How do you prove log2 7 is irrational?.

Answer:

4.5x + 27.5

Step-by-step explanation:

first you must simplify the equation using distributive property:

2.5(3x +8) - 1.5(2x - 5) = 7.5x + 20 - 3x - 7.5

Now, you and or subtract the like terms

7.5x + 20 - 3x - 7.5 = 4.5x + 27.5

Answer:

-4.5x - 27.5

Step-by-step explanation:

   1.5(2x - 5 ) - 2.5(3x + 8) -

=  3x -  7.5 - 7.5x  - 20

=  -4.5x - 27.5

Answer:

2 is multiplied by -4 and then a4 is gone to the bottom

Answer:

4

Step-by-step explanation:

To make the exponent -4 put it over 1.

[tex]\frac{1}{(2a)^{4} }[/tex]

[tex]\frac{1}{2^{4}a^{4} }[/tex]

[tex]\frac{1}{2x2x2x2xaxaxaxa}[/tex]

[tex]\frac{1}{16a^{4} }[/tex]

The reason that supports the property in statement 8 is substitution. The correct option is C.

Substitution is the process of replacing variables (letters) in an algebraic expression with numerical values. The total value of the expression can then be calculated.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The reason that supports the property in statement 8 is substitution. Because in the expression 6x - 7 the value of the variable x is substituted to get the value of the angle.

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Using Trigonometric ratios, Tan(20 ) = -24/7 and cos(20) = 7/25

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.

It can be simpler to use a calculator when necessary. (See under)

The reference angle will be less than 45° since the magnitude of the tangent is less than 1. If the angle is less than 90 degrees when doubled, it will remain in the fourth quadrant, where the tangent is negative and the cosine is positive.

Additionally, you can use the identities.

cos(2) is equal to (1 - tan()2)/(1 + tan()2).

cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

cos(2θ) = 7/25

Tan(2)=2tan()/(1 -tan(2)2) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

tan(2θ) = -24/7

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Mixture A is more redder than mixutre B.

Percentage concentration is a way to express the amount of a substance in a solution in terms of the percentage of the total solution that the substance represents.

The mixture have more concentration of red dye is more redder .

In order to calculate concentration of red dye  we will check percentage concentration of red color in each mixture.

In mixute A concentration of red dye is given by:

Volume of (red dye)*100 / (total volume of solution)

=> (3*100) / (20+3)

=> 13.043%

In mixute B concentration of red dye is given by:

Volume of (red dye)*100 / (total volume of solution)

=> (4*100) / (30+4)

=> 11.764%

This indicate that mixure A have more reddish color.

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30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.

What is interpretation ?

Interpretation is the process of understanding and explaining the meaning of something, such as a text, a piece of artwork, or a scientific data. In the context of mathematics and problem solving, interpretation refers to understanding the meaning of a mathematical expression or equation in the context of the problem or situation being described.

In this context, "30 and 1 half cups of oup" refers to the amount of soup that Avery has in the large pot, and "divided by 3" refers to the number of smaller containers Avery plans to divide the soup into. There are two different ways to interpret 30 and 1 half divided by 3 in this context ,

Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.

Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.

30 1/2 cups soup divided by 3: 10 1/6 cups or 10 1/2 cups per container.

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Avery will divide the 30 and 1 half cups of soup equally among 3 smaller containers. This means that each container will hold (30 + 1/2) / 3 = 10 and 1/6 cups of soup.

Avery will pour out 10 and 1/2 cups of soup from the large pot into each of the 3 smaller containers. This means that after Avery has poured out all the soup, the large pot will be empty and the 3 smaller containers will each contain 10 and 1/2 cups of soup.

$12188.04 is the cost that school to purchase agenda books for all of its students

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  Last year, the school purchased 350 books at a total cost of $1,137.50.

The school charges the same amount this year, but their population has grown to 375 students.

We have to find the cost the school to purchase agenda books for all of its students

Let us consider it as x.

Form an proportional equation.

350/1137.5=375/x

apply cross multiplication

350x=11375.5×375

350x=4265812.5

Divide both sides by 350

x=$12188.035

Hence, $12188.04 is the cost that school to purchase agenda books for all of its students

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Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo: 86.6 N.

Para calcular el valor de la normal y la fuerza de rozamiento, primero debemos calcular la componente de la fuerza de gravedad que actúa en dirección perpendicular a la superficie de apoyo. La componente de la gravedad en dirección perpendicular se calcula utilizando el seno del ángulo formado por la cuerda con la horizontal (30º):

F_normal = F_grav * sen(30º)

Donde F_grav es la fuerza de gravedad del cuerpo, que se calcula como:

F_grav = m * g

Donde m es la masa del cuerpo (40 kg) y g es la aceleración debida a la gravedad (9.8 m/s²)

Por lo tanto,

F_normal = (40 kg) * (9.8 m/s²) * sen(30º) = 392 N

La fuerza de rozamiento se calcula utilizando la fórmula:

F_fric = μ * F_normal

Donde μ es la coeficiente de rozamiento estático entre el cuerpo y la superficie de apoyo. Como no se especifica el valor del coeficiente de rozamiento, no se puede calcular la fuerza de rozamiento.

La tensión en la cuerda es igual a la fuerza neta en la dirección de la cuerda. Como la cuerda está formando un ángulo de 30 grados con la horizontal, la componente de la fuerza en la dirección de la cuerda se calcula utilizando el coseno del ángulo:

T = F * cos(30º) = 100 N * cos(30º) = 86.6 N

(Los valores de las respuestas están en notación científica)

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Explanation:

The log equation [tex]\text{x} = \log_b(\text{y})[/tex] is equivalent to its exponential form [tex]\text{y} = b^\text{x}[/tex]

For the exponential equation, we can replace x with any real number. We don't have to worry about things like dividing by zero. Therefore the domain of the exponential equation is "set of all real numbers".

The domain of  [tex]\text{y} = b^\text{x}[/tex] is the range of [tex]\text{x} = \log_b(\text{y})[/tex]. The domain and range swap roles when going from original to inverse.

Therefore, the range of any logarithmic function is "set of all real numbers".

On a graph notice how the log curve stretches forever upward and downward. The base of the log doesn't matter.

Three-fifths is equivalent to 6/10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let the number of fifth be = x

So,

(1/5)x = 6/10

Now,

Solve for x.

(1/5)x = 6/10

x = (6 x 5) / 10

x = 30/10

x = 3

Thus,

There are three-fifths to make 6/10.

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Answer:

Step-by-step explanation:

14+(-8)14+(-8)

-122+14=-108+-8=116

It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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Answer:

A reflection is a congruence transformation because it maintains the original shape and size of the pre-image. A reflection is a figure flipped over a line of reflection. A common example is a mirror but a reflection can also be shown in water, like with a picture of a lake, the line of reflection would be the divide between the water and the shore.

Using addition, the total amount of sugar sold equals  13 16/20 Kg .

The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum.

We add numbers in many different contexts.

The combination of at least two numbers constitutes basic addition. Once a student has mastered counting, they can begin to study basic addition.

By locating the addend at the top of the chart and tracing down to the row of the second addend, they can utilize an addition chart as a learning tool.

Given,

shopkeeper sold 7 3/4 kg, 2 1/2 and 3 3/5 of sugar to three customers in a day

Using addition,

⇒ 7 3/4 kg + 2 1/2 + 3 3/5

⇒ 31/4 + 5/2 + 18/5

⇒ 155 + 50 + 72 / 20

⇒ 277/20

⇒ 13 13/20 Kg

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The values that represent the inverse of the function which is represented in the table above include the following:

x  4    2    1    3   4

y -2   -3   6   7    5

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should interchange (swap) both the input value (x-value) and output value (y-value). This ultimately implies that, the inverse relation of any function has its input value (x-value) and output value (y-value) interchanged (swapped) as follows;

x           y

4          -2

2          -3

1           6

3          7

4          5

In conclusion, we can logically deduce that the above inverse relation is not a function because the same input value (4) appears more than once with different output values (-2 and 5).

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To have a unique solution for the given equations, k should not be equal to 3.

Given equations are:

kx - y = 2

and, 6x - 2y = 3

The second equation can be written as, 3x - y = 3/2

The system of equations kx-y=2 and 3x - y = 3/2 has a unique solution when the coefficients of x and y are not equal, meaning k is not equal to 3.

This is because when the coefficients are not equal, the equations are not dependent on each other and can be solved independently. If the coefficients were equal, then the equations would be parallel and have infinitely many solutions.

Additionally, the specific value of k does not affect the uniqueness of the solution, as long as it is not equal to 3.

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The formulas of closure property is

where a, b and R are real numbers.

In mathematics, the Closure property can be defined as when an arithmetic operation is performed on any two numbers from a set and the result obtained is a number from the set itself, it is considered closed.

Closure property of addition : The closure property of an integer says that when we add two real numbers, the result will always be a real number. The formula for this is written as

a + b = R; where a, b and R are real numbers.

For example, 6 + 13 = 19 ; (1/3) + (5/2) = 17/6

Closure property under multiplication: The product of two real numbers is always a real number, that is, real numbers are closed under multiplication. The formula, ab = R , where a, b, and R are real numbers. For example, 9 × 0 = 0

(3/4) × (-1/4) = -3/16, √3 ×√5 = √15.

The Closure Property of Subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will also be a real number. For example, 9 - 4 = 5. This property is only applicable to integers and rational numbers.

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The inverse of y = 3x is f⁻¹(x) = 1/3x.

The inverse is a function or an operation which reverses the order of operation of another function or an operation”.

There are a few steps to find the inverse of a number:

We will be using the concept of inverse function to solve this.

Given that, y=3x

Let f(x) =y=3x

Switch x and y

x=3y

Express y in terms of x.

y = 1/3x

From the definition of the inverse function. f(x)=y⇒x=f⁻¹(y)

⇒ f⁻¹(y)=1/3x

Thus, the inverse of y = 3x is f⁻¹(x)=1/3x.

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The border line is so much shaded below the inequality symbol (shown in purple).

A relationship among two expresses or values that is neither equal in mathematics is referred to by the term inequality. Thus, unequal results from imbalance. In arithmetic, an inequality explains the links between two non-equal numbers. Egality nor disparities are not the same. Were using the not equal symbol most usually when two values are just not equal (). Values of any size can be contrast using a variety of discrepancies. By changing the two sides till only the variables are left, many straightforward inequalities can be solved. However, a variety of factors support injustice: Both sides' negative values are split or added. Change the left and the right.

given

Gold costs $25 a gram, therefore y grams would cost $25. Because silver costs $0.40 per gram, x grams will cost you $0.0040. If the entire cost of the ring must be less than $90, then 25y+0.40x90, making the cost of the ring (25y+0.40x) dollars. For y, resolve this inequality: 25+0.40<90/25−0.40+90

Take 0.40 off of both sides.

<−0.016+3.6

25y+0.40x y900.40x+900.016x+3.6 = 25y+0.40x y900.40x+903.6

Remove 0.40x from both sides.

Add 25 to both sides.

The boundary line is therefore defined as =0.016+3.6 y=0.016x+3.6, which has a y-intercept of 3.6 and a slope of 0.016 0.016.

The border line is so much shaded below the inequality symbol (shown in purple).

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Answer:

-2x - 1

Step-by-step explanation:

3x - ( -2x - 1 )

=3x + 2x + 1

= 5x + 1

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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The experimental probability of landing on a number greater than 4 is 0.25 or 25%.

To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).

The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.

So, the experimental probability is 18/60 = 0.3 or 25%.

It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.

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the answer in fraction form is 18/60

if thats what you are looking for.

To find the direction and magnitude of the resultant of these three forces, we can use the law of cosines and the law of sines.

First, we need to resolve each force into its x and y components using trigonometry.

F1x = 80 * cos(30) = 69.28

F1y = 80 * sin(30) = 40

F2x = 95 * cos(45) = 67.08

F2y = 95 * sin(45) = 67.08

F3x = 125 * cos(120) = -62.5

F3y = 125 * sin(120) = -106.6

Then we can find the x and y components of the resultant force by adding the x and y components of each force respectively.

Rx = F1x + F2x + F3x = 69.28 + 67.08 - 62.5 = 74.86

Ry = F1y + F2y + F3y = 40 + 67.08 - 106.6 = 0.48

Finally, using these values we can use the law of cosines to find the magnitude of the resultant force:

R = sqrt(Rx^2 + Ry^2) = sqrt(74.86^2 + 0.48^2) = sqrt(5633.79) = 75.24

And we can use the law of sines to find the direction of the resultant force:

theta = atan2(Ry, Rx) = atan2(0.48, 74.86) = 0.01

Therefore, the magnitude of the resultant force is 75.24 pounds and the direction of the resultant force is 0.01 degrees.

Answer:

{-1, 2, 47}

Choice B

Step-by-step explanation:

Function is g(x) = x² - 2

Domain is the possible set of x values and range is the set of function values for that domain

Here Domain = {- 2, - 1, 7}. This means these are values for which the function value g(x) exists

(Note this is not the entire domain, only a subset of the domain)

At x = - 2, g(x) = (-2)² - 2 = 4 - 2 = 2

At x = - 1, g(x) = (-1)² -2 = 1 -2 = -1

At x = 7, g(x) = (7)² -2 = 49 - 2 = 47

These are the corresponding range values for the given domain

Both domain and range sets are expressed from lowest to highest so we get range of g(x) as

{-1, 2, 47}

Choice B

Step-by-step explanation:

UW must be equal to UV. the distance from the same point of origin of 2 tangents to their touching points in the circle must be the same.

so, UV = UW = 3

XV connects the tangential touching point with the center of the circle, and must therefore be perpendicular (90°) to the tangent UV.

we have therefore a right-angled triangle UVX and can use Pythagoras to find the Hypotenuse UX :

UX² = UV² + XV² = 3² + 1.6² = 9 + 2.56 = 11.56

UX = sqrt(11.56) = 3.4

Answer:

Step-by-step explanation:

You want the end behavior of the graphed line.

The end behavior of a graphed function is found by looking at the arrows on the ends of the graph. If the arrow points in a direction with positive slope, the sign of the function value (y) will match the sign of the independent variable (x).

If the arrow has negative slope, then the signs of the end behaviors will be opposite.

If the arrow points horizontally or vertically, then the end behavior will be an asymptote. The function value will approach the value of a horizontal asymptote. The function value will tend to infinity (up: +∞; down: -∞) as the independent variable approaches the location of the vertical asymptote.

Here, the line has positive slope everywhere, so the sign of y will match the sign of x as both go to ±∞.

__

Additional comment

Slope is positive if the sign of the "rise" matches the sign of the "run". A line that goes down to the left has positive slope, just as does a line that goes up to the right. (Right and up are positive directions.)

Answer:

milo can put 5 framed photos on each shelf

Step-by-step explanation:

4÷20=5

Answer:

The time t, in seconds, it takes a runner to finish a race depends on the distance in miles m of the race.

Step-by-step explanation:

Hope this helps !

The likelihood that the first question will be true is equally likely and unlikely.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

The teacher gave a true and false quiz where P(true) = 0.5 for each question.
From the above-given probability, it can be interpreted that the likelihood of giving a true answer is 50% and this is the same for the given wrong answer. So the likelihood that the first question will be true is equally likely and unlikely.

Thus, the likelihood that the first question will be true is equally likely and unlikely

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Answer:

The likelihood that the first question will be true is equally likely and unlikely.

Step-by-step explanation:

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

By examining the connection between natural selection and evolution, Darwin's theory of evolution is examined. Controlling natural selection in an interactive population will help you achieve this. Each species displays.

For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Evolution and Natural Selection A species' members do not all resemble one another. Each species displays. For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

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