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A dilation or combination of stiff movements and dilations constitutes a similarity transformation.

Similar figures don't always have to have the same size but share the same form.

A transition called a dilation keeps shape but not size. So a dilatation is a motion that is not rigid. A dilation or combination of stiff movements and dilations constitutes a similarity transformation. If and only if a similarity transformation translates one of the geometric figures onto the other, then two figures are said to be similar. Similar figures don't always have to have the same size but share the same form.

Similarity transformations include translation, reflection, rotation, and dilation. Rotation, reflection, and translation retain both size and form since they are rigid movements, whereas dilation just makes sure that the shape is preserved.

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An equation to find the discount price, y dollars, of the pendant is y=2d.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The original price of the pendant was $200.

Let d represent the percent discount, written as a decimal.

The discount price, y dollars, of the pendant.

y=d% of 200

y=d/100 ×200

y=2d

Therefore, an equation to find the discount price, y dollars, of the pendant is y=2d.

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The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1

When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).

If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.

Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1

Let  f(x) = x^6 + 3x^4 + 3x^2 + 1 and  g(x) = x^3 + 3x^2 + 3x + 1

We can write these polynomials as:

f(x) = x^6 + 3x^4 + 3x^2 + 1

f(x) = (x² + 1)^3

The factors of polynomial  f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and  (x² + 1)^3

And g(x) = x^3 + 3x^2 + 3x + 1

g(x) = (x + 1)^3

And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1

Therefore, the HCF of the polynomials f(x) and g(x) = 1

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Answer:

B

Step-by-step explanation:

180-152=28

t=180-(28+90)

t=62

Answer:

18.84

Step-by-step explanation:

x is the hypotenuse of the triangle.

For the 48° angle, 14 is the opposite leg.

The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine.

sin 48° = opp/hyp

sin 48° = 14/x

x × sin 48° = 14

x = 14/sin 48°

x = 18.84

Answer:

Step-by-step explanation:

Divide: 18 ÷3=?

The answer is 6

Answer:

488 adults and 276 children

Step-by-step explanation:

So, we need two linear equations here to start, and we do have them.

Our first linear equation tells us how we get the number of forks:

2c + 5a = 2992

And the second tells us the number of people there:

c + a = 764

I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:

c = 764 - a

Then, we will substitute this into our first equation, giving us:

2(764 - a) + 5a = 2992

Then, we will open the parentheses, giving us:

1528 - 2a + 5a = 2992

Combining like terms and subtracting 1528 from both sides gives us:

3a = 1464

Dividing by 3:

a = 488

So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:

488 + c = 764

Minus 488 from both sides gives us:

c = 276

So, there were 276 children. In total, we had 488 adults and 276 children.

Hope this helped!

If the leg of the triangle is equal to a, then:

The second leg is also equal to a.

the given hypotenuse is a√2.

The given area is equal to a²/2; and

The perimeter equals a (2 + √2).

Now, looks easy, but from where does it come? There are various of methods to prove that equation, the most popular of them are:

By using the Pythagorean theorem, we can do that.

As you know one leg length a, then you know the length of the other as well, as both of them are equal.

The given 45 45 90 triangle shows the remaining parameters. Now you know that:

hypotenuse length is - 9 in * √2 = 12.73 in.

area is - 9 in * 9 in / 2 = 40.5 in²; and

perimeter - 9 in + 9 in + 9 in * √2 = 30.73 in.

Find the hypotenuse from the Pythagorean theorem:

a² + b² = c² => a² + a² = c² so c = √(2a²) = a√2

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We are given that A bird flew from the ground onto a tree branch 5 feet above the ground.

We are supposed to find What could the bird do next that would make this situation a model of combining a number and its additive inverse

Additive inverse - What you add to a number to get zero is additive inverse.

The negative of a number.

Now we are told  What could the bird do next that would make this situation a model of combining a number and its additive inverse

Since it already flew 5 feet above the ground .

Additive inverse of 5 feet is -5 feet

So, to make the situation of combining a number and its additive inverse

Bird has to flew 5 feet return to the ground i.e.-5 feet

So, a model of combining a number and its additive inverse = 5+(-5)

= 0.

Fly down 5 feet and return to the ground.

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Answer:

Fly down 5 feet and return to the ground.

Step-by-step explanation:

have a nice day.

Answer:

2800

Step-by-step explanation:

20% of 14,000 is 2800

Multiply both sides by 14,000, then divide the left side to get the result.

Answer:

2800

is what the calculator says

Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that a taxi charges a flat rate of $1.75 and an additional $0.65 per mile.

Eli has at most $10 to spend on the cab ride

We need to find how far could he travel

1.75+0.65x≤10

Subtract 1.75 on both sides

0.65x≤10-1.75

0.65x≤8.25

x≤8.25/0.65

x≤12.6

So he could travel 12 miles.

Three-fourths times x added to two times x is more than eleven

3/4x+2x>11

Hence,  Eli could travel 12 miles and 3/4x+2x>11 inequality matches the statement Three-fourths times x added to two times x is more than eleven

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The value of x in this problem is 2.

Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.

Use the transposing method to isolate the variable x and then solve for it.

distribute brackets on both sides of the equation.

= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x

= 15x - 10 = 10 + 6 + 2x

collect terms in x to the left side and numeric values to the right side.

= 15x - 2x = 10 + 6 + 10

= 13x = 26

= x = 26/13 = 2

Therefore the final value of x in this equation will be 2.

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x² + 4x + 4, this is a perfect square trinomial, which is expressed as

(x + 2)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 4x + 4

= (x)² + 2(2x) + 4

= (x)² + 2(x)(2) + 2²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 2)²

= (x + 2) (x + 2)

so, this is a perfect square trinomial.

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The employee who receives the largest percentage of their gross pay in employee benefits is Employee D.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviation "pct". For instance, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentage can be used to express part-to-whole relationships, such as "25% of the students in the class". It can also be used to compare two or more values, such as "the temperature rose by 3% over the course of the day". In some cases, percentage can be used to calculate a quantity from a given value, such as finding the percentage increase from one number to another.

This is because they have the highest total job benefits ($34,700) when compared to their gross pay ($33,700). This results in a percentage of 103.3%, which is the highest of the four employee options.

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Answer: 256b

Step-by-step explanation: So, first we need to find the square root of 16b.

That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b

So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.

So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.

So, I'd be 256b

Answer: Sara's mean quiz score is 12

Step-by-step explanation:

Mean is the Sum of the Terms divided by the number of terms.

If we add up every score we get 60, we then will divide this by how many scores there were (5).

60/5 = 12

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

18. m∠1 = 104°

19. m∠2 = 79°

20. m∠3 = 65°

21. m∠5 = 73°

The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).

The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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a. E(B) = 9.5

b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

c. Standard variable shows how much deviation from mean variable.

In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.

The discrete distribution given is:

P(X = 0) = 0.3

P(X = 10) = 0.5

P(X = 20) = 0.15

P(X = 30) = 0.05

The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:

E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5

Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.

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Step-by-step explanation:

20 workers finish work in 21 days.

the necessary work effort is 20×21 = 420 workdays.

the same effort is needed even if the overall time is shorter.

x workers in 15 days.

x × 15 = 420

x = 420/15 = 28 workers.

so, 28-20 = 8 additional workers are needed to finish the work in 15 days.

both Square and Rectangle

because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)

The value of x in the shape we have here is given as 18.7 cm

In this question we are to find the value of x using the values that we already have in the shape.

The base of the diagram has its length as 40 cm.

The shape is made up of two right angled triangles.

since the top of the shape is 26 m, the triangles would be gotten by

40 - 26 = 14

14 / 2 = 7cm

each rectangular base is therefore 7 cm

we have to solve for the value of x using the Pythagorean theorem

hence we would have:

7² + x² = 20²

49 + x² = 400

x² = 400 - 49

x² = 351

x = 18.7 cm

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The terms of the expression are 5x², 9x and 6

Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.

They are also known to be made up of arithmetic operation, such as;

It is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.

They can be regrouped by the addition of  their coefficients. Like terms are those that has the same variables to the same powers or coefficients.

The types are;

5x², 9x and 6

Thus, they are 5x², 9x and 6

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A basis for the eigenspace corresponding to a = 11 is (1, -2, 0) and a basis for the eigenspace corresponding to a = 2 is (0,1,1).

An eigenspace is the set of all vectors that are multiplied by a matrix and remain unchanged. In this case, the eigenspace is the set of all vectors that when multiplied by the matrix A will result in a vector with a scalar multiple of the eigenvalue. The eigenvalue is found by solving the characteristic equation, which is the determinant of the matrix minus the eigenvalue multiplied by the identity matrix.

For the matrix A, the eigenvalues are 11 and 2. The corresponding eigenspace for each eigenvalue is then found by solving the homogeneous system of equations. For a = 11, the solution to the system is (1, -2, 0) and for a = 2, the solution is (0,1,1). Both of these vectors form a basis for the corresponding eigenspaces.

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Answer:

yes, the board is long enough

Step-by-step explanation:

5.5 in x 4 walls = 22 inches

The board is 24.5 in, so there is enough.

24.5 > 22, there is an extra 2.5 in left over.

Answer:

Enlargment and 5/4

Step-by-step explanation:

Answer:

7/15

Step-by-step explanation:

number of favorable outcomes (red jelly beans) = 7

number of total outcomes (total jelly beans) = 7 + 2 + 6 = 15

probability of red = number of favorable outcomes/number of total outcomes = 7/15

The probability of getting a red jelly bean is 7/15

Total number of jelly beans in the jar (sum of all the jelly beans): 7+6+2= 15

Total number of red jelly beans: 7

Therefore, the probability of getting a red jelly bean= number of red jelly beans/ total number of jelly beans

=7/15

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The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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The spring constant is 30 N/m and the stretch when the 420 N force is applied is 14 cm.

The force needed or applied to compress or extend a spring on any attached object is known as the spring force.

A spring exerts an equal and opposite force on an object when the object exerts a force on it. It always takes action to get mass back to where it should be for equilibrium. 

Given that when 180 N force is applied the spring stretched by 6 cm. The spring stretch when the 420 N force is applied is calculated as,

First, calculate the spring constant,

F = kx

180 = k x 6

k = 30 N / m

Calculate the deformation,

x = F / k

x = 420 / 30

x = 14 cm

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Real numbers are every  number that exists in the real line, The four types of real numbers are rational, irrational, Natural and Integers.

In mathematics, a real number is a value that can be represented on the number line. The set of real numbers includes both rational numbers (such as integers, fractions, and decimals) and irrational numbers (such as √2 and π). Real numbers also include positive numbers, negative numbers, and zero. The set of real numbers is usually represented by the symbol R, and it has the properties of being closed under the operations of addition, subtraction, multiplication, and division (except for division by zero).

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Rational number = 3/4, -6/2, or 0.5.

Irrational number = √2, π, or e.

Natural number = 1,2,3,4....

Integers = -4, -1, 0, 1, 4.

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