Is (0, 3) a solution to the inequality y > 2x + 3?
Answers
Answer:
Step-by-step explanation:
Related Questions
Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min. (The same conditions as in the previous problem). After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank.
(a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote thenumber of kilograms of salt in the tank at t minutes after the process begins and use the fact that rate of increase in A = rate of input - rate of exit.
(b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank. What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops?
Answers
Answer:
(a) 0.288 kg/liter
(b) 0.061408 kg/liter
Step-by-step explanation:
(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute
The mass of salt exiting the tank per minute = 5 × (5 + x)/500
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
Δ/dt = x - 5 × (5 + x)/500
The increase, in mass, Δ, after an increase in time, dt, is therefore;
Δ = (x - 5 × (5 + x)/500)·dt
Integrating with a graphing calculator, with limits 0, 10, gives;
Δ = (99·x - 5)/10
Substituting x = 1 gives
(99 × 1 - 5)/10 = 9.4 kg
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)
∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter
(b) With the added leak, we now have;
Δ/dt = x - 6 × (14.4 + x)/500
Δ = x - 6 × (14.4 + x)/500·dt
Integrating with a graphing calculator, with limits 0, 20, gives;
Δ = 19.76·x -3.456 = 16.304
Where x = 1
The increase in mass after an increase in = 16.304 kg
The total mass = 16.304 + 14.4 = 30.704 kg
The concentration of the salt in the tank then becomes;
Concentration = 30.704/500 = 0.061408 kg/liter.
Calculating the salt concentration per liter of water we will find:
(a) [tex]0.288 kg/liter[/tex]
(b) [tex]0.061408 kg/liter[/tex]
The mass of salt entering the tank per minute:
[tex]X= (0.2)( 5) = 1 kg/minute[/tex]
The mass of salt exiting the tank per minute:
[tex]\frac{5 * (5 + x)}{500}[/tex]
The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;
[tex]\frac{\Delta}{dt} = \frac{x - 5 * (5 + x)}{500}[/tex]
The increase, in mass, Δ, after an increase in time, dt, is therefore;
[tex]\Delta = (x - 5 * (5 + x)/500)dt[/tex]
Integrating with a graphing calculator, with limits 0 at 10, gives;
[tex]\Delta = (99X - 5)/10[/tex]
Substituting x = 1 gives:
[tex](99)( 1 - 5)/10 = 9.4 kg[/tex]
The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank). The concentration of the salt and water in the tank after 10 minutes:
[tex](5 + 9.4)/500 = (14.4)/500 = 0.288[/tex]
The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter.
(b) With the added leak, we now have;
[tex]\frac{\Delta}{dt} = \frac{ (x - 6 ) (14.4 + x}{500} \\\Delta = \frac{(x - 6)(14.4 + x)}{500} dt[/tex]
Integrating with a graphing calculator, with limits 0 at 20, gives;
[tex]\int\limits^{20} _0 {\frac{(x - 6)(14.4 + x)}{500} dt}[/tex]
Where x = 1:
[tex]\Delta = 19.76(1) -3.456 = 16.304[/tex]
The increase in mass after an increase in = 16.304 kg. The total mass:
[tex]16.304 + 14.4 = 30.704 kg[/tex]
The concentration of the salt in the tank then becomes;
[tex]30.704/500 = 0.061408 kg/liter[/tex]
Learn more: brainly.com/question/11762787
Find the cos of angle c
A.3/5
B.6/5
C.5/3
D.1
Answers
Please help me with this equation. It’s solving systems of equations.
Answers
Moving downstream (with the current), the boat moves at a rate of (252 mi)/(12 h) = 21 mph. Upstream (against the current), it moves at a rate of (252 mi)/(84 h) = 3 mph.
When traveling downstream, the boat's speed is the sum of its own speed in still water and the speed of the current. It's the same going upstream, but the boat and current move in opposite directions. Let b and c denote these speeds, respectively. Then
downstream: b + c = 21 mph
upstream: b - c = 3 mph
Adding these equations eliminates c and lets us solve for b :
(b + c) + (b - c) = 21 mph + 3 mph
2b = 24 mph
b = 12 mph
Now solve for c :
12 mph + c = 21 mph
c = 9 mph
f(x) = 3x - 8 and g(x) = -x - 4. Find (f + g)(x) and (f + g)(5).
Answers
Answer:
(f+g)(x) = 3x - 8 -x -4
(f+g)(x) = 2x-12
(f+g)(5) - substitute 5 into x
(f+g)(5) = 2(5)-12
(f+g)(5) = 10-12
(f+g)(5) = -2
Step-by-step explanation:
Which statements are correct interpretations of this graph?
Select each correct answer. (multiple choice question)
A. 3 boxes are filled every 4 min.
B. 4 boxes are filled every 3 min.
C. 1.3 boxes are filled per minute.
D. 0.75 boxes are filled per minute.
(Graph down below)
Answers
Answer:
A
Step-by-step explanation:
[tex]\boxed{~ Hello!\; here's\; your \;answer!}[/tex]
___________________________________________________________
[tex]\huge\boxed{A.}[/tex]
___________________________________________________________
A's Explanation...
The first point given is at 3 and 4. 3 is at "Boxes Filled" While 4 is at "Time (Min)". Therefore, your answer is A, 3 boxes are filled every 4 min.
___________________________________________________________
[tex]\boxed{Hope\;I\;helped!}\\\\\\\boxed{May\;I\;Have\;Brainliest?}\\\\\\\\\huge\boxed{Thanks,\;Plip.}[/tex]
___________________________________________________________
The cost of Kerri’s meal was $10. If she wants to leave a 15% tip, how much should she leave? Use the percent proportion to help you ( part/whole = percent/100).
Answers
Explanation: 10*0.15=$1.5
I hope this helps! :)
Time sensitive mark best as brainiest
The density of a certain material is such that it weighs 4 kilograms
per cubic foot of volume. Express this density in ounces per cubic
meter. Round your answer to the nearest whole number.
Answers
Answer:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
(-16t - 2)(t - 5) is the same as 10+78t-16t^2 but in factored form. Explain how you know,
basically help me convert the factored form into the standard form
Answers
Answer:
10+78t-16t^2
Step-by-step explanation:
(-16t-2)(t-5)
-16t × t= -16t²
-16t × -5=80t
-2 × t= -2t
-2 × -5=10
-16t²+80t-2t+10= -16t^2+78+10
PLease help with this question? I also need an explanation on how you got the answer
Answers
Answer:
25%
Step-by-step explanation:
1. there are 8 triangles
2. 2 twos
3. 2/8
4. 2/8=25%
9
show questions
Carol feeds her bird the same amount of food every day. Over the past 7 days, her bag of bird
food has decreased by 1 cups.
Answers
Answer: 1/7 of a cup
Step-by-step explanation:
7x=1 x=food per day
divide 7 from both sides
7 / 7x = 1 /7
x = 1/7
Harper Hospital treated 423 patients last week who were children, out of a total of 931 patients. The administrator calculates that they had 408 adult patients. Is the administrator's calculation reasonable? Estimate the number of adult patients by rounding the numbers to check the administrator's calculation.
Answers
Answer:
No, the administrator is wrong.
[tex]Adult = 500[/tex]
Step-by-step explanation:
Given
[tex]Total = 931[/tex]
[tex]Children = 423[/tex]
[tex]Adult = 408[/tex]
Solving (a): Is the administrator correct?
No, the administrator is wrong.
This is so because: when the number of children is subtracted from the total patient, the remaining number is not 408
Solving (b): Estimate the number of adults
By rounding up:
[tex]Adult = Total - Children[/tex]
Actual Figures
[tex]Adult = 931 - 423[/tex]
Round up
[tex]Adult = 900 - 400[/tex]
[tex]Adult = 500[/tex] -- approximately
BRAINLIEST PLEASE JELP
What is the slope of a line perpendicular to the given line?
Answers
Answer:
4
Step-by-step explanation:
The perpendicular slope means opposite reciprocal
opposite: 1/4
reciprocal: 4
Answer:
The slope is undefined
Step-by-step explanation:
Rate me please
Solve for n 3m+2n=8 how do you do theseee?
Answers
Covert 45 1/2 % to a fraction
Answers
What is the image of (-5, 6) after a reflection over the line y = -2
Answers
Answer:
I'm pretty sure it would be (5,6)
Step-by-step explanation:
Reflecting a point over the Y-axis would change the x-coordinate, but not the y-coordinate
Give 5 reasons explaining why math is your favorite subject.
Give 5 reasons why you dont like math.
Give 5 areas that math can help you now or in the future.
Answers
Answer:Math is important
Step-by-step explanation:
It could help you get into collage and get a good job and with that you could start your life.
Answer:
1.)
I love working with numbers
I love math because of what a challenge it is
I love math because I can become a engineer
I love math because I can also become a doctor with it
I love math because it is useful
2.)
I don't like math because of the word problems
I don't like math because it sometimes gets too easy
I don't like math because I usually have to help others
I don't like math because people call me a nerd
I don't like math because it makes me explain in words
3.)
when your in the store and it helps you with knowing how much your spending
lets you know about if the discount in the store is really good or bad
helps you with becoming certain things when you grow up
it will help you with most of your jobs
Will help others if you know it, you can share your knowledge
Step-by-step explanation:
brainlist pls :>
A nursery owner buys 9 panes of glass to fix some damage to his greenhouse. The 9 panes cost $22.05 Unfortunately, he breaks 4 more panes while repairing the damage. What is the cost of another 4 panes of glass?
Answers
Answer: $9.80
Step-by-step explanation:22.05/9=2.45x4= 9.80
Answer:
$4.30
Step-by-step explanation:
Two panes of glass cost $4.30.
Explanation
First find the cost of one pane of glass (the "unit cost")
7 panes of glass cost
$
15.05
, so one pane of glass costs
15.05
÷7∩
$2.15 ← cost of one pane of glass
Then use that answer to find the cost of two panes of glass
If one pane of glass costs $2.15, then 2 panes cost 2× $2.15 $4.30 ← cost of two panes of glass
Answer:
Two panes of glass cost $4.30.
encuentra el numero decimal equivalente a la fracción
7/10
198/100
85/100
45/100
1/4
3/2
3/8
1/9
Answers
7/10 = 0.7
198/100 = 1.98
85/100 = 0.85
45/100 = 0.45
1/4 = 0.25
3/2 = 1.5
3/8 = 0.375
1/9 = 0.11111111 ( goes on forever) ( sigue para siempre )
Hope it Helps!
¡Espero eso ayude!
⚠️⚠️marking brainliest⚠️⚠️
It’s a math question :((
Answers
Answer:
slope: 3 y-intercept: 9
Step-by-step explanation: 19-10 is 9, and 6-3 is 3 9/3 is 3.
28-19 equals 9. 19-10 is 9, so 9 fills out that blank beside 10.
Answer:
slope is 3 and in the blank goes 1. and y intercepts line at y=1
A rectangle has a length that is 4 ft more
than its width. What are the length and
width of the rectangle if the rectangle has
a perimeter of 48 ft?
Answers
Answer:
length = 14 width = 10
Step-by-step explanation:
48/4=12
10+10+14+14=48
Length = L = 14 ft
P = perimeter = 48 ft
Explanation:
P rectangle = 2L+ 2W
L = W + 4
P = 48
Substitute into formula:
P rectangle = 2L + 2W
48 = 2( W + 4 ) + 2W
48 = 2W + 8 + 2 W
48= 4W + 8
48 - 8 = 4W
40 = 4W
W = 40/4 = 10
W = 10
The rectangle has a length that is 4 ft more than its width : L = W + 4
Substitute : L = 10 + 4 = 14
L = 14 ft
I hope this help!!!
If f(1) = 1, what is f(3)?
Answers
Answer:
would be 3
Step-by-step explanation:
if 1 is 1 ,3 would be 3 ;-;
2. A package delivery service has a truck that can hold 4200 pounds of cargo
and has a capacity of 480 cubic feet. The service handles two types of
packages: small, which weigh up to 25 pounds each and are no more than 3
cubic feet each; and large, which are 50 pounds each and are 5 cubic feet
each. The delivery service charges $5 for each small package and $8 for each
large package. Let x be the number of small packages and y be the number of
large packages in the truck. What is the maximum revenue per truck?
Answers
Answer:
$680
Step-by-step explanation:
Capacity of the truck: 4200 pounds and 480 cubic feet of cargo.
Small package: 25 pounds and 3 cubic feet each.
Large package: 50 pounds and 5 cubic feet each.
For x number of small packages:
25x pounds and 3x cubic feet
Let x = 8,
200 pounds and 24 cubic feet.
For y number of large packages:
50y pounds and 5y cubic feet
Let y = 80,
4000 pounds and 400 cubic feet.
Since delivery service charges $5 for each small package and $8 for each large package.
The maximum revenue per truck = ($5x + $8y)
= ( $5 x 8) + ($8 x 80)
= $680
I need some help on this problem.
Answers
Answer:
It would be <XWY & <UTW.
Jimmy practices hitting baseballs every day. His first time at bat, the baseball goes 10 feet. For every day he
practices, the baseball goes 6 feet farther. Write an equation to describe this situation.
Answers
Answer:
I think it is 10 + (6x)
Step-by-step explanation:
because he starts at ten and every day it adds 6 and x represents the number of days
When I graph the inequality symbol > should it be a open or closed
circle on the number line?
Answers
Answer:
It should be open.
Step-by-step explanation:
Hope this helped!
(-2,-4) and (6,7)
Need help show steps too
Answers
Answer:
Step-by-step explanation:
period
Every Friday, Jesse puts $3 into his piggy bank. is it discrete or continuous?
Answers
Answer:
I would think continuous if she does it constantly every friday night
Step-by-step explanation:
Answer:
continuious
Step-by-step explanation:
Exit ticket help please
Answers
Answer:
The answer is B
Step-by-step explanation:
I am learning the same thing somehow
What is the factored form of 5x-625x^4
Answers
Answer:
5x(-125x+1)
Step-by-step explanation:
im not completely sure but yee
Identify the factored form of each polynomial. 4r + 11x + 6 4x + 10x + 6 11. 4r + 14x +6 (4x+3)(x+2) :: (x+3)(4x + 2) :: (2x+3)(2x + 2)
Answers
Answer:
1) 4x^(2)+11x+6 Factored--> (4x+3) (x+2)
2) 4x^(2)+10x+6 Factored--> (2x+3)(2x+2)
3) 4x^(2)+14x+6 Factored--> (x+3)(4x+2)
Step-by-step explanation:
Factor: 4x^(2)+11x+6 (step by step)
1) Split the second term (11x) into two terms
4x^2 + 8x + 3x + 6
2)Factor out common terms in the first two terms, then in the last two terms.
4x(x + 2) + 3(x + 2)
3) Factor out the common term x + 2
(x + 2) (4x + 3)
Repeat the above steps for similar questions!