Examine the following paragraph proof.
Consider parallelogram PQRS, where PQ = RS

In 120 minutes, all the three boats will next meet at the starting location. The solution has been obtained by using the concept of least common multiple.

What is least common multiple?

Least Common Multiple is abbreviated as LCM. The smallest multiple shared by two or more different numbers is referred to as the least common multiple.

We are given that three boats start cruising around a small island starting at the same time and from the same location, and following the same route.

They take one full circle around the island which is 2 km.

First boat:

It covers 5 km in 60 minutes.

So, it will cover 2 km in 60/5 * 2 = 24 minutes

Second boat:

It covers 4 km in 60 minutes.

So, it will cover 2 km in 60/4 * 2 = 30 minutes

Third boat:

It covers 3 km in 60 minutes.

So, it will cover 2 km in 60/3 * 2 = 40 minutes

Now, taking the LCM of 24, 30 and 40, we get 120.

Hence, in 120 minutes all the three boats will next meet at the starting location.

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Answer: Use the Pythagoream theorem: a²+ b² = c²

Step-by-step explanation: note that c = the hypotenuse

2² + 5² = c²

Simplify

4 + 25 = c^2

Combine like terms

29 = c^2

isolate the c. Root both sides

√29 = c

c = 5.38516481

5.39 is your answer

The shortest distance is 5.39 miles  between your home and the mall

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The distance from your home to the school is 2 miles south, which means the y-coordinate of the school is -2.

The mall is located 5 miles west of the school, which means the x-coordinate of the mall is -5.

So, we have two points on the coordinate plane: your home at (0, 0) and the mall at (-5, -2).

The distance between them can be found using the distance formula:

Distance=√(x₂-x₁)²+(y₂-y₁)²

=Distance=√(-5-0)²+(-2-0)²

=√25+4

=√29

=5.39 units

Hence,  the shortest distance is 5.39 units

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Answer:

p = 6.95 + (0.95 × t)

Step-by-step explanation:

A function rule explains how to convert an input value (x) into an output value (y) for any given function.

To get the total price (p) we need to add the cost of the pizza itself, and add each topping. The part of the equation (0.95 × t) can solve for the price of each topping, so we add that on.

The picture and the board are not mathematically similar because they have different areas when calculate which are = 80cm² and 120cm² respectively.

The dimensions of the picture is as follows;

The length = 8cm

The width = 10cm

The area of the picture = 8×10 = 80cm²

The dimensions of the board is as follows;

The length = 10cm

The width = 12cm

The area of the board = 12×10 = 120cm²

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She can compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.

To show that a design is symmetric across a line using coordinates, you can use the following steps:

Here's an example of how to use coordinates to show that a design is symmetric across the x-axis:

Suppose Yuson has a design with three points: A(2, 4), B(4, 6), and C(6, 4), and she drew a dashed line along the x-axis to represent the line of symmetry.

To check if the design is symmetric across the x-axis, she can reflect each point across the x-axis to obtain the following new coordinates: A'(2, -4), B'(4, -6), and C'(6, -4).

She can then compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.

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The base of the triangle is 9 inches and the height is 2 inches.

Let's denote the height of the triangle as h, and the base as b.

We know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Substituting the values we have:

9 = (1/2) * b * h

Multiplying both sides by 2 gives:

18 = b * h

We also know that the base is 5 inches more than 2 times the height:

b = 2h + 5

Substituting this expression for b in terms of h in the area equation, we get:

18 = (2h + 5) * h

Expanding the right-hand side, we get:

18 = 2h^2 + 5h

Rearranging this equation, we get:

2h² + 5h - 18 = 0

We can solve for h by using the quadratic formula:

h = [-b ± [tex]\sqrt{b² - 4ac}[/tex]] / 2a

where a = 2, b = 5, and c = -18.

Plugging these values into the formula, we get:

h = [-5 ± [tex]\sqrt{5^{2} - 4(2)(-18) }[/tex]] / (2 * 2)

Simplifying:

h = [-5 ± [tex]\sqrt{169}[/tex]] / 4

Taking the positive solution:

h = [-5 + 13] / 4

h = 2

Now that we know the height is 2 inches, we can use the equation b = 2h + 5 to find the base:

b = 2(2) + 5 = 9

Therefore, the base of the triangle is 9 inches and the height is 2 inches.

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One milliliter is equal to one cubic centimeter

To convert 1 milliliter to cubic centimeter , we can use the following formula:

1 mm = 1 cc

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The volume in cc = Conversion factor × The volume in ml

Substitute the values in the equation

The volume in cc = 1 × 1

Multiply the terms

= 1 cc

Therefore, one ml is 1 cc

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Standard conversions state that 375 cm is equivalent to 147.6 inches.

A fixed magnitude of a quantity that serves as a reference point for measuring other quantities of the same sort is referred to as a unit of measurement. Convention or legislation establish and adopt it. Every other amount of that sort can be expressed as a multiple of the unit of measurement.

One inch is 2.54 cm long.

We can compose,

2.54 cm equals one inch.

1 cm equals 0.54"

Thus, 375 cm will be equal to 375/2.54 inch.

175 cm = 147.6 in.

So, 375 cm equals 147.6 inches in inches.

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Complete question - what is 375cm in inches?

Answer:

The speed of the first ship= 30 knots The speed of the second ship= 20 knots The first ship started at noon and after three hours second ship started. The direction of the first ship is along South and that of second ship is East.

Step-by-step explanation:

The required two cords together is 5 1/8 yards long, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
We can add the two cords together in different ways:

2 6/8 yards = 22/8 yards

2 3/8 yards = 19/8 yards

Total length in eighths of a yard: 22/8 + 19/8 = 41/8 yards

Simplifying 41/8 yields 5 1/8 yards.

So the two cords together are either 4 19/36 yards or 5 1/8 yards long.

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The product of (3 x 107) and (2 x 107) is 6.8694 x 10^4

To find the product of (3 x 107)and (2 x 107), we can use the distributive property of multiplication which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can multiply the numbers outside the parentheses first, and then multiply the result by the common factor of 107 to simplify the expression:

(3 x 107) x (2 x 107) = 6 x (107 x 107)

Next, we can calculate the product of 107 and 107, which is 11,449:

6 x 11,449 = 68,694

In scientific notation, this can be written as:

= 6.8694 x 10^4

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The surface area for the given radius and height are For r = 5 and h = 2: TSA = 2π(5)(5+2) = 2π(5)(7) = 70π sq.cm. For r = 9 and h = 11: TSA = 2π(9)(20) = 360π sq. cm.

The entire area a cylinder occupies in three dimensions is known as the cylinder's area. The combined areas of the two circular bases and the curving surface make up the cylinder's surface area. In right cylinders, the axis line creates a right angle to the base, and the two circular bases are perfectly over one another. It is referred to as an oblique cylinder if one of the circular bases is misaligned and the axis does not make a right angle with the base.

The curving surface that sits in the center of the two circular bases opens to reveal a rectangular shape. A lateral surface is another name for this curved surface.

The total surface area of the cylinder is given by the formula:

TSA = 2πr(r + h)

For r = 5 and h = 2:

TSA = 2π(5)(5+2) = 2π(5)(7) = 70π sq.cm

For r = 9 and h = 11:

TSA = 2π(9)(20) = 360π sq. cm

For r = 9 and h = 8:

TSA = 2π(9)(17) = 306π sq. cm

For r = 4 and h = 7:

TSA = 2π(4)(11) = 88π sq. cm

For r = 6 and h = 5:

TSA = 2π(6)(11) = 132π sq. cm.

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The weighted average ROR of the investments, based on the provided investment portfolio, would be 2.1%.

By multiplying each data point by its weight and adding the resulting products, the weighted average is calculated. The weights for all the data points are then added. Divide the weight*value products by the total weights to finish. You've successfully determined the weighted mean.

Find the overall portfolio value first:

= 2,600 + 3,700 + 575 + 1,225

= $8,100

The investments' weighted average Rate of Return (ROR) is:

= (2,600 / 8,100 x 1.7%) + (3,700 / 8,100 x 3.2%) + (575 / 8,100 x 12.9%) + (1,225 / 8,100 x -5.6%)

= 2.076

= 2.1%.

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The conversion of 184 centimetres in feet is equals to the 6.03 feet. Thus, conversion factor from centimetres to feet is 6.03/184 = 0.032.

A conversion factor is a number used to convert one set of units into another set of units by multiplication or division. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So, 184meters

= 184× 3.28 feet

= 603.52 feet --(1)

But we need to convert 184 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 184 meters = 18400 centimeters --(2). Now from equations (1) and (2),

18400 centimeters = 603.52 feet,

Divide both parts by 100,

=> 184 centimetres = (603.52/100 ) feet

= 6.03 feet

Hence required value is 6.03 feet.

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The volume of the solid is 342.9 sq. cm.

The volume of an object is the amount of substance that the object can contain. Th three dimensions of the object is required in order to determine its volume.

Considering the question,

volume of a cylinder = [tex]\pi[/tex]r^2h

Where r is the radius and h is the height of the cylinder.

volume of the hole = length*width*height

Thus,

The volume of a cylinder = [tex]\pi[/tex]r^2h

                   = 22/7*4^2*10

                   = 502.86

The volume of the cylinder is 502.86 sq. cm.

The volume of the hole = length*width*height

                                     = 4*4*10

                                     = 160 sq cm.

The volume of the solid = volume of a cylinder  - volume of the hole

                                         = 502.86 - 160

                                      = 342.86

The volume of the solid is 342.9 sq. cm.

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[tex]{ \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}} [/tex]

lets find the equation of line in two point form, considering points (0 , 0) and (-3 , 4)

[tex]\qquad \rm\dashrightarrow \:y - 0= \dfrac{4 - 0}{ - 3 - 0} (x -0)[/tex]

[tex]\qquad \rm\dashrightarrow \:y = - \dfrac{4 }{ 3 } x [/tex]

That's the required equation ~

You can also simply it as :

[tex]\qquad \rm\dashrightarrow \:3y= - 4x[/tex]

[tex]\qquad \rm\dashrightarrow \:4x + 3y = 0[/tex]

Option C is correct. Meta-analysis takes all of the correlations found in studies of a particular relationship and calculates a weighted average of them.

In order to identify results on a broad scale, meta-analysis looks for common threads among various studies and applies weights to them. In essence, it expands on the numerous research that might be conducted on a certain relationship topic. For instance, one particular relationship might be investigated using various methods at various points in time. A meta-analysis attempts to compile all of these studies, assign weights to each study, and then determine the outcomes that are on a meta-level, or bigger picture, after taking into account all of the various correlations.

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The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

If line AB and line CD are parallel, and line EF intersects both lines at points G and H respectively, then the angles formed on opposite sides of line EF and on the exterior of the parallel lines are congruent.

The Alternate Exterior Angles Theorem states that when a pair of parallel lines is intersected by a transversal, the pairs of alternate exterior angles formed on opposite sides of the transversal are congruent.

In symbols, the theorem can be written as:

∠1 ≅ ∠4

where ∠1 and ∠4 are alternate exterior angles.

This theorem is useful in solving problems involving angles and parallel lines, and it is commonly used in geometry proofs.

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Answer:

The angles are 178.1° and 1.9°

Step-by-step explanation:

Supplementary angles add up to 180°
Let the angles be x and y with x being the larger angle

x = 176.2 + y
x - y = 176.2         (1)

Since they add up to 180 we also get
x + y = 180           (2)

Equations added: (1) + (2)

x - y + x + y = 176.2 + 180

2x = 356.2

x =  356.2/2 = 178.1°

y = 180 - 178.1 = 1.9°

The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

For new customers, there is an additional one-time $150 service fee.

Now, Let the number of months of service = x

And, the total amount paid in dollars by an customer = y

Hence, The correct linear equation is,

⇒ y = 150x

Thus, The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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The value of f(-7) in the given function, f(x) = -x^2 + 2x + 6, is -57

From the question, we are to determine the value of f(-7) in the given function

The given function is

f(x) = -x^2 + 2x + 6

To find the value of f(-7) in the given function,

We will substitute -7 for x in the expression for f(x) and evaluate the resulting expression

That is,

f(x) = -x^2 + 2x + 6

f(-7) = -(-7)^2 + 2(-7) + 6

Simplifying this expression gives:

f(-7) = -49 - 14 + 6

f(-7)= -57

Hence, the value of f(-7) is -57

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This equation can be used to predict the balance of the savings account after t years.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.


We can graph the data in a line graph to visualize the relationship between the two variables. The graph will have time (t) represented on the x-axis and the balance of the savings account (m) represented on the y-axis. The graph will demonstrate that the total balance of the two accounts increases over time.

The equation that models this data can be found by using the slope-intercept form, y = mx + b. Here, y represents the balance of the savings account (m), x represents the time (t), m is the slope of the line, and b is the y-intercept. To find the equation, we can first find the slope, which is the change in y divided by the change in x. This is (2,800 - 500) / (3 - 0) = 2,300 / 3 = 766.67. The y-intercept is the balance of the savings account when t = 0, which is 500. We can now write the equation as m = 766.67x + 500. This equation can be used to predict the balance of the savings account after t years.

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In this case, when you have a subtraction of -7a^2 and then an addition of +10a^2, you can simplify the expression by adding the coefficients of the two terms that have the same literal and exponent.

So, you have:

-7a^2 + 10a^2

To add or subtract these terms, we need to have the same literal and exponent, which is the case here. The coefficients of the terms are -7 and 10, so we can add them to get:

-7a^2 + 10a^2 = 3a^2

Therefore, the simplified expression is 3a^2.

In summary, when you have terms with the same literal and exponent, you can add or subtract their coefficients to simplify the expression.

The quotient of (5+21) (6-4) and (2+1) is 13/3, expressed in its simplest form

The quotient of two numbers is a way of expressing the ratio of their values. It is the result of dividing one number by the other, and can be written as a fraction or as a decimal.

The quotient of 4 and 8 is 0.5, since 4 divided by 8 is 0.5.

The quotient of (5+21) (6-4) and (2+1) can be expressed as follows:

First, we need to solve each parenthesis separately. The first parenthesis is (5+21), which equals 26. The second parenthesis is (6-4), which equals 2. Therefore, the quotient of (5+21) (6-4) is 26/2, which can be simplified to 13/1.

Now, we need to divide 26/2 by (2+1). The result is 13/3, which is the final quotient.

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The average cost of an entree on a restaurant menu that is $15 describes the mean, not the median.

The mean is the average value of a data set.

To compute the average, the total value of the data set is divided by the number of items involved.

The average value or mean is the quotient of the total value and the number of data items.

On the other hand, the median describes the middle value of an ordered list of data values.

Thus, when an entree on a restaurant menu costs $15 on average, it is a description of the mean value and not the median.

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Linear Equation and It's Application in Real Life

In the given problem, it is an application of linear equation and solving word problem about mathematical operation. It is a combination of general mathematics and algebra.

In word problem about time and work, the equation is 1/x + 1/y + 1/z + ... = 1/t, where

x is the amount of time consume by first person

y is the amount of time consume by second person

z is the amount of time consume by third person

t is the amount of time they consume working together.  

In this case, to solve for the amount of work that Rizal can finish the school project alone.

1/x + 1/y + 1/z + ... = 1/t

It can be derived as 1/x = 1/t - (1/y + 1/z + ... ), where x is the amount of work done by Joseph, and y for Maria.

Given

Joseph can finish the chores in 2 hours

Maria can finish the same chores in 4 hours.

Create  mathematical equation using the given formula for work problem.

1/x + 1/y = 1/t, where x = 2 hours, and y = 4 hours

½ + ¼ = 1/t, solve for t

The LCD of 2, 4 and t is 4t, the new equation will be

4t(1/2) + 4t(1/4) = 4t(1/t)

2t + t = 4

3t = 4

t = 4/3

t = 1 1/3 hours

Final Answer

1 1/3 hours to complete the task when they work together.  

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The price after the discount is,

⇒ $58.5

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A jersey originally cots $50.

And, It was marked up 30% after a championship win and then discounted 10% a few months later.

Now, The markup price is,

⇒ $50 + 30% of $50

⇒ $50 + 30/100 × $50

⇒ $50 + $15

⇒ $65

And, After 10% discount the price is,

⇒ $65 - 10% of $65

⇒ 65 - 10/100 × 65

⇒ $65 - $6.5

⇒ $58.5

Thus, The price after the discount is,

⇒ $58.5

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The value of x in the right triangle is 8.7 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The side of a right angle triangle can be found using trigonometric ratios or Pythagoras's theorem.

Hence, let's use Pythagoras's theorem,

c² = a² + b²

where

Therefore,

x² = 10² - 5²

x² = 100 - 25

x = √75

x = 8.66025403784

Therefore,

x = 8.7 units

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The slope is 0.625 or 5/8.

Remember: Rise Over Run(Up or Down is the numerator and left or right is the denominator)

M = Slope

M = 5 ÷ 8

5 ÷ 8 = 0.625

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