Which equation correctly represents how the total mechanical energy (ME) of
a system relates to its kinetic energy (KE) and gravitational potential energy
(GPE)?

1)

In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.

1 minute = 9 liters

⇒ 60 seconds = 9 liters

⇒ 20 seconds = 3 liters

We need to find the amount of water in the tank A

a) when 4 minutes

Given that, 1 minute = 9 liters

Let y1 liters of water in the tank A after 4 minutes

So, we get an equation,

y1 = 9 × 4

y1 = 36 liters

36 + 124 (initial water level) = 160 liters

Hence, 160 liters of water in the tank A after 4 minutes been passed.

b) when 80 seconds

From given information, 20 seconds = 3 liters

Let y2 liters of water in the tank A after 80 seconds

So, we get an equation,

20 (y2) = 3 × 80

y2 = 12 liters

12 + 124 (initial water level) = 136 liters

Hence, 136 liters of water in the tank A after 80 seconds been passed.

Now we need to find the amount of time passed when Tank A contains the following amounts of water.

i) 151 liters

151 - 124 = 27 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 27

t1 = 27 / 9

t1 = 3 minutes

This means, 3 minutes have passed when Tank A contains 151 liters of water.

ii) 191.5 liters

191.5 - 124 = 67.5 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t2 be the required time.

so, we get an equation,

9 × t2 = 1 × 67.5

t2 = 67.5 / 9

t2 = 7.5 minutes

t2 = 7 minutes 30 seconds

This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.

iii) 270.25 liters

270.25 - 124 = 146.25 liters of more water filled.

As we know,  1 minute = 9 liters ..............................(Given)

Let t1 be the required time.

so, we get an equation,

9 × t1 = 1 × 146.25

t3 = 146.25 / 9

t3 = 16.25 minutes

t3 = 16 minutes 15 seconds

This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.

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2)

In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.

⇒ 1 minute = 2.5 liters of water drained

⇒ 60 seconds = 2.5 liters

⇒ 10 seconds = 0.42 liters

We need to find the amount of water drained from tank B

a) after 30 seconds

Let x1 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

10 (x1) = 30 × 0.42

x1 = 3 × 0.42

x1 = 1.26 liters

b) after 7 minutes

Let x2 be the amount of water drained after 30 seconds

Given that, 1 minute = 2.5 liters

So, we get an equation.

x2 = 7 × 2.5

x2 = 17.5 liters

Now, we need to find the time in which the water is draining when Tank B contains

i) 75 liters

80 - 75 = 5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t1 be the required time.

so, we get an equation,

2.5 × t2 = 5

t1 = 5 / 2.5

t1 = 2 minutes

This means, after 2 minutes Tank B contains 5 liters of water.

ii) 32.5 liters

80 - 32.5 = 47.5 liters of more water drained.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t2 be the required time.

so, we get an equation,

2.5 × t2 = 47.5

t2 = 47.5 / 2.5

t2 = 19 minutes

This means, after 19 minutes Tank B contains 32.5 liters of water.

iii) 18 liters

80 - 18 = 62 liters of more water filled.

As we know,  1 minute = 2.5 liters water drained       ............(Given)

Let t3 be the required time.

so, we get an equation,

2.5 × t3 = 62

t3 = 5 / 2.5

t3 = 24.8 minutes

t3 = 24 minutes 48 seconds

This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.

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Answer:

f(x)=

1. 48x when x < or = 3,

2. 45x when 4 < or = x < or = 8

3. 42x when 9 < or = x < or = 19

4. 38x when x > 19

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ; cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Mean, median and mode are the three principles of describing data.

Describing data:- Describing data is also called descriptive statistics, that describes the data through several methods such as graphical representations, central tendency, variability. It summarizes the data efficiently, which helps to make any conclusion on that dataset.

The three principles of describing data are-

Thus we can conclude that, mean, median and mode are the three principles of describing data.

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Answer: x=12

Step-by-step explanation:

The range is: x-5

The mode is: 7

Hence,

x-5=7

x-5+5=7+5

x=12

Answer:

y = -2x - 3

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2

using m = -2, x = 2, y = -7

y = mx + b

-7 = (-2)(2) + b

-7 = -4 + b

b = -3

y = -2x - 3

Answer:

−8x − 12y − 18q − 42p

Step-by-step explanation:

-4 x 3y = -12y and only number 2 is correct

The solution is Option B.

The value of the equation is A = -8x - 12y - 18q - 42p

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = -4 ( 2x + 3y ) - 6 ( 3q + 7p )

Now , on simplifying the equation , we get

A = -4 ( 2x ) - 4 ( 3y ) - 6 ( 3q ) - 6 ( 7p )

The  value of A = -8x - 12y - 18q - 42p

Therefore , the value of A is -8x - 12y - 18q - 42p

Hence , The value of the equation is A = -8x - 12y - 18q - 42p

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1. The two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)

2. The slope is: B. 0.

The formula for finding the slope of a line is:

Slope (m) = change in y/change in x

1. To find the two points that has a slope of 2/3, calculate the slope of each of them:

Slope for A = (0 - 0)/(3 - 2) = 0

Slope for B = (-4 - 2)/(3 - 1) = -3

Slope for C = (3 - 0)/(2 - 0) = 3/2

Slope for D = (4 - 2)/(0 -(-3)) = 2/3

Therefore, the two points that lie on a line with a slope of 2/3 are: D. (–3, 2) and (0, 4)

2. Slope of the line = change in y / change in x = (-1 -(-1))/(-3 - 6)

Slope (m) = 0/-9

Slope (m) = 0

The slope is: B. 0.

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3000 ÷ 40 =

75 ⇐ Quotient

――――

40)3000 ⇐ Dividend

280

---

200

200

3000 divided by 40 is equal to quotient of 75 with no remainder.

To perform long division for 3000 divided by 40, Set up the long division format.

Determine how many times 40 can go into the leftmost digit of 3000 (which is 3).

The answer is 75. Write 75 on top of the division bar.

Now, subtract 3000 - 3000 to get the remainder.

The remainder is 0.

Hence,  3000 divided by 40 is equal to 75.

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if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

When we graph over intervals like (a, b) or [a, b] or something like that, we use dots to define the end of the intervals, and to denote that the function ends abruptly or we have a jump.

In this case, you can see that between the end and the second part and the beginning of the third part there is a jump, so the use of dots is correct there, but if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

That is the only error with the graph.

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The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.

How far is it between the two locations?

By calculating the sum of the absolute values of the y-coordinates, you may determine the distance between two places in different quadrants with the same x-coordinates.

What does a line's slope indicate?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Describe slope using an example?

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Answer:

2x-1=3×+8

Step-by-step explanation:

2×-3x=8+1

-x=9

x=-9

Answer: x=-1.75

Step-by-step explanation:

(6x +12) -2(x-7)= 19

6x+12-2x-(-14)=19

6x+12-2x+14=19

6x-2x+12+14=19

4x+26=19

4x+26-26=19-26

4x=-7

x=-7/4

x=-1.75

The discriminant is:

D = 5^2 - 4*3*(-8) = 121

Then we have two real solutions.

For a quadratic equation:

a*x^2 + b*x + c = 0

The discriminant is:

D = b^2 - 4ac

If D > 0, we have two real solutions.

If D = 0 we have one real solution (it is thought as two equal solutions)

if D < 0, we have two complex solutions.

In this case, the quadratic equation is:

3x^2 + 5x - 8 = 0

Then:

a = 3

b = 5

c = -8

The discriminant is:

D = 5^2 - 4*3*(-8) = 121

Then we have two real solutions.

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Heidi has to walk her bike for (1/8) mile to complete the loop.

Given that:-

Total distance of the loop = 7/8 mile

Distance Heidi rode on her bike before she stopped for rest = 1/2 mile

Distance Heidi rode on her bike after taking the rest = 1/4 mile.

We have to find the distance Heidi has to to walk to complete the loop because she had a flat tire.

Let the distance Heidi has to to walk to complete the loop because she had a flat tire is x miles.

We know that,

Total distance of the loop = Distance Heidi rode on her bike before she stopped for rest + Distance Heidi rode on her bike after taking the rest + distance Heidi has to to walk to complete the loop because she had a flat tire.

Hence, by adding the fractions, we get

7/8 = 1/2 + 1/4 + x

7/8 = (2+1)/4 + x

7/8 = 3/4 + x

7/8 - 3/4 = x

7/8 - 6/8 = x

1/8 mile = x

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I don't know helpp me with the mathhh pleaseee

Step-by-step explanation:

Answer:

I need this question too... HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

The total number of matches played is 552

The given parameters are

Teams = 24

Matches against each other = 2

So, the total number of matches played is

Total = Teams * (Teams - 1)

This gives

Total = 24 * (24 - 1)

Evaluate

Total = 552

Hence, the total number of matches played is 552

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Answer:

3*x+4*7p

3x+28p ok hard

Answer: 0

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

I don't know about that and I don't understand

If the midpoint of segment lm where j(5, -1) and m(0, 6), then the coordinates of end point l is (10,-8)..

Midpoint:

Midpoint of a line segment is the point that is halfway between the endpoints of the line segment.

The formula for the midpoint is,

[tex](x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

where,

[tex](x_m,y_m)[/tex] = coordinates of the midpoint

(x₁, y₁)   = coordinates of the first point

(x₂, y₂) = coordinates of the second point

Given,

Midpoint = j = (5,-1)

Second point =  m = (0,6)

Now, we have to find the first midpoint l.

Let (x,y) be the coordinates of l.

Then apply the values on the formula,

Then we get,

[tex](5,-1)=(\frac{x+0}{2},\frac{y+6}{2})[/tex]

Compare the values in order to find the coordinates,

=> 5 = (x + 0) / 2

=> 5 x 2 = x + 0

=> 10 = x

Similarly,

=> -1 = (y + 6) / 2

=> -1 x 2 = y + 6

=> -2 = y + 6

=> -2 - 6 = y

=> y = -8

Therefore, the coordinates of l is (10,-8).

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Answer:

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]

Step-by-step explanation:

Answer:

iakajakakam kwokwmajsj kakajnsnsj wjjsjajsj sjsjjsjs

Step-by-step explanation:

The time difference between Melbourne and London is 11.00 hours.

Here we need to find the time difference between Melbourne and London.

Here we have that the time difference between Melbourne and Singapore is 3 hours ahead.

And the Time difference between Singapore and Wellington is 5 hours behind then the difference between wellington and Melbourne is 3 hours.

Now the time difference between Wellington and London is 12 hours.

Through this we know that the time difference between Melbourne and London 11.00 hours.

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Answer:

The decimal is 2.8 The 8 is the repeating decimal I just couldn't add the line to the top. So it would be 2.88888...

Step-by-step explanation:

The cost of the mesh measuring 25 m is 2300 euros .

The perimeter of the sq. is outlined because the total length of the boundary of a sq.. we want to feature all the edges of sq. to seek out its perimeter. By the formula of perimeter of polygonal shape, we know;

Perimeter = add of all sides

Perimeter of sq. = add of the lengths of four sides

= aspect + aspect + aspect + aspect

= 4 × side

First , we will calculate the the perimeter of the square

Perimeter of square = 25 × 4.

                                     = 100 m

Total cost = perimeter required  × cost per meter .

Cost of mesh = 100 × 23

                        = 2300 euros

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Answer:

[tex]4^{27}[/tex] and 18014398509482000

The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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