Two ferries travel across a lake 50 miles wide. One ferry goes 5 miles per hour slower than the other. If the slower ferry leaves 1 hour before the faster and arrives at the opposite shore at the same time as the other ferry, what is the speed of the slower ferry

Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

y = x+5

2.When x = 10,y = x+5 = 10+5 = 15

3.When x =15,y = x+5 = 15+5 = 20

4.When x = 20,y = x+5 = 20+5 = 25

Consequently, the equation y = x + 5 describes the relationship between the x and y values in the table.

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The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.

The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,

Now solve the polynomial by putting the value of x equal to -1:

5(-1) - 4(-1)^2 + 3        ,  x =  - 1

-5 - 4 ( 1 ) + 3             , squaring -1 gives + 1

minus 5 minus 4 plus 3

( - 9 + 3)

( - 6 )

Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.

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B: (0, -1) , ( -4,0) , ( -2, -1) , (7, -7)

Image result for ordered pair definition

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair’s numeric values can be integers or fractions.

The origin is the place where both axes cross. Every point on the coordinate plane is represented by an ordered pair (x, y), with the first element x referred to as the x-coordinate and the second element y referred to as the y-coordinate.

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The missing angle of a triangle where only the measure of all sides are given can be calculated by using the Cosine Law .

What is Law Of Cosine ?

The law of cosine is also known as Cosine Rule. This law is useful in finding  the missing information of  any triangle.

For example, if you know the lengths of three sides of a triangle , this rule helps to find the angle between the two sides of the triangle.

Let a , b and c be the sides of the triangle and let A , B and C be the angle corresponding to the respective sides .

Then by the Cosine Law the angles are represented as : [tex]CosA = \frac{b^{2} +c^{2} -a^{2} }{2bc}[/tex] ;

[tex]CosB = \frac{c^{2} +a^{2} -b^{2} }{2ac}[/tex] ; [tex]CosC = \frac{a^{2} +b^{2} -c^{2} }{2ab}[/tex] .

Therefore , The Law Of Cosines is used to find the missing angle .

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The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of the line as -

y = 14x - 4

The given equation of line is -

y = 14x - 4

Slope of the line perpendicular to the given line is -

m{p} = -1/14

The equation of this line will be -

y = -(1/14)x + c

For the point (28, 16), we can write -

16 = -(1/14) x 28 + c

c = 16 + 2

c = 18

So, the equation will be -

y = - (1/14)x + 18

Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

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Answer:

h = 4 ft

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 8 and h = 3 , then

A = 8 × 3 = 24 ft²

Now consider the other base b = 6 with perpendicular height h , then

6h = 24 ( divide both sides by 6 )

h = 4

Answer:

x = 2

Step-by-step explanation:

If you look at the equation:

(x + 2) = 4

We just need to solve for x.

To solve for x, we can subtract the total by the addend, to get the variables value.

4 - 2 = 2

Therefore, the value of x is 2.

The answer to 7 to the power of 2 is 49.

This is because when a number is raised to a power, it means that it is multiplied by itself that number of times. 7 to the power of 2 is 7 multiplied by itself 2 times, which is 7 x 7, which equals 49.

An expression known as "power" denotes the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.

As an illustration, the power 63 demonstrates how three times the number 6 is multiplied.

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The unknown number deduced by solving the equation 4x - 1 = 6x +9 is -5.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let the unknown number be x.

First multiply the number by 4 = 4x

Then subtract 1 from it = 4x -1

This results in the same number as when the number is multiplied by 6 and 9 is added to it = 6x + 9.

So the equation will be -

4x - 1 = 6x +9

4x - 6x = 9 + 1

-2x = 10

-x = 10/2

x = -5

Therefore, the number obtained is -5.

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If you take a number, times by 4 then subtract 1. You get the same as if you took the number, times by 6 then add 9. What is the number?

Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

What are Trigonometric functions?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here,

We have to find out why trigonometric ratios are used only for right triangles.

We concluded that when we are dealing with triangles other than right triangles, the solution is to draw a perpendicular line to create right triangles. For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

Hence, for Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

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Answer:

A rectangle and a square are quadrilaterals with four right angles. ​

Step-by-step explanation:

Hope it helps! =D

The plane will fly 392 miles in 28 minutes. Therefore, the answer is D) 124 miles.

What is the relationship between distance and time?

The important thing is that speed is always the ratio of the distance traveled to the time needed to travel that distance: distance/time.

To find out how far the plane will fly in 28 minutes, we need to substitute x = 28 into the equation y = 14x.

y = 14x represents the relationship between the distance flown (y) and time flown (x).

Substituting x = 28 into the equation:

y = 14 * 28 = 392

Hence, the plane will fly 392 miles in 28 minutes.

Therefore, the answer is D) 124 miles.

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Given that the sum of two numbers is 71 and one number is 27 more than the other, we can set up the following system of equations:

What is the straightforward definition of a system of equations solution?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

x + y = 71 (equation 1 represents the fact that the sum of the numbers is 71)

y = x + 27 (equation 2 represents the fact that one number is 27 more than the other)

To solve the system of equations, we can use the substitution method. We'll substitute equation 2 into equation 1:

x + (x + 27) = 71

Combining like terms:

2x + 27 = 71

Subtracting 27 from both sides:

2x = 44

Dividing both sides by 2:

x = 22

Now we can substitute x = 22 back into equation 2 to find the value of y:

y = x + 27

y = 22 + 27

y = 49

So the two numbers are x = 22 and y = 49, and they satisfy the given conditions that the sum of the two numbers is 71 and one number is 27 more than the other.

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Answer: 18pi + 36 + (36-4.5pi)+4.5pi= 22.5pi + 36 + (36-4.5pi)

Step-by-step explanation:

CDEF is a square so all sides of CDEF are 6cm.

This tells us the area of CDEF which is 36cm squared

This tells us the radius of AE which is the side FE which we know is 6cm.

Area of a half circle= pi x r squared/2

Area of AE= pi x 36/2= 18pi

Now, look at the square with the half circle inside ABCF. If the half circle was part of the shaded square, the area would be 36cm squared. But since it isn't we need to minus the area of the half circle from 36cm square (area of ABCF)

Area of half circle BC= pi x 3 squared/2= pi x 9/2= 4.5pi.

So the area of ABCF is 36-4.5pi.

CD would also have an area of 4.5pi as it is the exact same half circle.

Area of AE=18pi cm squared

Area of CDEF= 36cm squared

Area of ABCF= 36-4.5pi

Area of CD= 4.5pi

18pi+36+(36-4.5pi)+4.5pi

simplified to:

22.5pi + 36 + (36-4.5pi)

The best estimate for the circumference of a circle with 3 units radius is equal to 18 units. The correct option is A.

Given the radius of the circle is equal to 3 units.

The formula for the circumference of the circle is equal to

[tex]C=2*\pi *r[/tex].

By substituting the value of the radius and pi we will get:

[tex]C=2*3.14*3\\C=18.86[/tex].

Therefore the best estimate will be 18 units.

Complete question:

Which is the best estimate of the circumference of this circle?

radius = 3 units.

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The set of ordered pairs represents the function.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

The set of ordered pairs:

(7,9), (4,18), (−3,11), (16,18), (4,−11)

Pairs written as input and output of the relation.

In the attached table,

To prove function:

A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function.

And here each input is connected to precisely one output.

Therefore, this is a function.

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If a company found that raising the price of its muffins resulted in an absolute value of.35 < 1, then the demand for muffins is inelastic.

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The total area of the two rectangles is given by the equation A = 33 units²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the total area of the 2 rectangles be A

Now , each grid square represents = 1 square unit

Now , let the first rectangle be represented as P

The length of P = 4 grid squares

The width of P = 3 grid squares

Let the second rectangle be represented as Q

The length of Q = 7 grid squares

The width of Q = 3 grid squares

So , Area of Rectangle = Length x Width

The area of rectangle P = 4 x 3

The area of rectangle P = 12 units²

The area of rectangle Q = 7 x 3

The area of rectangle Q = 21 units²

So , the total area of figure A = area of P + area of Q

On simplifying the equation , we get

Total area of figure A = 12 units² + 21 units²

Total area of figure A = 33 units²

Therefore , the value of A is 33 units²

Hence , the area is 33 units²

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When sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is  -4/5

The terminal side of an angle refers to the line that intersects the initial line to make an angle

In the problem the terminal side is said to be in the third quadrant and the in the third quadrant sin θ = - 3/5

sin θ = opposite / hypotenuse

using Pythagoras the adjacent is 4, in third quadrant we have -4

cos θ = - adjacent / hypotenuse = -4/5.

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Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.

Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.

Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.

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Answer:

  the median will go up 2.5 points from 76 to 78.5

Step-by-step explanation:

You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.

The median is the middle value when the list is sorted into order. The ordered list is ...

  41, 69, 76, 81, 96

The median is 76.

When 85 is added to the list, the sorted list becomes ...

  41, 69, 76, 81, 85, 96

There are two middle scores, so the median is their average:

  (76+81)/2 = 78.5

The median increases 2.5 points from 76 to 78.5 when the score is added.

Yes, 6 is an positive number.

Now, According to the question:

What Is A Positive Number?

A positive number is any number that represents more than zero of anything. If you are talking about dollars in your bank account, a positive number will definitely make you feel positive too.

1, 2, 3, 4, 5, 6, 7, ........ are positive integers and -1, -2, -3, -4, -5, -6, -7, ........ are negative integers. 0 is an integer which is neither positive nor negative. On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.

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Step-by-step explanation:

the given ratio is

8 / 20/10 = 8 / 2 = 4

for x mathletes we need to keep the same ratio :

x / 30/5 = 4

x / 6 = 4

x = 4×6 = 24

24 mathletes.

The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit

The ratio of nuts to fruits is -

r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)

r = 5/1

5 : 1

For every 5 cups of nuts, there is 1 cup of dried fruit cup.

Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

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Answer:

Slope = -5

Step-by-step explanation:

Slope Formula:

y2-y1/x2-x1

So

-6-4/2-0=

-10/2

Therefore -5 is the Answer

Hope this helps

Driving from North Carolina to Florida at an average speed of 70 mph takes about 7 hours and 12 minutes.

Velocity is a term used to describe how fast an object is moving in a particular direction. It is measured as distance traveled in a period of time and is usually expressed in units of meters per second (m/s). Velocity is an important concept in physics and is used to calculate how fast an object moves in a given environment. Velocity is related to speed, which is the rate of change of distance in a particular direction. Speed ​​is an important factor in many sports and activities such as running, cycling and driving. It is also used in different ways in our daily life. For example, it is used to determine how fast a car can go from A to B, or how long it will take to walk to a destination.

Speed = Distance/Time

55 = Distance/9

Distance = 495 miles

When speed is 70 mph:

70 = 495/Time

Time = 495/70

Time = 7 hours and 12 minutes

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A polynomial is an expression involving variables and coefficients, which is formed by adding, subtracting, multiplying, and taking non-negative integer exponents of the variables. A mathematical statement that two expressions are equal is known as an equation.

A mathematical statement that two expressions are equal is known as an equation.

Example of a polynomial:

2x^2 + 3x + 5

Example of an equation:

2x^2 + 3x + 5 = 0

Let's say we are solving the equation 2x^2 + 3x + 5 = 0

Step 1: Subtract 5 from both sides.

2x^2 + 3x = -5

Step 2: Divide both sides by 2.

x^2 + 3/2 x = -5/2

Step 3: Use the quadratic formula to solve for x.

x = (-3 ± √17) / 4

Step 4: Simplify the answer.

x = (-3 ± 4.12) / 4

Step 5: Solve for the two values of x.

x = -0.78 or x = 3.28

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