Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of
1.2 gallons per minute,
Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of
0.8 gallon per minute.
After how many minutes will both aquariums contain the same amount of water?

Answer:

Find an nth-degree polynomial function.

Step-by-step explanation:

n= 3;

- 2 and 6 + 2 i are zeros;

f(-1)= 53

Answer:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.

Step-by-step explanation:

The possible degrees are 0, 1, and 2. Let's explain why by assuming the following is given:

P = 6x² - 3x - 2

Q = 3x² + 2x - 6

Let R = P - Q

Thus:

(6x² - 3x - 2) - (3x² + 2x - 6)

Open parentheses by distributing the factor of -1

6x² - 3x - 2 - 3x² - 2x + 6

Add like terms together

6x² - 3x² - 3x - 2x - 2 + 6

R = 3x² - 5x + 4

The leading term of R has a degree of 2. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 2.

Also, let us assume the following:

P = 4x² + 4x - 3

Q = 4x² + x - 8

Let R = P - Q

R = (4x² + 4x - 3) - (4x² + x - 8)

R = 4x² + 4x - 3 - 4x² - x + 8

Collect like terms

R = 4x² - 4x² + 4x - x - 3 + 8

R = 4x + 5 (4x² cancels 4x²)

The leading term of R has a degree of 1. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 1.

Also, let us assume the following:

P = x² + 2x - 3

Q = x² + 2x - 8

Let R = P - Q

R = (x² + 2x - 3) - (x² + 2x - 8)

R = x² + 2x - 3 - x² - 2x + 8

Collect like terms

R = x² - x² + 2x - 2x - 3 + 8

R = 5 (x² cancels x², and 2x cancels 2x)

The polynomial R has a degree of 0. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 0.

Therefore we can conclude that:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.

Part A:

The y-intercept is $1,500

The x-intercept is 20 days

Part B:

Equation of the line in point-slope form is  y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form  is y + 75·x = 1500

Part C:

f(x) = -75·x + 1500

Part D:

$1,125

Step-by-step explanation:

The information given are;

x,                 g(x)

0,                 $1,500

2,                 $1,350

4,                 $1,200

The equation of a straight line relation between the x, and y, coordinates in slope and intercept form is  y = m·x + c

Where;

m = The slope

c = The y-intercept

From the data, we have two points, (x₁, y₁), (x₂, y₂) given as (0, 1,500), (2, 1350);

The y-intercept = y at x = 0 = 1,500

y = -75·x + 1500

x = 1500/75 = 20

Part B:

The equation in point-slope form is y - y₁ = m×(x - x₁)

Which gives;

Equation of the line in point-slope form is  y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form  is y + 75·x = 1500

Part C:

The equation of the line using function notation is f(x) = -75·x + 1500

Part D:

The balance in the bank after 5 days is f(5) = -75 × 5  + 1500 = $1,125

Answer:

the answer is 5

Step-by-step explanation:

f(4) = 3(4) -2

7 - 2 = 5

Answer:

600

Step-by-step explanation:

Sense 2 hours has passed you divide the amount of distance the plane has traveled by the amount of time it took. :)

Answer:

600 mph

Step-by-step explanation:

its the speed of the plane

the solution is distance travel which is 1,200 miles divided by the time 2 hours will be equal to 600 miles per hour (mph).

Answer:

7

Step-by-step explanation:

Answer:

Noah is correct.

Step-by-step explanation:

Noah is correct, a proportional relationship can be formed by observing two conditions:

1) Knowing at least two distinct collinear points on coordinate grid.

2) Ratio between dependent and independent variables must be the same on each point.

3) Relationship must include origin.

Makayla used two points: (0, 0) and (3, 33). Therefore, she observed all conditions described above:

Condition 1: Makayla plotted (0,0) and (3,33). According to Geometry, two distinct point on coordinate grid are always collinear.

Condition 2: The proportionality ratio is:

[tex]k = \frac{33}{3}[/tex]

[tex]k = 11[/tex]

Condition 3: The relationship included origin: (0, 0).

Answer:

the square root of -1 is i

Step-by-step explanation:

Well, actually, the square root of -1 (or any negative number at that) is not a real number. What I mean by that is that there is no way to square a real number to get a negative number (ie [tex]2^{2} = 4, -2^{2} =4[/tex], there is no way to square a real number to get -4).

To solve this, mathematicians came up with the "imaginary number" i which, when squared, equals to -1. This allows us to get the square root of negative numbers ([tex]\sqrt{-4} = 2i[/tex]) or get negative numbers through squaring ([tex]2i^{2} = -4[/tex]).

The required value of the square root of -1 is i. The correct answer is option B.

As we know that complex number is made up of real and imaginary values. It is represented by the equation z = a + ib, where a, b, and i are real values and i is an imaginary number.

The square root of -1 is denoted as "i" in mathematics, where "i" represents the imaginary unit.

The imaginary unit is defined as the square root of -1. It is important to note that the square root of a negative number is not a real number, but an imaginary number.

⇒ √(-1)

⇒ √(i²)

⇒ i

So, the correct answer is "i."

Learn more about complex numbers here:

brainly.com/question/19007885

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Answer:

-8 degrees

Step-by-step explanation

Half of negative 16 would be negative 8.

Answer:

-8

Step-by-step explanation:

-16 ÷ 2 = -8

You could also do:

16 ÷ 2 = 8

and then put a negative in front of 8

And to prove it's true,

8 x 2 = 16

-8 x 2 = -16

Answer:

y = -1/4x - 1

Step-by-step explanation:

First, put the equation in slope intercept form:

4x - y = 2

4x - 2 - y = 0

4x - 2 = y

y = 4x - 2

Perpendicular lines have opposite reciprocal slopes. Since the original slope is 4, the other line's slope will be -1/4

Plug in the given point and the slope into y = mx + b, then solve for b:

y = mx + b

-2 = -1/4(4) + b

-2 = -1 + b

-1 = b

Plug in the slope and b into the equation:

y = -1/4x - 1 is the equation

Answer:

the 2nd one

Step-by-step explanation:

Answer:

d) 3

Step-by-step explanation:

4t^2 +5t -1

in this equation there are 3 terms:

4t^2,      5t,        and  -1

Answer:

1 2. 3

Answer:

20 cookies and 15 cupcakes (20:15)

Explanation:

First you need to multiply 4 by 5 which equals 20. Then 3 by 5 which equals 15. Then you need to add them together to get 35!

Ratio Table!

   4    |    3   x4

  16    |   12  + 4:3

 20   |   15   = 35!

I Hope This Helps!

Answer:

382

Step-by-step explanation:

540 - 158

Answer:4 and 35

Step-by-step explanation:

Am from the future

The extremes are 4 and 35.

The extremes are the values of the proportion that are furthest apart when written in ratio form using a colon. For example: In the proportion a : b = c : d, ‘a’ and ‘d’ are the extremes.

In general, four numbers are said to be in proportion, if the ratio of the first two quantities is equal to the ratio of the last two. In general, the symbol for representing a proportion is “: :”

(i) The numbers a, b, c and d are in proportional if the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., a : b : : c : d and is read as ‘a is to b is as c is to d’. The symbol ‘ : : ‘ stands for ‘is as’.

(ii) Each quantity in a proportion is called its term or its proportional.

(iii) In a proportion; the first and the last terms are called the extremes; whereas the second and the third terms are called the means.

If four numbers a, b, c and d are in proportional (i.e., a : b : : c : d), then a and d are known as extreme terms and b and c are called middle terms.

(v) The fourth term of a proportion is called fourth proportional.

Given:

4/7 = 20/35

Now, by the definition of extremes

the first and the last term is extremes

So, 4 and 35 are the extremes.

Learn more about proportion here:

https://brainly.com/question/26974513

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Answer:

37/8

Step-by-step explanation:

Answer:

37/8

Step-by-step explanation:

gh

Answer:

13/48

Step-by-step explanation:

13/6 / 8 = 13/6 x 1/8

13 x 1 = 13

6 x 8 = 48

13/48

Answer:

13/48

Step-by-step explanation

Answer:

I think that's wrong

Step-by-step explanation:

1000+1000+1000+1000+1000+1000+1000+1000+1000+ 900+40+3 ?????? not sure but it welcome

Answer:

D

Step-by-step explanation:

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Answer:

4.16 × 10 ^17

Step-by-step explanation:

Answer:

Week 1 = 80

Week 2 =88

Week 3 = 96.8

Week 4 = 106.48

Week 5 = 117.128

Step-by-step explanation:

Given

Week 1 = 80

Growth = 10%

Required

Fill week 1 to 5

We have week 1 already.

Week 2 is calculated as thus:

Week 2 = Week 1 + 10% * Week 1

Week 2 = 80 + 10% * 80

Week 2 = 80 + 8

Week 2 = 88

Week 3 is calculated as thus:

Week 3 = Week 2 + 10% *Week 2

Week 3 = 88 + 10% * 88

Week 3 = 88 + 8.8

Week 3 = 96.8

Week 4 is calculated as thus:

Week 4 = Week 3 + 10% * Week 3

Week 4 = 96.8 * 10% *96.8

Week 4 = 96.8 + 9.68

Week 4 = 106.48

Lastly, week 5 is calculated as thus:

Week 5 = Week 4 + 10% * Week 4

Week 5 = 106.48 + 10% * 106.48

Week 5 = 106.48 + 10.648

Week 5 = 117.128

Answer:

28 inches

Step-by-step explanation:

Answer: A) 52 ft  B) $134.68

Step-by-step explanation:

First find the surface area by multiplying the dimensions together.

2 x 4 = 8

2 x 3 = 6

4 x 3 = 12

Then add them up and multiply by two because there are two of each side.

26 x 2 = 52

To find the cost, multiply 52 by $2.59 to get the price.

52 x $2.59 = $34.68

Answer:

Step-by-step explanation:

If one solution of a quadratic equation is a complex number (a + bi),

Other solution of the equation will be the conjugate of the first solution.

So the other solution will be in the form of (a - bi)

If one solution is, x = -4 - 5i

Other solution will be, x = -4 + 5i

If one solution is, x = 4 + 5i

Other solution will be, x = 4 - 5i

If one solution is, x = 5 - 4i

Other solution will be, x = 5 - 4i

Answer:

I counted 32 squares in and out

Answer:

A=a^2, so A=4^2=16 , or 4*4=16

Step-by-step explanation:

All sides of a square are equal, so the length of the sides are all 4. Put 4 in for a in the formula A=a^2 or Area = side length squared.

A = 4^2

A = 4 * 4

A = 16

Answer:

A. (3V/B) = h

Step-by-step explanation:

V = (1/3)Bh

3V = Bh

(3V/B) = h