a flight from boston to london took only 5 hours because of a strong tailwind. The flight back to Boston against the same wind took 6 hours. What was the speed of the wind if the speed of the plane in still air is 550 miles per hour?

A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe this measure of central tendency.

What does the mode mean?

By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.

            A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                    Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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x + 2y = 12 and x = 4y represents the given word problem in equations

How to form an equation for a word problem?

Here are some steps to follow:

1. Understand all the words used in stating the problem. Understand what you are asked to find.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Use substitution, elimination or graphing method to solve the problem.

According to the given question:

Isaiah scored a total of 12 points. In this game, he made some free throws (worth one point each) and some two point shots.

Let number of free throws be x and number of two point shots be y.

x(1) + y(2) = 12

x + 2y = 12

This equation defines the total number of points scored with free throws and two point shots.

He made 4 times as many free throws as two point shots.

Using the pre defined variables to form the equation as

x = 4y

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Answer:

Step 2

Step-by-step explanation:

3x-24=5x

he did -3x on each side but added 3x to 5x instead of subtracting

Justin and Tim have played the same game a total of 10 times.

There are 10 players in Crestwood Elementary's four-square league, including Justin and Tim. Over the course of a semester, each possible match-up of five players occurs once. This means that Justin and Tim have played the same game a total of 10 times.

To calculate this, we need to consider the different combinations of players that can make up a five-person game. There are a total of 10! (10 factorial) permutations of the 10 players, meaning that each possible game is made up of different players.

This includes the combination of Justin and Tim, which occurs 10 times. Therefore, Justin and Tim have played the same game 10 times during the semester.

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Answer: 1.5 and 20

Step-by-step explanation:

The nature of the roots of a quadratic equation is described by the discriminant calculated by seeing the equation and comparing it with the standard equation which is given by -

[tex]ax^{2} + bx+c[/tex] , where a , b , c are real numbers .

The root of the equation is given by -

x= (-b )± [tex]\frac{\sqrt{b^{2} - 4ac}}{2a}[/tex]

Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .

This discriminant is the defining factor of the nature of the roots.

Now, here arise three cases-

(i) If (b^2 - 4ac) > 0, the roots are real and distinct .

(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.

(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.

Hence, it is the discriminant which determines the nature of roots.

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A root of degree 5 is called a fifth root.

A radicand, or nth root, in mathematics is a number r that, when raised to the power n, equals the number x: rn = x, where n is a positive integer, also known as the degree of the root. A root of degree 5 is called a fifth root.

The required number is the result of multiplying a fifth root by itself five times.

Due to the fact that two multiplied by itself five times is 32, 532 = 2

Seven multiplied by itself five times is 16807.

Hence 516807 Equals 7 since 7 x 7 x 7 x 7 = 16807.

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The image of (-4, 5) after a translation right 5 units and 2 units up is (1, 7).

What is the image of the point?

The given point P is "reflected" in the mirror and appears on the other side of the line an equal distance it. Drag the point P to see this. The reflection of the point P over the line is by convention named P' (pronounced "P prime") and is called the "image" of point P.

Going right means the x value goes up. In this case, it went to the right 5 spaces. so, all you have to do is add 5 with -4 which is 1.

When going up on a graph, the y value goes up as well. Add 2 with 5 which is 7.

Therefore, the answer is  (1, 7).

Hence , the image point (-4, 5) after a translation right 5 units and 2 units up is (1, 7).

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To find potential rational roots, we make use of the rational root theorem

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

Task: How the potential rational root is calculated

To make use of the potential rational root, we use the rational root theorem using the following steps

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Answer:

D is the answer

Step-by-step explanation:

Answer: Angle C

Step-by-step explanation:

The length of C-T and T-B would be longer then C-B and push C-B out making angle C the biggest.

Answer:

Step-by-step explanation:

Square's mission statement is simple. Square deliver “Economic Empowerment” to the thousands of business owners who use Square to manage their businesses.

The linear function rule to model the distance d in feet of the car traveled after t seconds is d = 83t.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distance traveled after 9 seconds = 747 ft.

The function rule to model the distance d after t seconds.

d = 83t

When t = 9,

d = 83 x 9 = 747 ft

Thus,

The linear function is d = 83t.

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The solution for z in the equation is z = 3y - 1/16(5y + 7x)⁴

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

2(5y+7x)²=8√(3y-z)

Rewrite the equation

So, we have the following representation

2(5y + 7x)² = 8√(3y - z)

Take the square of both sides

This gives

4(5y + 7x)⁴ = 64(3y - z)

Divide both sides by 64

1/16(5y + 7x)⁴ = 3y - z

So, we have

z = 3y - 1/16(5y + 7x)⁴

Hence, the solution is z = 3y - 1/16(5y + 7x)⁴

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Answer:

B. (w)(y)

Step-by-step explanation:

(w)(y)

= 2 * √8 * 3 * √2

= 2 * √(2*2*2) * 3 *√2

= 2 * √2 * √2 * √2 * 3 * √2

= (2*3) * (√2 * √2) * (√2 * √2)

= 6 * 2 * 2

= 24

Answer:

∠MGN = 24°

∠NGO = 24°

Step-by-step explanation:

⭐What is an angle bisector?

Thus, ∠MGN ≅ ∠NGO.

To solve for ∠MGN and ∠NGO, we need to:

1. Create an equation about their relationship:

If ∠MGN ≅ ∠NGO, then...

[tex]5x-6 = 11x -42[/tex]

2. Solve for "x":

[tex]5x - 6 = 11x -42[/tex]

[tex]42 - 6 = 11x - 5x[/tex]

[tex]36 = 6x[/tex]

[tex]6 = x[/tex]

3. Substitute "x" back into the equations to find the angle measures:

[tex]< MGN = 5x - 6[/tex]

[tex]< MGN = 5(6) - 6[/tex]

[tex]< MGN = 30 - 6[/tex]

[tex]< MGN = 24[/tex]

❗❗❗At this point, you could write that ∠MGN and ∠NGO = 24°, as they are congruent, but you should still substitute "x" into  ∠NGO to make sure "x" is correct.❗❗❗

[tex]< NGO = 11x - 42[/tex]

[tex]< NGO = 11(6) - 42[/tex]

[tex]< NGO = 66 - 42[/tex]

[tex]< NGO = 24[/tex]

∴ ∠MGN = 24°

∴ ∠NGO = 24°

The factors of 6x² 5x 6 are: 1, 2, 3, 5, 6, 10, 15, 30, x, 2x, 3x, 5x, 6x, 10x, 15x, 30x, x², 2x², 3x², 5x², 6x².

1. Find the common factors of 6x², 5x, and 6:

The common factors are 1, 2, 3, 5, and 6.

2. Find the factors of each individual term:

For 6x²: 1, 2, 3, 6, x, 2x, 3x, 6x, x², 2x², 3x², and 6x².

For 5x: 1, 5, x, and 5x.

For 6: 1 and 6.

3. Combine the factors from each term to get the full list of factors:

The full list of factors is: 1, 2, 3, 5, 6, 10, 15, 30, x, 2x, 3x, 5x, 6x, 10x, 15x, 30x, x², 2x², 3x², 5x², and 6x².

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Answer: x=-3, y=2

Step-by-step explanation: to solve using substitution, we need either x or y by itself in one equation. let's use x from the 2nd equation since it doesn't have a constant.

so the first equation stays the same at 2x+3y=0

for the second equation, rearrange to solve for x by moving the 2y to the right -> x=2y-1

then, we can plug in this x value to x in the first equation to get,

2(2y-1)+3y=0

then solve for y,

4y-2+3y=0

4y-3y=2

y=2

then to solve for x, plug in y in either of the initial equations. lets choose the second one.

so you'd have,

x+2(2)=1

x+4=1

x=-3

The Positive Infinity is called the Lemniscate.

Infinity:

Infinity is anything greater than infinity, infinity, or any natural number. Often represented by the infinity symbol {\displaystyle \infty }\infty. The most interesting point about infinity is – ∞ < x < ∞. This is a mathematical shorthand for negative infinity less than real and positive infinity greater than real. where 'x' represents a real number.

Positive Infinity:

Numbers approach negative infinity as they move left on the number line and positive infinity as they move right on the number line. Negative infinity is always less than any number and positive infinity is always greater than any number.

Positive Infinity: Differs from mathematical infinity in that:

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Answer:

The greatest common monomial factor of [tex]3x^2 - 6x[/tex] is 3x.

Step-by-step explanation:

To understand what the problem is asking us, let's define the terms.

⭐What does greatest common factor mean?

⭐What does monomial mean?

Thus, we need to find the greatest term that is a factor of [tex]3x^2 -6x[/tex]. This term must be a monomial.

First, divide both terms of the polynomial [tex]3x^2 -6x[/tex] by the largest term that is common between the terms.

[tex]3x[/tex] is the largest term.

[tex]3x[/tex] is also a monomial.

Therefore, [tex]3x[/tex] is the greatest common monomial factor.

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The distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is about 4.5 units, rounded to the  nearest tenth.

The distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is equal to the length of the perpendicular line from point [tex]$a$[/tex] to the line[tex]$y=3x$[/tex]. The formula to find the distance from a point [tex]($x_1, y_1$)[/tex] to a line [tex]$ax+by+c=0$[/tex] is given by:

[tex]$$\frac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}.$$[/tex]

Substituting[tex]$$\frac{|ax_1+by_1+c|}[/tex] into the formula, we get:

[tex]$$\frac{|-3(-1)+1(7)+0|}{\sqrt{3^2+1^2}} = \frac{20}{\sqrt{10}}.$$[/tex]

Therefore, the distance from point [tex]$a\left(-1,\ 7\right)$[/tex] to the line [tex]$y=3x$[/tex] is about 4.5 units, rounded to the nearest tenth

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Answer: x-intercepts

Step-by-step explanation:

basic math

Answer: X intercept

Step-by-step explanation:

The x-intercept is the point at which a graph crosses the x-axis. The y-intercept is the point at which the graph crosses the y-axis. To find the x-intercept of a line, substitute 0 for y into the equation and solve for x.

Answer:

The solution on a graph is the point where two lines interesect

Step-by-step explanation:

The value of k where the roots of the quadratic equation are real and equal is k = 9.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3x + 6 = 9 is an equation.

We have,

3x² + 2kx + 27 = 0

This is in the form of ax² + bx + c.

a = 3

b = 2k

c = 27

Now,

The roots are real and equal.

D = 0

D = b² - 4ac

Now,

b² - 4ac = 0

(2k)² - 4 x 3 x 27 = 0

4k² - 324 = 0

4k² = 324

k² = 324/4

k² = 81

k = √81

k = ±9

Thus,

The value of k is 9 0r -9

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Answer:

----------------------

Given options:

A) f(x) = 2x² + 5x − 12,

B) f(x) = 2x + 5,

C) f(x) = 2(x + 5)² − 12,

D) f(x) = 2(x + 5)(x − 12),

Since the provided expression [tex]2x^{2} +8x-x^{2} +16[/tex]  is quadratic, the solution of x are "-4" and "-4" .

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases.

Expression:    [tex]2x^{2} +8x-x^{2} +16[/tex]  

This means that you need to add the two x² terms and the two x terms, which gives you [tex]x^{2} +8x+16[/tex].

Next, you can simplify the equation by taking out a common factor of x from the consecutive two terms, which gives you  [tex]x(x + 4) +4(x+4).[/tex]

Then the equation becomes [tex](x + 4)(x+4).[/tex] which on solving i.e [tex](x+4)=0[/tex]

you will get x= -4 and -4.

Therefore the solution to this equation is x = -4 or x = -4.

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Answer:

  2. negative infinity to five thirds and five thirds to infinity

Step-by-step explanation:

You want the domain of the rational function f(x) = (x +4)/(3x -5).

The domain is the set of input values for which the function is defined. A rational function is undefined when its denominator is zero. f(x) is undefined when ...

  3x -5 = 0

  x = 5/3

So, the value 5/3 must be excluded from the domain of f(x). The domain of f(x) is ...

  -∞ < x < 5/3  ∪  5/3 < x < ∞