Mathematics Middle School

The function m=30-3r represents the amount m (in dollars) of money you have after renting r video games.

Find the domain and the range of the function. Is the domain discrete or continuous? Explain.

Answers

Answer 1
The domain of the equation are all the possible values of the independent variables that would make the equation reasonable, possible or true. In this item, the independent variable is r. This could take a value of 0 up to the point when m is equal to zero.
        m = 30 - 3r = 0
              r = 10

The domain is therefore [0, 10]. 

The range is the value of the dependent variable which would be from 0 to the point when no video game is played. This is, [0, 30]. 

The function is discrete because r and m cannot take every value in the number line. 
Answer 2

Domain and Range of the function are  [tex][0, 10] \; \&\; [0,30][/tex] and it is a discrete function.  

Explanation:

Given: The function [tex]m=30-3r[/tex] represents the amount [tex]m[/tex] (in dollars) of money you have after renting [tex]r[/tex] video games.

According to question,

Function is  [tex]m=30-3r[/tex].

Domain of function is calculated as [tex]30-3r=0[/tex]

                                                                 [tex]-3r=-30\\[/tex]

                                                                     [tex]r=\frac{-30}{-3} \\r=10[/tex]

Domain of function is [tex][0, 10][/tex].

Now, range of the function is the value which is dependent variable on domain of the function.

Range of the function is [tex][0,30][/tex].

Here, The given function  [tex]m=30-3r[/tex] is discrete because the values of  [tex]r[/tex] and [tex]m[/tex] cannot take every value in the number line.

Therefore, Domain and Range of the function are  [tex][0, 10] \; \&\; [0,30][/tex] and it is a discrete function.  

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Related Questions

what is the distance between 3/4 and 7/8

Answers

difference:

7/8-3/4

= 7/8 - 6/8
= 1/8

difference 1/8

because when you subtract a fraction from another, you'll have to make the denominator the same, then subtract the numerator to get the answer.


The distance between 3/4 and 7/8 is 11/8

What is an absolute value?

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

The expressions are 3/4 and 7/8.

To find the distance:

Subtract the number with another number.

And take the absolute value of the number.

So,

distance = 7/8 - 3/4

Distance = (14 - 3)/8

Distance = 11/8

Therefore, 11/8 is the required distance.

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what is the function for a table with a domain of 5, 10, 15, 20 and a range of 40, 80, 120, and 160

Answers

To find the range we need to find the vertex of the parabola which is at (-b/2a , y)

-b/2a would be 2/2 = 1 ... so find the y value at x = 1

12 - 2(1) - 15 = 1-17 = -16

So the vertex is at (1,-16)

Since the parabola opens upward from that point the minimum value of the range is y = -16

The range would include the point -16 so it is actually

R = [-16,infinity)

Two forms to write the number 304,001

Answers

304001 (number form)

300000 + 4000 + 1 (expanded form)

three hundred four thousand and one (word form)

hope this helps

PLEASE WILL GIVE YOU BRAINY IF YOURRIGHT!!!!!!!!!!!!
What is the value of d?
 
−5.5(d−2)=−12.1
 
Enter your answer in the box.

Answers

d=4.2

-5.5(d-2)=-12.1
distribute
-5.5d+11=-12.1
subtract 11 from both sides
-5.5d=-23.1
divide -5.5 on both sides
d=4.2

Answer:

4.2

Step-by-step explanation:

Find the value of x for which l is parallel to m. The diagram is not to scale.

a. 31

b. 62

c. 93

d. 149

Answers

Answer:

The answer would be A because x is the exact same length as the other side which is 31

Step-by-step explanation:


The mass of the sun is 2.13525×10^30 kilograms. The mass of Mercury is 3.285×10^23 kilograms.

How many times greater is the mass of the sun than the mass of Mercury?

Answers

it is 6.5*10^52 kilograms greater

which equation to 4.8+2.2x-1.4x+2.4

Answers

Combine Like Terms
4.8 & 2.4 are common terms.
2.2x & -1.4x are common terms. 

4.8 + 2.4 = 7.2
2.2x - 1.4x = 0.8x

The answer is 7.2 + 0.8x or 0.8x + 7.2
You add 4.8 to 2.4 which equals to 7.2.Then you subtract 2.2x-1.4 which equals to 0.8 so your answer is 0.8x+7.2

Three apples weigh a pound . About how much would one Apple cost

Answers

0.33 pounds do the math

Answer: 5.3oz/0.33 lbs

Step-by-step explanation:

Since a lb is 16 oz divide by 3 (number of apples) and get 5.3 oz each then convert into lbs which is 0.33lbs

1. The pizza bot travels an average of 4 miles per hour. If he gets sent on a delivery to a house 1.5 miles away. How long will it take for the bot to make the delivery and return to the restraint.



Write in scientific notation

A. 401,570,000 miles
B. 403,440,000 miles
C. 782,690,000 miles
D. 1,669,490,000 miles
E. 1,202,100,000 miles


Please help

Answers

For the first question, since they travel 4 miles per hour, we want to figure out a common factor of 4 and 1.5 - 0.5 works. Since 4/0.5 is 8, we can divide 1 hour =60 minutes by 8 to get 60/8 minutes for 0.5 miles, and since 1.5/05=3, we can multiply 60/8 by 3 to get how many minutes it would take to get 1.5 miles, which is 180/8=22.5 minutes

For A, we have to write it in <number>.<numbers>*10^<number>. Since 4 is the first number, we write it as 4.01570000*10^<number>. Since there are 8 numbers after 4, we have 4.01570000*10^8. I challenge you to use this for the rest of your problems!

The pizza bot travels an average of 4 miles per hour. If he gets sent on a delivery to a house 1.5 miles away. The scientific notation is A. 401,570,000 miles.

How is the time taken for travel, distance traveled, and the average speed related?

We have this below shown relation between them

[tex]\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Total time taken to travel that distance}= \dfrac{\text{Distance traveled}}{\text{Average speed} }[/tex]

The pizza bot travels an average of 4 miles per hour. If he gets sent on a delivery to a house 1.5 miles away.

The pizza bot is doing delivery which means it will go to the destination and return back.

So, the total distance traveled should be 2x of distance to the delivery target. Then the time needed for the bot to back to the restaurant would be:

Time needed = distance traveled / average velocity

                       = 2 x 1.5mi / 4mph

                        = 0.75 hour

                        = 45 minutes

For A, we have to write it in <number>.<numbers>*10^<number>.

Since 4 is the first number, we write it as 4.01570000 x 10^<number>. Since there are 8 numbers after 4, we have 4.01570000 x 10^8.

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A rectangular painting with a length of 54 centimeters has an area of 2,052 square centimeters.
 
What is the width of the painting?
 

Answers

To get the area, you need to multiply length and width together.

2052/54 = 38

38 is your width

38 (width) x 54 (length) = 2052 (area) True

hope this helps

I need -35+345 and I need to show work

Answers

-35 + 345

345 - 35 = 

345
- 35
-----
310

hope this helps

Sally had 2/9 of a cup of pudding as a snack after school and she had 1/4 of a cup of pudding as dessert after dinner. Sally estimated that that she had about of a cup of pudding today. Is Sally's estimate reasonable?
A.
Yes, because and .
B.
No, because .
C.
Yes, because he added the numerators.
D.
No, because and .

Answers

Sally had about a half cup of pudding. If you make both numbers have the same denominator, you would get 8/36 and 9/36. Add them together, and you get 17/36, which is almost half. 

do NOT answer if you don't know.

Which of the following best describes the life cycle of a star similar to the Sun?
A.
nebula − red dwarf − yellow star − supernova
B.
nebula − yellow star − red giant − white dwarf
C.
white dwarf − blue giant − supernova − black hole
D.
white dwarf − red giant − nebula − white star
E.
yellow star − red dwarf − black hole − supernova

Answers

Towards the end of its life, a star like the Sun grows up into a red giant, before losing its outer layers as a Planetary Nebula and finally shrinking to become a white dwarf.

Last week Alexandra was paid $56 for 7 hours of work. How much money does Alexandra's pay per hour?

Answers

The answer would be $8 per hour
The answer would be $8

They want me to start with one triangle and add 2 tooth picks each time but how do I do that

Answers

add them all around the top pointing down
if you have three toothpicks first, you have 1 triangle. If you add two on each time, you add it on to the existing triangle, which means you use one side of the existing to form the new one. 

Let me know if you don't understand!  :)

The blacktop at school os 75 yards long and 40 yards wide. What is the length and width of the blacktop area in feet?

Answers

1 yard = 3 feet
75*3 = 225 feet long
40*3 = 120 feet wide

In the table, the parts of strawberry concentrate and the parts of water to prepare a strawberry drink are given. There is a proportional relationship between these two quantities. Find the value of x.

Answers

I think 12. Lol I might be wrong maybe 9 can you list your answers choices?

Answer:


Step-by-step explanation:

its 12 D

Can you please help me?

Answers

If the amount of students who listed basketball as their favorite sport is x, we have 3 times x - 17 = 487 due to that soccer has 17 fewer players than 3 times basketball. Adding 17 to both sides, we get 3*x=504 and by dividing both sides by 3, we get x=168

The fifth-grade classes at Brookfield School used five identical buses to go on a field trip. •There were a total of 40 seats on each bus. •All of the seats on four buses were filled. •The fifth bus had 4/5 of the seats filled. •1/8 of all the passengers on the buses were adults. How many adults went on the field trip.

Answers

For the first 4 buses divide 40 by 8 to get the number of adults for those buses, it should be five.
For the bus with 4/5 of the seats filled you'll first need to find out how many seats 4/5 of the bus would amount to.  To do this multiply 40 by 4/5, you should get 32.  Then you divide 32 by 8 and you'll get 4.
The adults on the 5 buses would be 5 + 5 + 5 + 5 + 4 = 24.

Please help. I am stuck on this algebra question:
A homeowner wants to increase the size of his deck that now measures 15 feet by 18 feet. His homeowner's association declares that no deck is to be more than 928 square feet. if the length and the width of the deck are to be increased by the same amount, find, TO THE NEAREST TENTH, the maximum number of feet by which the length of the deck may be legally increased.

a) 14 feet
b)21 feet
c)28 feet
d)32 feet

Answers

Right now the deck (rectangle) is 15 feet (l) by 18 feet (w).
The area is not allowed to be more than 928 square feet.

A ≤ 928
The area of a rectangle = lw
lw ≤ 928

The variable 'x' will be the max number of feet the deck can be increased.
(x + 15)(x + 18) ≤ 928

Use FOIL to solve this.
First- (x)(x)
Outer- (x)(18)
Inner- (15)(x)
Last- (15)(18)

x² + 18x + 15x + 270 ≤ 928
x² + 33x + 270 ≤ 928

Now you can either factor or do the quadratic formula.
 x² + 33x - 658 ≤ 0
(x + 47)(x - 14) ≤ 0
x = -47 ; x = 14

-47 ≤ x ≤ 14

So the number has to be greater than/equal to -47 or less than/equal to 14.

The answer is 
A) 14 feet.

four workers are hired to weed a field by hand. each is given a plot which is 10 x 7 ft in size. what is the total area of the field?

Answers

1) Area = a*b
= 10*7
= 70
2) Four workers with four 70ft plots
= 4*70
=280 ft

Hope this helps!

The total area of the field is 280 sq. ft.

What is unitary method?

"A process of finding the value of a single unit, and based on that value we can find the required value."

What is the area of the rectangle?

"[tex]A=l\times w[/tex], where l is the length and w is the width."

For given question,

We have been given the dimension of a plot which is 10 x 7 ft

From the dimension we can say that, a plot must be rectangular in shape.

Here, length (l) = 10 ft

and width = 7 ft

Using the formula for the area of the rectangle,

[tex]\Rightarrow A=l\times w\\\Rightarrow A=10\times 7\\\Rightarrow A=70~ft^2[/tex]

This means, the area of each plot is 70 sq. ft.

Four workers are hired to weed a field by hand.

Using unitary method the total area of the field would be,

[tex]70\times 4= 280~sq.ft.[/tex]

Therefore, the total area of the field is 280 sq. ft.

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67 percent of 8.7 estimate

Answers

.67*8.7= 5.829


Estimated is about 5.8 or 6

What is 0.46 repeating as a fraction

Answers

Umm, assuming in this case it would be 0.4646464646464646...

Then you would just assign it a variable in the beginning:

x = 0.46464646...

Then multiply it by 100, to get:

100x = 46.46464646464646...

Now you just want to subtract x from 100x, or

46.464646464646464646... - 0.46464646464646...

Which would result in 99x = 46.

Now just divide 99 from both sides to get:

x = 46/99

So it would be 46/99.

I think.

what subset does 17/4573 belong to

Answers

The subset of rational numbers because it is written in the form a/b where a and b are integers ( not = 0)

what math do u do in 8th grade? as in algebra, geometry

Answers

The math curriculum is constantly evolving but when I was in 8th grade I took what is called Integrated Math 1 which would be algebra and geometry both combined, rn I'm a senior so that was a few years ago. It also depends on the school district I would assume. I live in California so, my school district is the San Diego Unified School District.

x + 2 = 6.3



What is the number to replace the variable x

Answers

4.3 would be the number to replace x

There are 2 leaves along 3 in. of an ivy vine. There are 14 leaves along 15 in. of the same vine. Which equation models the number of leaves y along x in. of vine?

Answers

Doing a bit of guess and check, we can notice that the amount of leaves is one less than the number of inches of vine. Writing it out, we get x-1=y (the amount of inches-1=the amount of leaves)
Final answer:

The equation that describes the relationship between the number of leaves and the length of the vine in inches is y = x + 1. This is derived by calculating the slope of the line that fits the data points and the y-intercept.

Explanation:

The subject of this question is mathematics, specifically with a focus on linear relationships. To find an equation modeling the number of leaves y along x inches of vine, we can use the data given. Two points can be derived from this data: (2,3) and (14,15).

A line can be described by the equation y = mx + b, where m is the slope and b is the y-intercept. The slope of the line can be calculated as rise over run, or the change of y divided by the change of x. This gives us (14-2)/(15-3) = 12/12 = 1, so m = 1.

The y-intercept is the 'y' when 'x' equates to zero. By rearranging the equation to b = y - mx, and by substituting any given point and the slope, we can find b. For instance, using the point (2,3), b = 3 - (1*2) = 1. Therefore, the equation that models the number of leaves y along x inches of vine is y = x + 1.

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A magazine photographed is 24 cm long and 16 write each ratio

Answers

Since the length is 24 and the width is 16, we have the length to width ratio equal to 24/16. Since 8 goes into 24 3 times and into 16 2 times, we have 3/2. For width to length, we have 16/24=2/3 using the same reasoning as last time (except the numerator and denominator are flipped)
Final answer:

The requested ratios of the width to length and length to width of the magazine photograph are 2:3 and 3:2 respectively.

Explanation:

The question is asking for the ratios relating to the dimensions of the magazine photograph. In this case, the photo is 24 cm long and 16 cm wide. Therefore, you can derive various ratios from this.

The first is the ratio of width to length, which is 16 : 24. This can be simplified by finding the highest common factor of 16 and 24, which is 8. So divide both sides of the ratio by 8 to get 2 : 3.

Another ratio is the ratio of length to width, which is 24 : 16. Similarly, this can be simplified to a ratio of 3 : 2 by dividing both sides by 8.

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I need help wiith this math problem 6:1=12:_
i need to fill in the blank

Answers

The answer is:  " 2 " .
__________________________________________________
Note:  Given:  6:1::12:x ;  Solve for "x" ;

Rewrite as:

6/1 = 12/x ;

6x = (12)*(1) ;

6x = 12 ;

Divide EACH SIDE of the equation by "6" ; to solve for "x" ;

6x / 6 = 12 / 6 ; 

 x = 2 .
_______________________

Answer:

6:1 = 12:2

Step-by-step explanation:

In the second statement, we see that 12 is double the amount of the original, meaning it had been multiplied by 2.  

Apply the same rule to the second part of the ratio.

Equation: 1 x 2 = 2

Conclusion: 6:1 = 12:2

What is the communitive property of addition?

Answers

X+y or y+x
1+2 or 2+1

Final answer:

The commutative property of addition is a mathematical principle that states the sum of two numbers remains the same regardless of the order in which they are added; for example, 2 + 3 is the same as 3 + 2. It applies to both ordinary numbers and vector addition.

Explanation:

The commutative property of addition states that when two numbers are added, the sum is the same regardless of the order of the addends. In other words, if you have two numbers A and B, then A + B will equal B + A. This property is true for the addition of ordinary numbers, as well as for more complex structures like vectors.

For example, with ordinary numbers, adding 2 + 3 yields the same result as 3 + 2, which is 5 in both cases. The same property applies to vector addition, where the resultant vector from combining A + B is the same as B + A, confirming the commutative nature of this operation.

The commutative property is fundamental in mathematics as it provides flexibility in calculation, making it easier to solve problems and understand the underlying structure of mathematical systems.

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