 16.2)
C) (3, 3.9)(65, 84.5)(24, 31.2)
D) (11, 13.2)(99, 118.8)(20, 24)
the correct anwser is b
Write a linear function f with f(-3) = 1 and f(13) = 5
Linear function f with f(-3) = 1 and f(13) = 5 is given by [tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex] and this can be determined by using the given data.
Given :
f(-3) = 1 and f(13) = 5.
The generalised linear function is given by:
f(x) = ax + b --- (1)
Now, it is given that (f(-3) = 1) that means at (x = -3) the above function is equal to 1.
f(-3) = a(-3) + b
1 = -3a + b
b = 1 + 3a ---- (2)
Now, it is also given that (f(13) = 5) that means at (x = 13) the function (f(x) = ax + b) is equal to 5.
f(13) = 13a + b
5 = 13a + b
Now, put the value of 'b' in the above equation.
5 = 13a + 1 + 3a
4 = 16a
[tex]\rm a = \dfrac{1}{4}[/tex]
Now, put the value of 'a' in equation (2).
[tex]b = 1 +3\times \dfrac{1}{4}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
Now, put the value of a and b in equation (1).
[tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]
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Can i see a long division version of 534÷3 and have it solved with the work
Wilma works at a bird sanctuary and stores bird seed in plastic containers. she has 3 small containers that holds 8 pounds of bird seed each and 6 large containers that hold 12 pounds of bird seed each. Each container was full until she used 4 pounds of bird seed. She wants to put some of the remaining bordered into 30 bird feeders that can hold 2 pounds each. How much birdseed does she have left over? Show the expression you used to find your answer.
The correct answer is:
32 pounds
Explanation:
She has 3 containers that hold 8 pounds each; 3(8) = 24 pounds of bird seed.
She has 6 containers that hold 12 pounds each; 6(12) = 72 pounds of bird seed.
This gives her a total of 24+72 = 96 pounds of bird seed.
She used 4 pounds of this; this gives her 96-4 = 92 pounds left.
She wants to use 30 containers that hold 2 pounds each; 30(2) = 60 pounds. This would give her 92-60 = 32 pounds left.
The amount of birdseed leftover is 32
The number of containers is:
[tex]\mathbf{Small = 3}[/tex]
[tex]\mathbf{Large = 6}[/tex]
The number of pounds is
[tex]\mathbf{Small = 8}[/tex]
[tex]\mathbf{Large = 12}[/tex]
So, the total number of pounds is:
[tex]\mathbf{Total = 3 \times 8 + 6 \times 12}[/tex]
[tex]\mathbf{Total = 96}[/tex]
From the question, 4 pounds were used.
So, the amount left is:
[tex]\mathbf{Amount = 96 - 4}[/tex]
[tex]\mathbf{Amount = 92}[/tex]
She wants to use 30 containers that contains 2 pounds each.
So, the left over is:
[tex]\mathbf{Left= 92 - 30 \times 2}[/tex]
[tex]\mathbf{Left= 92 - 60}[/tex]
[tex]\mathbf{Left= 32}[/tex]
Hence, the amount of birdseed leftover is 32
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Heather is saving for retirement and has been doing a lot of research on how much she should put aside each month. The newest article says that 1 36 of her salary should be put into a retirement account. If she makes $63,000 a year, how much will she put into her retirement account each month (rounded to the nearest dollar)?
Heather should be saving 1/36th of her annual salary for retirement. Based on her annual salary of $63,000, this amounts to about $1,750 per year or approximately $146 per month.
Explanation:According to the information provided, Heather should be saving 1/36 of her annual salary for retirement. If Heather's annual salary is $63,000, she will need to find 1/36 of this total. In mathematical terms, this can be achieved by dividing $63,000 by 36. After calculating this, we get $1,750 yearly. However, Heather is interested in knowing how much she should save each month.
To find this, we need to take her annual saving of $1750 and divide it by 12 months. When we calculate this, we find that Heather should be saving approximately $146 per month. This is rounded to the nearest dollar. This is a simple and effective way to determine how much of one's salary should be allocated toward retirement savings each month based on a given fraction of that yearly salary.
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What is 2688 divided by 16
At the concession stand medium soda cost $1.25 hot dogs cost $2.50. Natalie's group brought in pizza but is buying the drinks at the concession stand how many medium sodas can Natalie group buy with $20 make a table to show your work