Write the following using index notation:

2 x 2 x 2

b) 3x3

3 x 3

c)

6 x 6 x 6 x 8 x 8 x 8

d)

3 * 4 * 3 x 4 * 3

The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x)=√x - 2 + 3.

The inverse function can be found as shown below,

f⁻(x) = √(y - 2) + 3  (Replace x by y)

x = √(y - 2) + 3

solve the equation as shown below,

x - 3 = √(y - 2)

Squaring both sides,

(x - 3)² = [√(y - 2)]²

x² + 9 - 6x = y - 2

x² + 9 - 6x + 2 = y

y = x² - 6x + 11 or y = (x - 3)² + 2

Thus, the inverse of the function is  (x - 3)² + 2.

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The polynomials which, when added to the polynomial 3x²+3x-1, is equivalent to the following expressions: 1, 2x²-3, and x+5 include the following below:

This is referred to as algebraic expressions that consist of variables and coefficients.

For 1; it is calculated as:

3x²+3x-1 + P = 1.

P = 2 - 3x² -3x.

For 2x²-3, it is calculated as:

3x²+3x-1 + P = 2x²-3

P = -2 -x² -3x

For x +5; it is calculated as:

3x²+3x-1 + P = x +5

P = 6 -2x -3x².

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The full question is:

Find a polynomial which, when added to the polynomial 3x^2+3x-1, is equivalent to the following expressions: 1, 2x^2-3, and x+5

An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.

Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.

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Translation is a rigid transformation. As such, it preserves sizes and angles. Isometric is an alternative way to say the size is preserved. Hence; B, C and E are the correct choices.

A triangle is a three-sided polygon. A closed shape consisting of three straight lines and three corners. The sum of the three angles of a triangle is always 180 degrees. Triangles come in a variety of shapes and sizes and can be classified according to their angles and sides. The most common type of triangle is the right triangle, which has 90 degree angles.

Translation is the transformation that happens when we move the image without changing anything in it. Therefore, the shape, size, and orientation remain the same.

In this case the triangle ABC has been transformed to A'B'C'. This means that the triangle has been moved in one direction to form a new triangle A'B'C' without changing its size or orientation. This is an example of translation transformation.

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The complete question is follows:

Triangle ABC was translated to form A’B’C’. Which describes the transformation? Check all that apply

A. It is non rigid

B. The size is preserved

C. It is rigid

D. The angles are not preserved

E. It is isometric

The average speed of Luna I is 1.78 x 10^-3 kilometers/minute.

To find the average speed of Luna I, we need to divide the total distance traveled (3.8 x 10^5 kilometers) by the total time it took to travel that distance (2.16 x 10^4 minutes). The quotient of these two numbers is 1.78 x 10^-3 kilometers/minute.

It's the ratio of distance covered to the time taken to cover that distance. The unit of speed is distance/time, which in this case is kilometers/minute. The speed of Luna I is in scientific notation, which is a way to express very large or very small numbers in a more manageable form.

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The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .

What is Law Of Sines ?

The Law Of Sines states that  the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known  are Sine Law, Sine Rule and Sine Formula.

The Sine Law  is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.

Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .

So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;

Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .

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The percent of the people surveyed who were completed satisfaction with the car will be 48%.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.

In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.

The percent of the people surveyed were completed satisfaction with the car will be:

= 24 / 50 × 100

= 48%

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Complete question

A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?

The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.

In its most basic form, an equation is a mathematical statement that indicates 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 statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

x(x-3)=10

x²-3x=10

x²-3x-10=0

x²-5x+2x-10=0

(x-5)(x+2)=0

x=-2,5

x=5 units

x-3=5-2

=2 units

The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.

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The GCF of the given expressions is 4x⁷⁶

The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.

Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4

and x⁷⁶ is a factor of  8x⁹²

∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶

Hence, The GCF of the given expressions is 4x⁷⁶

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The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.

LEt consider

→ dimes = d

→ nickels = n

→ quarters = q

Now the expression will be;

22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels

22d + 7n + 15q - 8d - 3n = $4.85

22d + 7n + 15q - (8d + 3n) = $4.85

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Answer:

A fraction is a mathematical expression that represents the division of two numbers, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the number of parts in the whole. A fraction with a numerator of 6 and a denominator of negative 8 can be simplified to -3/4. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number without changing the value of the fraction. In this case, the fraction with a numerator of negative 8 and a denominator of 6 is equivalent to -4/3.

Step-by-step explanation:

Factor -20 x-5 y, where x+y=4 and x+y=5. Our prime numbers become much, much harder to factor as we add a few extra digits.

When you factor in mathematics, you divide a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of an amount into its factors or divisors. The factorization of the integer 12, for instance, might be 3 times 4 or something similar. [tex]N = X^{a} * Y^{b} * Z^{c}[/tex] is used to represent the general factorization formula. In this instance, X, Y, and Z stand for a number's factors. Get a polynomial's GCF (Greatest Common Factor).

GCFs of polynomials should be factored out. By grouping the terms, factor a polynomial with four terms. trinomial of the form, and factor it. The size of our goods and the size of the data we use to check mean that each check takes an average amount of time longer. It is clear from this that factoring the product becomes significantly more difficult when we add a few digits to our prime integers.

Therefore the correct answer is option A)5(4x+y)

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]5x+4y=16\implies 4y=-5x+16\implies y=\cfrac{-5x+16}{4} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{5}{4}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -5/4 and it passes through (8 , -7)

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{8}) \implies y +7= -\cfrac{5}{4} (x -8) \\\\\\ y+7=-\cfrac{5}{4}x+10\implies {\Large \begin{array}{llll} y=-\cfrac{5}{4}x+3 \end{array}}[/tex]

Answer:

Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.

Answer:

The perimeter is the distance around a figure.

Step-by-step explanation:

For example, if I have a square where each side is 5 inches.  The perimeter would be 20 inches.  5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.

Answer:

25x^6y^2

Step-by-step explanation:

Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

Solve the inequities:

k^2-7k+12. 25>0

2. 25y^2-3y+1<0

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.

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The length of the chord of the larger circle can be found by taking the square root  [tex](5r)^2 - (2r)^2[/tex] which is equal to r√21, where r is the radius of the smaller circle.

The given problem states that there are two concentric circles with radii in the ratio of 3:5. This means that the radius of the smaller circle is 3r and the radius of the larger circle is 5r. The distance between the center of these two circles is 2r.

Also, it is given that the length of the chord of the larger circle that is tangent to the smaller circle is 40 cm. Using this information, we can find the length of the chord of the larger circle by using the Pythagorean theorem.

The length of the chord of the larger circle is found by taking the square root of [tex](the radius of the larger circle)^2[/tex] - [tex](the distance between the two centers)^2[/tex] which is √21[tex]r^2[/tex]= r√21.

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Answer:

Step-by-step explanation:

Depreciation means wearing and tearing in the value of an asset over the years

(a) Given:

p = initial value of an asset

i% = depreciation per year

n = number of years

Depreciation after n years (d) = [tex]p(1-\frac{1}{100} )^{n}[/tex]

Value of machine after n years = p-d

(b) Given:

p = RM100000

i% = 5

n = 10
Depreciation after 10 years = [tex]100000(1-\frac{5}{100} )^{10} = 59873.69392[/tex]

Value of machine after 10 years = p-d = RM100000 - RM59873.69392 = RM 40123.30608

Value of machine after 10 years to nearest ringgit = RM40123

The coeficient of y² in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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Answer:

3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18.

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C) there is a 5% probability of rejecting a false null hypothesis

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.

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Answer:

x = 13

Step-by-step explanation:

There is more than one 98-degree angle since they are all corresponding interior angles.

The supplementary angle to the 98-degree angle next to the triangle is:
180 - 98 = 82 degrees

In addition, another angle inside the triangle is an 85-degree angle. This is because this 85-degree angle is opposite adjacent to the other 85-degree angle.

Hence, the angles inside the triangle are: x, 85, and 82

x + 85 + 82 = 180 ==> Triangles add up to 180 degrees

x + 167 = 180  ==> simplify

x = 13 degrees ==> subtract 167 on both sides

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The number of units that tile will he need to surround his pool is 19.82units.

this question is of quadratic equation ,

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have,

AB = 4.24 units

BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units.

The number of units that tile will he need to surround his pool is 19.82units.

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a) The total amount of pizzas that they ate is given as follows: 2.92 pizzas.

b) The difference between the number of cheese pizzas and the number of vegetarian pizzas is given as follows: 4/3, which is the amount that they ate more of cheese pizzas than vegetarian pizzas.

The fractions relative to the amount of each type of pizza eaten are given as follows:

The total amount of pizzas eaten is given by the addition of these fractions, hence:

1/4 + 2 + 2/3 = 3/12 + 24/12 + 8/12

(as the least common factor between 4, 1 and 3 is of 12).

3/12 + 24/12 + 8/12 = (3 + 24 + 8)/12

(3 + 24 + 8)/12 = 35/12

2.92 pizzas.

The difference between the number of cheese pizzas and the number of vegetarian pizzas is obtained as follows:

2 - 2/3 = 6/3 - 2/3 = 4/3.

(as the least common factor of 1 and 3 is of 3).

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Answer:

I could find the slope of a line by looking at the gradient of a graph that the line creates. If the line is linear, then the gradient will be a constant value, which I can use to find the value of the slope. If the line is not linear, then I can use a derivative to find the slope at a given point. However, if the line is concave or concave up, then I will need to take the second derivative of the equation to determine which point on the line is closest to the point that I'm trying to calculate.

Step-by-step explanation:

Answer: (0, 1), (2,3), (x,x), (-5,x) (I put x's in for the missing numbers)

Step-by-step explanation: Hope this helps!!

Here is the graph:

The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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Answer: 1/7

Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.