Mathematics High School

(50 points) Here are descriptions of four situations in which the volume of water in a tank is
a function of time. Match each description to a corresponding graph. Each graph
is used only once.
Available Responses:
Graph 1
Graph 2
Graph 3
Graph 4
Situation A: An empty 20-gallon water tank is filled at a constant rate for 3
minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.
Situation B: A full 10-gallon water tank is drained for 30 seconds, until it is half
full. Afterwards, it gets refilled.
Situation C: A 2,000-gallon water tank starts out empty. It is being filled for 5
hours, slowly at first, and faster later.
Situation D: An empty 100-gallon water tank is filled in 50 minutes. Then, a dog
jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The
tank is refilled afterwards.

Answers

Answer 1

Answer:

A = 3

B = 1

C = 2

D = 3

Answer 2

Situation A is graph 3, situation B is graph 1, situation C is graph 2 and situation D is graph 4.

What is Slope?

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Situation A :

The water tank is empty at first. So the graph must start at origin.

Tank is filled at a constant rate for 3 minutes until it is half full, that is until it is 10 gallons.

Then the tank is emptied at a constant rate for 3 minutes, which is also 10 gallons.

So the slope must be equal.

And the graph must start from 0 and ends at zero which is graph 3.

Situation B :

Water tank is already full. So the graph must start at higher value in the Y axis.

The only possibility for this is graph 1, since all others starts at origin.

Situation C :

Water tank starts at empty. So the graph starts at 0.

First the rate is slower, then it becomes faster. So there will be an increase in the slope, which is graph 2.

Situation D :

Graph starts at origin since the tank is empty.

Then there is a slight decrease in the water for some time. So the graph turns down slightly, again tank is refilled, so the graph goes up.

Hence each of the graph corresponds to the situation is found.

Learn more about Slope here :

https://brainly.com/question/29283638

#SPJ2

Related Questions

does 12 11 and 7 make a right triangle

Answers

Answer: no

Step-by-step explanation: hope it helps

24 feet/second to inches/minute

Answers

Answer:

4.8 inches a minute is probably the answer

Answer:

4.8 inches a minute

Step-by-step explanation:

Can someone plz help me? :(

Answers

the answer to your question is B.) 12x

DONT ASNWER IF YOU DON"T KNOW THE ANSWER
Are the two triangles similar? Why or why not?

Answers

yes because they are congruent just dilated in size

This is a 45-45-90 triangle.
What is the measure of x?
Х
14
Х
x = [?]V

Answers

Answer:

x = 14[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Since the triangle is 45- 45- 90 then it is isosceles with the 2 legs being congruent, both 14

Using Pythagoras' identity in the right triangle

x² = 14² + 14² = 196 + 196 = 392 ( take square root of both sides )

x = [tex]\sqrt{392}[/tex] = [tex]\sqrt{196(2)}[/tex] = [tex]\sqrt{196}[/tex] × [tex]\sqrt{2}[/tex] = 14[tex]\sqrt{2}[/tex]

What is the simplified form of the following expression? 5 StartRoot 8 EndRoot minus StartRoot 18 EndRoot minus 2 StartRoot 2 EndRoot 2 StartRoot 2 EndRoot 5 StartRoot 2 EndRoot 9 StartRoot 2 EndRoot 15 StartRoot 2 EndRoot.

Answers

The simplified form of the given expression is [tex]5\sqrt{2}[/tex].

Given expression,

[tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex].

We have to simplify the above expression.

So, [tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\\[/tex]

First solve for the square root,

[tex]5\sqrt{2\times2\times2} -\sqrt{3\times3\times2} -2\sqrt{2} \\\\10\sqrt{2} -3\sqrt{2}-2\sqrt{2} \\[/tex]

[tex]7\sqrt{2} -2\sqrt{2}[/tex]

[tex]5\sqrt{2}[/tex]

Hence the simplified form of the given expression is [tex]5\sqrt{2}[/tex].

For more details follow the link:

https://brainly.com/question/2719671

What is the gradient of the graph shown?

Give your answer in its simplest form.

Answers

Answer:

Step-by-step explanation:

Choose 2 points on the graph: (0, -2) and (1, 0)

[tex]\boxed{ gradient = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Gradient of graph

[tex] = \frac{0 - ( - 2)}{ 1 - 0} [/tex]

[tex] = \frac{0 + 2}{1} [/tex]

= 2

Answer:hope it helps!

Step-by-step explanation:

cannot be bothered

PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls

Answers

Answer:

See below

Step-by-step explanation:

x + 5 = 12, subtract 5 from both sides

x = 7

Subtraction property of equality

a = ba - c = b - c

x + y = 20 and y = 5, substitute 5 into first equation

x + 5 = 20

Substitution property of equality

a + b = c and b = da + d = c

2x - 3 = 11, interchange the sides of equality

11 = 2x - 3

Symmetric property of equality

a = bb = a

Answer:

1. if x + 5 = 12, then x = 7

:Subtraction property of equality

2. If x + y = 20, and y = 5, then x + 5 = 20.

:Substitution property of equality

3. If 2x3 = 11, then 11 = 2x - 3.

:Symmetric property of equality

Please help, I dont know how to get the other angle measurement.

Answers

Answer:

Angle E is 88º

Step-by-step explanation:

If angle A is 46, then angle B is 46. Angle C in triangle ABC then has to be 88. Because of this, angle C in triangle CDE has to be 88 as well. Hence, E is 88.

Where did this student make the mistake when solving this inequality?

2x + 4 > 5x - 5

-2x -2x

4 < 3x - 5

+5 +5

9 < 3x

/3 /3 (divide by 3)

3 < x

options:

When subtracting the same value from both sides you don't need to switch the inequality sign

There is no mistake, it was solved correctly

You don't subtract 2x from each side, you add 2x to each side

When dividing by 3 you should switch the inequality sign

Answers

Answer:

You don't subtract 2x from each side, you add 2x to each side

Find the value of x

3x = 9²

Answers

[tex]\huge\boxed{Hi\:there!}[/tex]

[tex]\huge\sf{3x=9^2}[/tex]

[tex]\huge\sf{3x=81}[/tex]

[tex]\huge\sf{Divide\:both\:sides\:by\:3\:to\:isolate\:x:}[/tex]

[tex]\huge\sf{x=27}[/tex]

[tex]\huge\boxed{Hence,\:x=27.}[/tex]

[tex]\huge\sf\underline{Hope\:it\:helps}[/tex]

[tex]\boxed{CheerfulGirlie\:here\:to\:help}[/tex]

Question:-

Find the value of x

3x = 9²

Answer:-

x = 27

Explanation:-

=> 3x = 9²

=> 3x = 81 [9² = 9×9 = 81]

=> x = 81/3

=> x = 27

i need help on this asap

Answers

Answer:

Step-by-step explanation:

PLEASE PLEASE HELP IM TIMED!! Just look at the picture

Answers

The first one A 7/2
You can just round up 6.75 -> 7 and 1.67->2

the answer is the first one :) 7/2

A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Moussa measures the distance from the pole to the stake and from the pole to the tower. Find the length of the guy wire, to the nearest foot.

Answers

Answer: The answer is 189 ft.

what is the probability

Answers

Answer:

1/4

Step-by-step explanation:

the probability on getting blue on spinner is 1/2

1/2 x 1/2 =1/4

а 5. Protein Bar A has 15 grams of protein in
a 40 gram bar. Protein Bar B has 20 grams of protein in a 60 gram bar. Which bar has more protein per gram?

Answers

The answer is Protein Bar A

Simplify using combining like terms: 3a + 6 + 2a - 8

Answers

Answer:

a = 2

Step-by-step explanation:

Simplifying

3a + 6 = 2a + 8

Reorder the terms:

6 + 3a = 2a + 8

Reorder the terms:

6 + 3a = 8 + 2a

Solving

6 + 3a = 8 + 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

6 + 3a + -2a = 8 + 2a + -2a

Combine like terms: 3a + -2a = 1a

6 + 1a = 8 + 2a + -2a

Combine like terms: 2a + -2a = 0

6 + 1a = 8 + 0

6 + 1a = 8

Add '-6' to each side of the equation.

6 + -6 + 1a = 8 + -6

Combine like terms: 6 + -6 = 0

0 + 1a = 8 + -6

1a = 8 + -6

Combine like terms: 8 + -6 = 2

1a = 2

Divide each side by '1'.

a = 2

Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?

Answers

Answer:

[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]

Step 2: Differentiate

Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation: [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

From here, if you would like, you can take the 3rd derivative of the last piece.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Simplify the variable expression below as much as possible.
X + 8 .z
Answer here

Answers

Answer:

It will stay at x + 8

Step-by-step explanation:

Each time Bobby rides the JUTC bus, money will be deducted from the value of his card. He rode the bus 5 times and his card was charged $100. What integer best represents the the amount by which the balance of the card changed each time it was used?

Possible Answers

A. -$500
B. $20
C. -$20
D. $500

Answers

Answer:

Step-by-step explanation:

100/5= 20

he was charhed 20

find an ordered pair that represents the vector from (-3.7, 2) to (-4, -5)

Answers

Answer is (-0.3 ,7) I am sure this answer

Can you help this is a lot. I don't really get it

Answers

Answer:

country is 15 30 45 60 75 90 105 120 135 150 pop is 5.75 11.5 17.25 23 28.75 34.5 40.25 46 51.75 57.5

why you take my profile picture hello.....

Simplify this question

Answers

[tex]\\ \sf\longmapsto √64+√-81-i^2[/tex]

[tex]\\ \sf\longmapsto 8+√81i-(-1)[/tex]

[tex]\\ \sf\longmapsto 8+9i+1[/tex]

[tex]\\ \sf\longmapsto 9i+9[/tex]

The area of a rhombus is 40 sq cm and one of its diagonals is 8 cm long. Find the length of the other diagonal.

Answers

Answer: The length of the other diagonal is 10 cm...

So the diagonal formula is - 1/2* (d1*d2) d1 is the first diagonal and d2 is the second diagonal.

So,

1/2 * (8*d2) = 40

8d2= 40*2

d2= 80/8

d2= 10

can someone help me for this?

Answers

Answer:

500000N=2m

x. =6m

cross multiply, it'll be

6×50000÷2

=150,000N

write the equation of a line that passes through the points (-7,-4) and (-5,-6)

Answers

Answer:

y=-x-11

Step-by-step explanation:

Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 68 km/h faster than the other. If the two planes are 5052 kilometers apart after 3 hours, what is the rate of each plane?

Answers

Step-by-step explanation:

the slower plane travels x km in 3 hours.

the faster plane travels x + 3×68 = x + 204 km in 3 hours.

x + x + 204 = 5052 km

2x = 4848 km

x = 2424 km (in 3 hours).

so, the slower plane's speed is 808 km/h.

the faster plane's speed is 808 + 68 = 876 km/h.

answer this pleaseeeee

Answers

Answer:

Each goat gets 3 carrots and there are 4 extra carrots left

Step-by-step explanation:

5*3=15

OR: If you wanted to do it exact you give each goat 3 carrot's and an 1/8th of one and you'd have no extra carrots left.

5*3.8=19

Answer:

the answer is simple 3 remainder of 4

Step-by-step explanation:

so he had 5 goats and 19 carrots

19/5=3.8 which mean 3 and 4 left

Can you calculate problems involving percent? pls help i WILL make as brainlyst pls i dont wanna fail

Answers

Calculating percent in easy, if you turn in into fractions like 20% is 20/100 or 2/10 if you look at it that way it should help you understand it

Answer:

45 is 150% of 30.

Step-by-step explanation:

To find what percent of 30 is 45 first we must turn it into a fraction and simplify.

fraction form: 45/30

simplified fraction form: 3/2

now to find percent you have to put a number over one hundred.

3/2 = ?/100

Right now our denominator is 2. By what number can we multiply 2 to get to 100? The answer is 50.

Now that we have multiplied the denominator by 50, we also have to multiply the numerator (3) by fifty. 3 x 50 = 150

so now we put the new numerator and denominator together and get 150/100

The answer is 150%

I have no idea how to do this. Please help.

Answers

Answer:

Area is 5 cm and perimeter is 12 cm

Step-by-step explanation:

Area: top left sqare:

1cm * 1cm = 1 cm

bottom rectangle:

1cm * 3 cm = 3 cm

top right square:

1cm * 1cm = 1 cm

Perimeter:

1 cm + 2 cm+ 3 cm+ 2 cm+ 1 cm + 1 cm + 1cm + 1cm = 12 cm

Other Questions

use order of operations 7-2(-7-4) Tworzymy tekst (minimum 20 zda) o wolnoci i jej zwiastunach, ludziach, ktrzy powicili swoje ycie, dziaalno i twrczo idei wolnoci Which statement concerning simple sugars and amino acids is correct Where did this student make the mistake when solving this inequality?2x + 4 > 5x - 5-2x -2x 4 < 3x - 5 +5 +5 9 < 3x /3 /3 (divide by 3) 3 < xoptions:When subtracting the same value from both sides you don't need to switch the inequality signThere is no mistake, it was solved correctlyYou don't subtract 2x from each side, you add 2x to each sideWhen dividing by 3 you should switch the inequality sign 5. What would happen if all of the bird types in this activity flew to an island where no birds hadbeen before and the only food available was rice? Which birds would be most successful? Whichbirds would be least successful? A sample of Ammonia gas at 650mmHg and 15 degree has a mass of 56.8g.calculate the volume occupied by the gas. Take N=14, H=1,R=8.3145jk. What is the gradient of the graph shown?Give your answer in its simplest form. how many pounds of gold are present in 1 cubic mile of seawater? the first international passenger air service traveled along which route? 4. How did the Allies defeat the Axis powers? Can someone plz help me? :( how long do mashed potatoes stay good in the fridge What is [tex]rs^{3}[/tex] divided by 8-2r if r=8 and s=3? The backyard of a new home is shaped like a trapezoid with a height of 44 nt and bases of 86ft and 106ft What is the cost of putting sod on the yard, if thelandscaper charges $0.25 por square foot for sod? DONT ASNWER IF YOU DON"T KNOW THE ANSWERAre the two triangles similar? Why or why not? Can yall please help me it isn't college work it is 6th grade math walt produced educational films for the u.s. government regarding what? PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS 20 POINTS Write a letter to your friend from another country how you are going to spend the summer holiday which of the inventions from today would have been included in the agricultural revolution.