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Answer:

1.) A prime factor is any prime number that can be multiplied to give the original number.

For example, the prime factor of 24 is:

1, 2, 3, 4, 6, 8, 12, and 24.

2.) A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Step-by-step explanation:

You're welcome.

Answer:

No they do not

Step-by-step explanation:

Sides 5 cm and 12cm can form a right angled triangle because 5 + 12 = 17 which is a greater number than 13 meaning it cannot

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:

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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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We have to reflect over x- axis to transform parallelogram ABCD to create A'B'C'D'.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The Coordinates of ABCD are:

A( -4, 1), B(-3, 2), C(-1, 2) and D(-2, 1)

and,  Coordinates of A'B'C'D' are:

A'( 4, -1), B'(3, -2), C'(1, -2) and D'(2, -1)

Now, Reflection over the x-axis.

A"(-4, 1)- 2(0, 1) ---> A"( -4, -1)

B"(-3, 2) - 2(0, 2)----> B"(-3, -4)

C"(-1, 2)-2(0, 2)--->C"(-1, -2)

D"(-2, 1)- 2(0,1)--->D"(-2, -1)

and,  Reflection over the y-axis.

A"(-4, 1)- 2(-4, 0) ---> A"( 4, 1)

B"(-3, -4) - 2(-3, 0)----> B"(-3, -4)

C"(-1, -2)-2(-1, 0)--->C"(1, -2)

D"(-2, 1)- 2(-2, 0)--->D"(2, -1)

So, we must reflect over the x-axis and then reflect over the y-axis to map parallelogram ABCD onto parallelogram A'B'C'D'.

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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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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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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.

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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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:

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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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

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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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

All values of z are negative numbers less than -5, which are -6, -7 and -8 so on.

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.

Given that, the opposite of z is greater than 5.

So, we have the following absolute value inequality.

|z|>5

This can be written as z>5 or z<-5

5 is a positive number.

So, we make use of the inequality z<-5.

From the above inequality, the possible values of z are -6 and -7

Note that there are other values of z

The values that z cannot be

We have: z>5 or z<-5

The values that z cannot be, are represented with the inequality z>5.

From the above inequality, z cannot be 6 and 7

The true statement about the values of z are, they are all negative numbers less than -5.

Therefore, all values of z are negative numbers less than -5, which are -6, -7 and -8 so on.

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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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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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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 graph of the player two's function g(t)=16(t-5)²+290 is given in the attachment. The baseball's maximum height is 290 ft. At 5 seconds the baseball was at its maximum height. After 9.25 second the baseball hit the ground.

A function is a mathematical device that converts one value to another in a predictable manner. We can think of it as a machine. You give the machine an input, it performs some calculations on it, and then returns another value - the result of the calculations.

The function's name is f. We can call it anything we want, but single letters are common. The input* value is referred to as x. Again, we could use anything, but x is common. What the function does with the input is shown to the right of the equals sign.

In this case, the function takes the input x, multiplies it by three, and returns the result.

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Answer:

45 cents

Step-by-step explanation:

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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The function in terms of balance of the savings account is B(a) = 200 - 5a.

A formula known as an equation uses the equals sign to express how two expressions are equal. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfil the equality are known as the equation's solutions.

Let the number of months be represented as a.

The fee that would be deducted ever month can thus be represented as 5a.

The initial deposit in the bank is $200, and if we include the deduction the equation is as follows:

B(a) = 200 - 5a

Hence the function in terms of balance of the savings account is B(a) = 200 - 5a.

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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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Answer:

6

5^2 + square root 11^2 = 36

square root 36= 5

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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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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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?

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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