A 450 gallon tank full of water is draining at a rate of 20 gallons per minute. We can represent the situation with the equation:

y
=
450
−
20
x
y
=
450
-
20
⁢
x

where x is the number of minutes that have passed by, and y is the amount of water in the tank. How long will it take for the tank to have 200 gallons?

A.
12.5 minutes

B.
32.5 minutes

C.
2.15 minutes

D.
20 minutes

Answer:

Step-by-step explanation:

Given function

Finding zero's

Zero's are

See the graph attached

Correct end behavior as per graph:

Answer:

As x approaches negative infinity, f(x) approaches negative infinity

Step-by-step explanation: Plato

Answer:

Orville caught up with Wilbur in 2.5 hours

Step-by-step explanation:

Here, we want to calculate the number of hours it took for Orville to catch up to Wilbur

Mathematically,

distance = speed * time

The distance traveled before Orville restarted his own journey is ;

distance = 10 mph * 0.5 = 5 miles

(30 minutes is 30/60= 0.5 hours)

So this means that Wilbur was now 5 miles ahead of Orville

Now, let the number of hours it took to

catch up Wilbur be h

In h hours,

Wilbur would have traveled 5 miles + 10h

In this same time, Orville would have traveled

12 * h = 12h

So the distance traveled by the two will be equal at this h hour

5 + 10h = 12h

12h-10h = 5

2h = 5

h = 5/2

h = 2.5 hours

Answer:

20x + 5 < 30

Step-by-step explanation:

To make a profit, the price on supplies must be less than the amount at which they sold their wares

Since they received $5 in tip, the amount of profit left to be accounted for is 30-5 = 25

So now, we need the smallest price at which they will sell per lemonade to make a profit

Mathematically, that will be;

20x + 5 > 30

Using this inequality X they will know the value of x that will give them profit

Answer:

1/2

Step-by-step explanation:

(1,1) (2,3)

you have to do the difference of the x axis and y axis then divid them by each other

Answer:

20%

Step-by-step explanation:

Given parameters:

Marked price  = Rs. 100

Selling price  = Rs. 80

Unknown:

Discount rate  = ?

Solution:

The price on the label of an article is the marked price;

   Discount amount  = Marked price - selling price

                                  = Rs. 100  - Rs. 80

                                  = Rs. 20

Discount rate  = [tex]\frac{Discount }{Marked price } x 100[/tex]  

Discount rate  = [tex]\frac{20}{100}[/tex]  x 100  = 20%

Answer:

109°

Step-by-step explanation:

there are two ways to slove this kind of questions.

simply,x = 64 + 45

or x = 180-(180 - 64- 45)

Answer:

11w + 6g ≥ 120

Step-by-step explanation:

Let's set:

w = number of hours Lauren spent washing cars

d = number of hours Lauren spent walking dogs

Lauren makes $11 per hour washing cars, thus she earns 11w in total for washing cars.

Lauren makes $6 per hour walking dogs, thus she earns 6d in total for walking dogs.

The total earnings are:

T = 11w + 6g

Lauren must earn not less than $120 this week, thus:

11w + 6g ≥ 120

This is the required inequality

Answer:

11w+6d≥120

Step-by-step explanation:

this is straghit from my delt math so it has to be right

Answer:

1 ft / 0.3048 m

Step-by-step explanation:

Answer:

7x+15y

Step-by-step explanation:

Answer:

15y+7x

Step-by-step explanation:

Simply the equation by combining like terms

Answer:

Assuming we have the same question, the answer would be: D) h = 45tan59° ft

Step-by-step explanation:

Answer:

3.8 is the answer of this question

Answer:

[tex]\frac{x}{8}[/tex]

Step-by-step explanation:

When solving inverse functions, switch the x and y's:

x=8y

Then solve for y: (divide 8 on both sides)

[tex]\frac{x}{8}=y\\[/tex]

Answer:

1) Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

2) The slope of the given equation, shows that the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

Step-by-step explanation:

1) The function modelling the height of the balloon is h(x) = -11x + 330

Where;

x = The time of elevation of the balloon

The data for the graphing derived from Microsoft Excel are as follows

x    [tex]{}[/tex]   h(x)

0    [tex]{}[/tex]   330

5    [tex]{}[/tex]   275

10    [tex]{}[/tex]  220

15    [tex]{}[/tex]  165

20    [tex]{}[/tex]  110

25    [tex]{}[/tex]  55

30    [tex]{}[/tex]   0

Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

Comparing the given function to the general equation of a straight line, y = m·x + c, we have that the slope, m = -11

2) The slope of a straight line graph gives the rate of change of the dependent variable, per unit change in the independent variable

Therefore, the slope of the given equation, -11 gives the rate of change of the function per unit increase in the independent variable x

Therefore, the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

Answer:

I had the same problem! Here is my work, pretty sure its the right answer!

Step-by-step explanation:

Answer:

-4, 3

The answer to the next question is: A (+4/3), B (+2/3), D (+2), E (+4), G (+1/3), H (+1)

Step-by-step explanation:

For edge:)

Rational root theorem is used to determine the potential roots of a function

The potential roots are: [tex]\mathbf{ \pm 1, \pm 2, \pm 4, \pm \frac{1}{3} ,\pm \frac{2}{3}, \frac{4}{3}}[/tex]

The function is given as:

[tex]\mathbf{f(x) = 3x^2 - x - 4}[/tex]

p represents the leading coefficient, while q represents the constant term.

So, we have:

[tex]\mathbf{p = 3}[/tex]

[tex]\mathbf{q = 4}[/tex]

The factors of p and q, are:

[tex]\mathbf{p =\pm 1, \pm 3}[/tex]

[tex]\mathbf{q =\pm 1, \pm 2, \pm 4}[/tex]

So, the potential roots are:

[tex]\mathbf{Roots = \pm\frac{q}{p}}[/tex]

[tex]\mathbf{Roots = \pm\frac{\pm 1, \pm 2, \pm 4}{\pm 1, \pm 3}}[/tex]

So, we have:

[tex]\mathbf{Roots = \pm 1, \pm 2, \pm 4, \pm \frac{1}{3} ,\pm \frac{2}{3}, \frac{4}{3}}[/tex]

Hence, the potential roots are: [tex]\mathbf{ \pm 1, \pm 2, \pm 4, \pm \frac{1}{3} ,\pm \frac{2}{3}, \frac{4}{3}}[/tex]

Read more about rational root theorems at:

https://brainly.com/question/9353378

Answer:

x = 1.6

Step-by-step explanation:

Given f(x) = 10x + 3 and f(x) = 19, then equate right sides, that is

10x + 3 = 19 ( subtract 3 from both sides )

10x = 16 ( divide both sides by 10 )

x = 1.6

Answer:

Step-by-step explanation:

Given

and

Solution

Answer:

y = -16

Step-by-step explanation:

y = -3(12) + 20

y = -36 + 20

y = -16

Hope this helps and pls do mark me brainliest if you can:)

Answer: x=3

Step-by-step explanation:

6x + 3x - x + 9 = 33

Combine like terms:

6x+3x-x=8x

The equation is now 8x+9=33

Subtract 9 on both sides:

8x+9-9=33-9

8x=24

Divide 8 on both sides:

8x/8=24/8

x=3

Answer:

[tex] \frac{3x}{5} - \frac{1}{10} = \frac{x + 2}{10} - 2 \\ \frac{6x - 1 = x + 2 - 20}{10} \\ 6x - x = - 18 + 1 \\ 5x = - 17 \\ x = - \frac{17}{5} [/tex]

Answer:

x= -17/5 or x=-3.4

Step-by-step explanation:

1. multiply both sides of equation by 10 (6x-1 = x+2-20)

2, calculate the difference (6x -1=x-18)

3. move the terms ( 6x-x-1=-18)

4. collect like terms ( 5x=-18+1)

5. divide both sides (x=-17/5)

Answer:

 ≈ 3.4

Step-by-step explanation:

Coordinates of the point that divide segment with endpoints A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] ) in a ratio a : b are

[tex]\frac{bx_{1} +ax_{2} }{a+b}[/tex] , [tex]\frac{by_{1} +ay_{2} }{a+b}[/tex] )

A(- 4, - 7)

B(8, - 4)

Ratio 8 : 5

x-coordinate is [tex]\frac{5(-4)+8(8)}{8+5}[/tex] = [tex]\frac{44}{13}[/tex] ≈ 3.4

Answer:

The answer x = 75

Step-by-step explanation:

A triangle's angles must add up to 180 degrees.

We already have 47 and 58 which is 105. 180 - 105 = 75.

Answer:

The answer is D

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{5}[/tex] ( perform multiplication before addition )

= [tex]\frac{3}{10}[/tex] + [tex]\frac{2}{10}[/tex]

= [tex]\frac{5}{10}[/tex] ( divide numerator/ denominator by 5 to simplify )

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

Answer:

0.5

Step-by-step explanation:

first put the given below:

1/2 × 3/5 + 1/2 × 2/5 = 0

second take the first and second for the first answer to make the whole answer:

((1/2 × 3)/5) = 0

( 1/2 ) × 3 = 1.5

1.5/5 = 0.3

FIRST SOLVATION ( ANSWER ): 0.3

third , after we take the first solvation the second is we need to compute the remaining given or number:

((1/2 × 2)/5) = 0

( 1/2 ) × 2 = 1

1/5 = 0.2

SECOND SOLVATION ( ANSWER ): 0.2

and the last but not the list , the last is add the first solvation and second solvation and you will see what is the answer:

0.3 + 0.2 = 0.5

FINAL ANSWER: 0.5

Answer:

x=-1

Step-by-step explanation:

Answer:

x=3/5 y=-2.5

Step-by-step explanation:

3x-2y=5, first find the x value which is 3x get rid of the 2y by during 2 times ,then 5/3 since you can't lower it down keep it 5/3, after is 2y same thing you did for 2y to get rid of it you will do 3x, now is 5/2 to get 2.5 or 5/2.

Answer:

Four and two hundred nine thousandths

Answer

four and two hundred nine thousandths. or, simpler: four point two hundred nine. or, even simpler: four point two zero nine.

Step-by-step explanation:

Answer:

y = 50 is answers and it is alternate angle

Answer:

B

Step-by-step explanation:

The two angles are the same

Answer:

8 units right 2 units down

Step-by-step explanation:

The magical answer that you are looking for is D.

Answer: Abdul traveled 130 miles

Step-by-step explanation:

Step 1

Using the formula  to calculate how far Abdul traveled

Distance = speed x time.

Step 2---- Solving

In heavy traffic

Distance covered = speed x time = 30miles /hour x 1 hour = 30 miles

In light traffic

Distance covered = speed x time = 50miles/ hour x 2 hour = 100 miles

Total distance covered = Distance covered in heavy traffic + distance covered in light traffic = 100+ 30 = 130miles

since we know supplementary angles equal 180 degrees, we know that 67 plus x must equal 180 degrees, so the equation for this problem would be

67+x=180, and x is equal to 113