Reflections; rotations and translations are transformations that change the what?

Answer:

Step-by-step explanation:

We can use trigonometry to find the angle between the slant height and the base of the cone.

The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).

Using the Pythagorean theorem, we can find the height of the cone:

height^2 = (slant height)^2 - (radius)^2

height^2 = (4.70 cm)^2 - (1.65 cm)^2

height^2 = 19.96 cm^2 - 2.72 cm^2

height^2 = 17.24 cm^2

height = sqrt(17.24) cm

height = 4.15 cm (rounded to two decimal places)

Now we can use trigonometry to find the angle between the slant height and the base of the cone.

tan(angle) = opposite / adjacent

tan(angle) = height / radius

tan(angle) = 4.15 cm / 1.65 cm

tan(angle) = 2.515

Taking the inverse tangent (or arctan) of both sides, we get:

angle = arctan(2.515)

angle = 70.32 degrees (rounded to two decimal places)

Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.

Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer: 1050$

Step-by-step explanation:

im a math teacher

To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Answer:

D. 50 square centimeters

Answer:

$6235 1

' 1 . ' 8

Answer:

Step-by-step explanation:

Answer:

2n + 14 = 30

Step-by-step explanation:

Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.

This model represents the total on the top and the 2 parts on the bottom.

The correct option is 1 and 4  of the given inequality  –3(2x – 5) < 5(2 – x)

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x

x < 5

Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.

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The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).

Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.

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The supplementary angle will be 60°.

What are supplementary angles?

Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.

For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.

Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.

Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.

Now,

Let x = measure of the angle.

Then, the supplement angle is 180 - x.

According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:

180 - x = 2x

Solving for x, we get:

180 = 3x

x = 60

Therefore, the angle measures 60 degrees.

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Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.

Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.

Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.

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It switches between negative and positive every 40 seconds.  it switches between positive and negative every 80 seconds. So correct statements are B and E.

Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.

Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.

As a result, every 40 seconds it alternates between negative and positive.

B is accurate.

We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.

As a result, every 80 seconds it alternates between positive and negative.

E is accurate.

The complete question is:

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Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.

Given the following definition of functions

a₁ = 5

aₙ = 2aₙ₋₁ + 3

To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:

a₂ = 2a₁ + 3 = 2(5) + 3 = 13

a₃ = 2a₂ + 3 = 2(13) + 3 = 29

a₄ = 2a₃ + 3 = 2(29) + 3 = 61

Therefore, the fourth term of the sequence is 61.

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Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²

Factoring polynomials simply means separating a polynomial into its component polynomials.

Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.

We have the equation:

(3y - 2)² - (3y - 2)⁻²

Let 3y - 2 be denoted by S and as such we have:

S² - S⁻²

= S² - 1/S²

Using the denominator as factor, we have:

= (S⁴ - 1)/S²

Plugging 3y - 2 for S gives us:

((3y - 2)⁴ - 1)/(3y - 2)²

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Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

Answer: I think its C

Answer:

Step-by-step explanation:

C is false. [tex]\angle BEC = \angle AED=126[/tex]   (vertically opposite).

The rest are correct.

In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.

A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:

[tex]V = \pir^2h[/tex]

Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.

[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]

Therefore, the volume of the tank is approximately 301 cubic feet.

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Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

Using trigonometric functions, we can find that the value of the angle N is 3°.

The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.

Here, using the cosine theorem:

CosM = n² + l² - m²/2nl

⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70

⇒ -0.981 = 729 + 4900 - m²/3780

⇒ 5629 - m² = -3708

⇒ m² = 9337.

Now Cos N = m² + l² - n²/2ml

= (9337 + 4900 - 729) / (2 × √9337 × 70)

= 0.9985

Cos N = 0.9985

Putting [tex]Cos^{-1}[/tex] on both sides:

[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985

⇒ N ≈ 3°

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The complete question is:

In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.

Answer:

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

Step-by-step explanation:

To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.

The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:

(7/9) x 84 = 66.67

Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

The wrestler's weight before he went on his diet was 78.0 kilograms.

What is y-intercept?

In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.

To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.

We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:

(1.5, 85.8) and (3.0, 93.6)

The change in weight over the time interval of 1.5 to 3.0 months is:

93.6 - 85.8 = 7.8

The change in time over that interval is:

3.0 - 1.5 = 1.5

So the slope of the linear function is:

7.8 / 1.5 = 5.2

Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:

y - 85.8 = 5.2(x - 1.5)

where y represents the wrestler's weight and x represents the time in months.

To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:

y - 85.8 = 5.2(0 - 1.5)

y - 85.8 = -7.8

y = 78.0

Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.

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Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

Answer:

the answer is supposably 75900000