A rectangle’s length is three times its width, w. Its area is 243 square units. what would the equation be to find the width of the rectangle?

Answer:

0.32958 kilometers per minute

Step-by-step explanation:

Distance covered = 26.219 miles

Step 1: Convert this distance to kilometers using the conversion( 1mi = 1.609  km)

==> 26.219 miles = 26.219 miles x 1.609 km/mile = 42.186371 km

This distance was covered in 128 minutes

Step 2: To find the speed in km/min, divide 42.186371 by 128
= 42.186371/128

= 0.32958 kilometers per minute
------------------------------------------------------------------------------------
We could also solve this problem using the following alternative technique
Step 1 Determine speed in miles/minute = 26.219/128 = 0.2048 m per min

Step 2: Multiply by conversion factor 1.609:
0.2048 x 1.609 = 0.32958 kilometers per minute

The number of books to read per month is 3 or more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

14x ≥ 42

Solve for x.

14x ≥ 42

Divide both sides by 14.

x ≥ 42/14

x ≥ 3

This means,

The number of books to read per month is 3 or more.

Thus,

The number of books to read per month is 3 or more.

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The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

[tex]dv/dt = -k v^2[/tex]

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]

The differential equation is separable:

[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =[tex]∫0^120 v(t) dt[/tex]

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.

When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:

WWx (two women and one of either gender)

WMx (one woman, one man, and one of either gender)

MWx (one man, one woman, and one of either gender)

MMx (two men and one of either gender)

In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.

In outcome 1 (WWx), a woman is selected twice, so x = 2.

In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.

In outcome 4 (MMx), no women are selected, so x = 0.

Therefore, the possible values of x are 0, 1, 2, and 3.

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The polynomial expression cannot be divided

From the question, we have the following parameters that can be used in our computation:

(x + 1) /x³ − 3x² + 6x +11.

The degree of the numerator is 1

While the degree of the denominator is 3

For a polynomial quotient to be evaluated, the degree of the numerator must be greater than the degree of the denominator

Because 1 is less than 3, then the polynomial expression cannot be divided

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The profanity filter refused my answer.

Please find it in the txt file.

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Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.

Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.

Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.

Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.

Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.

Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.

Answer:

We can start by finding the total number of learners who participate in jogging and cycling by multiplying the ratio by the total number of learners. Let's say x is the number of learners who jog. Then, the number of learners who cycle is 2x.

The total number of learners who jog and cycle is 125, so:

x + 2x = 125

3x = 125

x = 125 / 3

x = 41.67

Since x represents the number of learners who jog, there are 41.67 learners who jog. Since the number of learners who cycle is 2x, there are 2 * 41.67 = 83.33 learners who cycle.

Since these are whole numbers of learners, we round up to the nearest whole number to get 42 joggers and 83 cyclists.

The number of students participating in each of the sports will be 75 for jogging and 50 for cycling.

Solution:

Let's assume that the number of students who participated in jogging will be 3x and those in cycling will be 2x

Given,

3x + 2x = 125

5x = 125

So, x = 25

Therefore, the number of students in jogging will be 3*25 = 75 and in cycling will be 2*25 = 50

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Answer:

-47

Step-by-step explanation:

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^2−4 (ac)

Substitute in the values of a, b, and c.

1^2 − 4 (4 x 3)

Evaluate the result to find the discriminant.

Simplify each term.

One to any power is one.

1 − 4 (4 x 3)

Multiply

−4 (4 x 3)

Subtract 48 from 1.

-47

The hourly rate that the batches of cookies were made is given as follows:

4.85 batches per hour.

The hourly rate is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate is obtained dividing the total production by the time in hours.

The parameters for this problem are given as follows:

Hence the rate is given as follows:

40/8.25 = 4.85 batches per hour.

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Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's call the number of hours Camden works babysitting "x".

We know that x + 9 (hours of lifeguarding) cannot be more than 14 and that his total earnings must be at least $180. So we can write two equations based on these conditions:

x + 9 ≤ 14 (hours worked can't exceed 14)

10x + 18 × 9 ≥ 180 (earnings must be at least $180)

Now we can substitute the first equation into the second:

10x + 18 × 9 ≥ 180

10x + 162 ≥ 180

10x ≥ 18

x ≥ 1.8

Since x has to be a whole number of hours, we round up to find that Camden must work at least 2 hours babysitting.

So, Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

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The total area of the quilt is: 166.5 square inches

The six-sided figure is given, and we can deduce the following parameters from the question:

The shape is made of a triangle and a rectangle

The side lengths derived from the question are:

The triangle on top:

base: 6 inches and height: 7.5 inches

The rectangle at the bottom:

Base: 16 inches with a height of 9 inches

So, we have the total area of the figure to be

Area of figure = (1/2 * 7.5 * 6) + (16 * 9)

Area of figure = 22.5 + 144

Area of figure = 166.5 in²

Based on the parameters, the total area is 166.5 square inches

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The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.

The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.

The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.

The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.

The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.

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Based on the information provided, the number of guests was 8 guests and the equation to represent this situation is 3/8 x + 2 = 5.

The first step to get to know the number of guests is to write an equation, this will help us discover the number of x  or guests. To write the equation, let's include the variable and values given:

3/8 x + 2 = 5

Now, let's solve this equation:

0.375x + 2 = 5

x = 5 -2/ 0.375

x = 3 / 0.375

x = 8 guests

Based on the above, it can be concluded that the number of guests, in this case, was 8.

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Which quantity is unknown?

the number of guest

_____________________________________

Write an equation that represents the situation.

3/8g + 2 = 5

_____________________________________

How many guests does David have?

g = 8

Answer:

I didn't understand the question 100% but I think the question is asking you to give an equation from the given one

so the answer will be

-s divided over tq

Answer:

The ratio computed shows that the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

How to illustrate the ratio?

From the information given, there are 36 marbles in the bag. The number of red marbles will be:

= 5/9 × 36

= 20 marbles

The number of blue marbles will be:

= 4/9 × 36

= 16 marbles

When a student removes 1 blue marble from the bag, the number of blue marbles will be:

= 16 - 1

= 15 marbles.

Therefore, the ratio of red to blue marbles will be:

= 20:15 = 4:3

Therefore, the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

Answer:

So the answer is C. (x - 3)^2.

Step-by-step explanation:

The complete square corresponding to x^2 - 6x is (x - 3)^2.

A complete square is a trinomial that can be written in the form (x - a)^2, where a is a constant. To find the complete square of x^2 - 6x, we need to rewrite x^2 - 6x into the form (x - a)^2. We do this by adding and subtracting a constant term to make the trinomial a perfect square.

x^2 - 6x + 9 = (x - 3)^2

So the answer is C. (x - 3)^2.

The absolute value function on the graph is:

f(x) = |x + 2| + 3

We know that for an absolute value function with a vertex at (a, b), then the absolute value function is:

f(x) = |x - a| + b

Here we can see that the vertex is at the point (-2, 3)

Then:

a = 2

b = 3

The function will be:

f(x) = |x + 2| + 3

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Answer: D

Step-by-step explanation:

If a plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. the length of the first pipe originally is 702 cm.

Let's call the original length of the first pipe "L"

Let the length of each of the 5 equal pieces "x".

set up the equation:

5x + 27 = L

Each piece of the second pipe is "x" cm long. The second pipe is 15 m long, which is equivalent to 1500 cm. The plumber cut 11 pieces of the same length as each of the 5 equal pieces from the first pipe, so the total length of the 11 pieces is:

11x

The plumber had 15 cm of the second pipe left over after cutting 11 pieces, so we can set up another equation:

1500 - 11x = 15

Solving for "x" in the second equation:

11x = 1485

x = 135

So each piece of the second pipe is 135 cm long.

To find the original length of the first pipe, we can substitute x = 135 into the first equation and solve for L:

5x + 27 = L

5(135) + 27 = L

L = 702

Therefore, the original length of the first pipe was 702 cm.

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Answer:

6 is not the solution.  7 is the solution.

Step-by-step explanation:

5(x -3) = x + 13  Substitute 6 for x

5(6 -3) = 6 + 13

5(3) = 19

15 ≠ 19

6 is not a solution because it results in a false statement.  The two sides do not equal each other.

5(x - 3) = x + 13   Distribute the 5

5x -15 = x + 13  Subtract x from both sides

5x - x - 15 = x - x + 13

4x - 15 = 13  Add 15 to both sides

4x - 15 + 15 = 15 + 13

4x = 28  Divide both sides by 4

x = 7

7 is the solution to the equaion.

[tex]above \: the \: line[/tex]

Answer:

AAS

Step-by-step explanation:

[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.

If the length of the rectangular plot  is 180m , then the width of the rectangular plot is 51.2 m .

The Area of square plot is ⇒ Area = (Side) × (Side),

In this case, Side is = 96m,

So , the area of the square plot is : A = 96m x 96m = 9216 m² .

The Area of  Rectangular Plot is ⇒ A = (Length) × (Width) ;

We know that the area of the rectangular plot is the same as that of the square plot,

that means ⇒ Length × Width = 9216 m² ;

We also know that Length = 180m, so we substitute this value in the equation above ;

⇒ 180m × Width = 9216 m² ;

Dividing  both sides by 180m ;

we get ;

⇒ Width = 9216/180 ;

⇒ Width = 51.2 m ;

Therefore, the width of the rectangular plot is 51.2 meters.

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The given question is incomplete , the complete question is

In exchange of a square plot of side 96 m, a man wants to acquire a rectangular plot of 180m long and of the same area of the square plot .

Find the width of the rectangular plot .

Answer:

10/x is a nonlinear equation. Linear equations represent a straight line in a graph, whereas nonlinear equations are used to represent curves. In this case, the degree of variable y is 1 and the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

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Answer: s≥3

Step-by-step explanation: fist you need to get the variable by itself on one side. So subtract the 10 from each side and you have 3s≥9. Then you divide each side ny 3 to get s by itself, divide 9 by 3. Then your answer is s≥3

Answer:

(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b

Step-by-step explanation:

Add like terms

6a^2 + 12b

Answer: Correct answer is -1

Step-by-step explanation:

The height of the flagpole is 110 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

tan 19 = f/x

tan 21 = f/(600 - x)

Now,

tan 16 x = tan 21 x (600 - x)

0.34x = 0.38 x 600 - 0.38x

0.34x = 230 - 0.38x

0.34x + 0.38x = 230

0.72x = 230

x = 319

Now,

tan 19 = f/319

0.34 x 319 = f

f = 109.8

f = 110 feet

Thus,

110 feet is the height of the flagpole.

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