Identify the property demonstrated by the equation. x + (3 + 5 ) = (x + 3 ) + 5

Answer:

45 cents

Step-by-step explanation:

i³³ simplified is i.

What is the Complex Number?

A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

When raising a complex number to a power, we can use the property [tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]

It is also possible to simplify the powers of complex numbers using De Moivre's Theorem:

[tex](a + bi)^n = a^n + (na^{(n-1)})bi + (n(n-1)/2!)a^{(n-2)(bi)^2} + .... + (n(n-1)...21)(a*bi)^n[/tex]

Where [tex](a + bi)^n = r^n * (cos(n\theta) + i*sin(n\theta))[/tex]

Where r is the magnitude, θ is the argument, and n is an integer.

For example, if we raise i to the power of 3, we can use De Moivre's Theorem:

i³ = (cos(90) + isin(90))³ = cos(270) + isin(270) = -i

So, i³ = -i

When raising complex numbers to powers, the magnitude will be raised to the power of n while the argument will be multiplied by n.

i² = -1, so i³³ can be written as (i²)¹⁶ * i = (-1)¹⁶ * i = i

Therefore,  i³³ simplified is i.

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Answer:

number 6, y=-6 number 7 x=2 and

Step-by-step explanation:

and number 10, 4 - 6 / -3 + 5, 4 - 6/2, - 2 / 2, Solution: -1

Answer:

6

5^2 + square root 11^2 = 36

square root 36= 5

The equivalent expression is RootIndex 12 StartRoot 8 EndRoot Superscript x. Option C

An equivalent expression can be described as an expression that has the same solution as the original expression.

The equivalent always have a different arrangement of variables, terms and factors but the solution is the same with the initial expression.

From the information given, we have that;

3Root 8 Superscript one-fourth x

This is represented as;

[tex]\sqrt[3]{8}^\frac{1}{4} ^x[/tex]

Now, take the cube root of 8, we have;

[tex]8^\frac{1}{3} * \frac{1}{4}^x[/tex]

Multiply the exponents, we get;

[tex]8^\frac{1}{12}^x[/tex]

Now, represent in root for, we have;

[tex]\sqrt[12]{8} ^x[/tex]

Hence, the correct option is C

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Answer:

C

Step-by-step explanation:

;)

Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.

Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following is a list of a circle's attributes:

Look closely at the above illustration; if we divide the circle into smaller pieces and arrange them in a particular order, a parallelogram will result. The circle progressively becomes the shape of a rectangle as it is split into smaller and smaller segments. The likelihood that it will have the above-illustrated rectangle form increases with the number of parts it has.

A rectangle's area equals its length times its width.

The ratio of a circle's radius to a rectangle's width (r)

When we compare a rectangle's length to a circle's circumference, we can see that the length is equal to half the diameter of the circle.

Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.

Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².

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The solution would be 2.The point's y value at x = -2 provides a clue as to how f(-2) would behave.

What do you mean By graph Intercept function?

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The correct option regarding the domain and the range of the quadratic function y = (x + 3)² - 5 is given as follows:

B. Domain all real values, Range [-5, infinity.]

The function for this problem is defined as follows:

y = (x + 3)² - 5.

Which is a concave up quadratic function with vertex at (-3,-5).

The quadratic function has no restrictions regarding the input, hence the domain is composed by all real values.

The minimum value of the function is of -5 at the vertex, hence the range is all values that are -5 or greater.

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The Exponential Form of the number root 2 , is represented as [tex](2)^{\frac{1}{2} }[/tex] , because the term "root" means the exponent is [tex]\frac{1}{2}[/tex] .

The Root of a number x ; is defined as another number, which when multiplied by itself by given number of times is equal to x .

The Square Root of a "number x" is ; denoted by symbol "[tex]\sqrt{x}[/tex]" .

we have to express the number root 2 in exponential form ;

So, we write root 2 as  ⇒ [tex]\sqrt{2}[/tex] ;

we know that the square root of any number x , in exponential form is written as [tex]x^{\frac{1}{2} }[/tex] ;

So , the exponential form of root 2 is [tex](2)^{\frac{1}{2} }[/tex] .

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A dilation is a transformation that changes the size of an object by a scale factor. To dilate a triangle by a scale factor of 2/3, you will need to follow these steps:

Note that the center of dilation C and the dilation factor are the same for all points on the triangle, also if the dilation factor is less than 1, the image is smaller than the original and if the dilation factor is greater than 1, the image is larger than the original.

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The complete question is -

How do you dilate a triangle by a scale factor of 2/3?

To find the endpoint with the midpoint and one endpoint formula, use the following steps:

Step 1: Identify the midpoint of the line segment. The midpoint is the point that is exactly halfway between the two endpoints.

Step 2: Identify one endpoint of the line segment. This is the point that you already know.

Step 3: Use the midpoint and one endpoint to find the other endpoint. To do this, add or subtract the difference between the x-coordinates of the midpoint and one endpoint from the x-coordinate of the midpoint to find the x-coordinate of the other endpoint. Then, add or subtract the difference between the y-coordinates of the midpoint and one endpoint from the y-coordinate of the midpoint to find the y-coordinate of the other endpoint.

Step 4: Write the coordinates of the other endpoint. The point (x,y) represents the other endpoint of the line segment.

Note: The x-coordinate of the other endpoint is the x-coordinate of the midpoint + or - the difference of x-coordinate of the midpoint and one endpoint, and the y-coordinate of the other endpoint is the y-coordinate of the midpoint + or - the difference of y-coordinate of the midpoint and one endpoint.

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Reflection across the y = -x line is equivalent to a rotation of 180 degrees about the origin.

The coordinates of X(-4,-3) after reflecting across the y = -x line would be (3, 4)

The coordinates of M(-3,-2) after reflecting across the y = -x line would be (2, 3)

The coordinates of (-1,-5) after reflecting across the y = -x line would be (5,1)

So, after reflecting across the y = -x line, the coordinates of the points are flipped along the line x = y and they are moved to the opposite quadrant.

A function y = 10 a not linear function

We know that the general form of linear function is f(x) = a + bx

A linear function has one independent variable (for above function x) and one dependent variable(here, f(x)).

The graph of linear function is always a straight line.

Let y = f(x)

So, y = a + bx

where b is the slope of line

and a is the y-intercept

here, the independent variable is x and the dependent variable is y.

We have been given a function y = 10

The graph of y = 10 is a horizontal line parallel to x -axis and intersects y-axis at (0, 10)

There is no y-intercept and the slope is undefined.

Therefore, given function is not a linear function

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Answer: y = -2x+3.

Step-by-step explanation:

To answer this question, you must first use the FOIL method.

now the equation is this

y+3=-2x+6, since a negative * a negative is equal to a positive.

subtract 6 from both sides.

y-3=-2x

add three to both sides

y=-2x + 3

The  greatest common factor of the polynomial 20x^3-14x is D. 2x.

The concept that will be sued here is common factor. A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.

For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.

The common factor that ca be gotten from 20x² : are:  1, 2, 4, 5, 10, 20, x

The  common factor that ca be gotten from 14x are : 1, 2, 7, 14, x

Then greatest common factor of the polynomial is 2x.

Hence,  2x(10x² - 7)

Therefore, option D is correct.

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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So the strength of a man who is 200 pounds is approximately 2649.2 newton, rounded to the nearest tenth.

Weight is a measure of the force exerted on an object due to gravity. It is measured in units of force such as pounds, kilograms, or newtons. The weight of an object is equal to the force of gravity acting on it and is equal to the mass of the object multiplied by the acceleration due to gravity.

Newton (N) is the unit of force in the International System of Units (SI). It is named after Sir Isaac Newton, the famous English physicist, mathematician, and astronomer. It is defined as the force that is required to accelerate an object with a mass of one kilogram at a rate of one meter per second squared.

f = 500 ln(200 + 1)

f = 500 ln(201)

then we can calculate the value of ln(201) using a calculator, and the result is 5.298317366548036

then we can substitute the result into the original equation and get

f = 500 * 5.298317366548036 = 2649.15868

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Therefore , the solution of the given problem of trigonometry comes out to be base distance is 20.174 foot.

Trigonometry is a branch of mathematics that examines the relationship between the square line segment and The field first appeared inside the Seventeenth century, most likely beginning in the third century BC, as a result of the fusion of astronomy and mathematics studies. Numerous geometric equations and potential uses in calculations are covered by precise mathematical techniques. Trigonometry is the study of the six basic trigonometric operations. They go by many different names and abbreviations, such as sine, divergence, tangential, secant, etc (csc). In trigonometry, triangle characteristics are investigated, particularly those of right triangles. But to master geometry, one must be fully conversant with the properties of every polygon.

Here,

Greg has ladder of 24 foot

thus,

to find the : how much distance ladder should be placed.

We use trigonometry ratios:

=> h²= p²+ b²

=> 24² = 13² + b²

=> √576 - 169 =  b

=>20.174 = b

Therefore , the solution of the given problem of trigonometry comes out to be base distance is 20.174 foot.

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The following statements are true for all the numbers. The proof is shown as follows.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

We know z₁ = a + bi and zbar= a-bi

z1+z1bar=2a that is purely real. Similarly with z2 +z2bar

z1-z1bar=-2bi that is purely imaginary. Similarly with z2-z2bar

Again

z1bar+z2bar= a-bi+c-di

z1+z2(whole bar)=a+c-(b+d)i

Hence Z₁ + Z₂ = Z₁ + Z₂

Similarly

z1bar.z2bar=z1.z2(whole bar)

Hence proved

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Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

The ratios of the lengths of corresponding sides are equal AB/XY = BC/YZ = AC/XZ, then ΔABC and ΔXYZ  proven similar through SSS .

To prove two triangles similar using the SSS (Side-Side-Side) similarity criterion, all three pairs of corresponding sides of the two triangles must be proportional .

The SSS similarity criterion states that if the ratio of the lengths of corresponding sides in two triangles is equal, then the triangles are similar.

Given that we have a list of triangles,  to compare the ratios of their corresponding sides to see if any pairs satisfy the SSS similarity criterion.

The three pairs of corresponding sides in the triangles are denoted as follows:

Side A: Sides that are corresponding in length between the two triangles.

Side B: Sides that are corresponding in length between the two triangles.

Side C: Sides that are corresponding in length between the two triangles.

Since the specific list of triangles is not provided, I cannot give you the exact pairs that  proven similar through SSS similarity. However, I provide with an example:

Example:

Consider two triangles, ΔABC and ΔXYZ, where the corresponding sides are as follows:

ΔABC: AB, BC, and AC

ΔXYZ: XY, YZ, and XZ

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There is no function in the first set of ordered pairs. It is not a function because the X value of 7 repeats.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

Only the first set of ordered pairs is a function; the second, third, and fourth do not represent functions.

This is due to the need that each x value have a unique y value. So you note that, with the exception of the first set of ordered pairs, all sets of ordered pairs have two distinct x-values that share a same y-value, which is not possible.

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A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.

Here is an example of a full table of 5:

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.

It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.

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1. The value of the m∠2 is 67°.

2. The third length in the triangle is 10 cm.

3. It should be noted that this is a rotation.

An equation is a expression that shows the relationship between numbers and variables.1)

In the triangle:m∠1 + 21 + 46 = 180° (sum of angles in a triangle)

m∠1 = 113°m∠1 + m∠2 = 180 (angle in a staight line)1

113 + m∠2 = 180

m∠2 = 180 - 113

= 67°

2. Let x represent the third length:

x + 12 + 13 = 35 (perimeter)

x = 35 - 25

x = 10

3. It should be noted that the diagram illustrated is a a rotation.

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Registered nurses is expected to add the greatest number of jobs from 2006 to 2016.

Hence, Option A is correct

What do you mean by graph Growth Rate?

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Answer:

a

Step-by-step explanation:

x using the change of base formula will be B) -0.207519.

What is logarithm ?

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8

Have given ,

4x + 2 = 12

equation. We can do this by subtracting 2 from both sides:

4x = 10

Next, we divide both sides by 4:

x = 2.5

So, the solution is x = 2.5

x using the change of base formula will be B) -0.207519.

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The point that lies in the fourth quadrant is (1, -2).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates are:

(1,−2), (1, 8), (-5, -4), and (-5, 2).

(1, -2) is in the fourth quadrant.

(1, 8) is in the first quadrant.

(-5, -4) is in the third quadrant.

(-5, 2) is in the second quadrant.

Thus,

(1, -2) lies in the fourth quadrant.

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Answer:   (5,−2) is the only point in the fourth quadrant.

Step-by-step explanation:

The value of 0.55 hectometers expressed in decimeters is 550 decimeters. The result is obtained by using the concept of unit ladder system.

The common length units are kilometers to milimeter. The conversion can be described in a unit ladder system as follows.

km (kilometers)

  hm (hectometers)

     dam (decameters)

        m (meters)

           dm (decimeters)

              cm (centimeters)

                  mm (millimeters)

Every time the length unit goes down, it is multiplied by ten. Every time the length unit goes up, it is divided by ten.

We have 0.55 hectometers. Express that value in decimeters!

From hectometers to decimeters, it goes down 3 times. So,

0.55 hectometers = 0.55 × 10 × 10 × 10 decimeters

0.55 hectometers = 0.55 × 1000 decimeters

0.55 hectometers = 550 decimeters

Hence, 0.55 hectometers is equal to 550 decimeters.

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