Convert the following fraction to a decimal: ⅖ *

Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

The true statement is: "Octave is the name of a particular interval size."

In music theory, an octave refers to the interval between two pitches where the higher pitch has a frequency that is exactly twice that of the lower pitch. It represents a doubling or halving of the frequency. For example, if we start on the note A and move up to the next A, we have traversed an octave.

An interval, on the other hand, refers to the distance between two pitches. It is the numerical representation of the difference in pitch between two notes.

The statement mentioning "interval as the name of a particular octave size" is incorrect because the octave is a specific interval size, not the other way around.

The statement suggesting that "the fifth is a kind of octave" is also incorrect. The fifth is a specific interval that represents the distance of five diatonic scale steps between two pitches.

Lastly, the statement that "a synonym for distance is octave" is not true. While an octave represents a specific interval size, the term "distance" is a more general term that can refer to the measurement between any two pitches, regardless of the specific interval size.

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The statement that is NOT equivalent to the others is option c. "P(0) = r."

In the context of polynomials, a factor of a polynomial is a term or expression that divides evenly into the polynomial. So, if (x - r) is a factor of P(x), it means that when P(x) is divided by (x - r), the remainder is zero. This is equivalent to saying that r is a zero or root of the polynomial P(x). In other words, if r is a zero of P(x), then P(r) = 0.

Option c, on the other hand, states that P(0) = r. This means that when x is equal to zero, the value of the polynomial P(x) is equal to r. This statement does not provide any information about whether (x - r) is a factor of P(x) or if r is a zero of P(x). It simply relates the value of the polynomial at x = 0 to the constant value r.

To summarize, options a, b, and d are equivalent because they all refer to the fact that r is a zero of the polynomial P(x), while option c does not provide the same information and is therefore not equivalent to the others.

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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The areas listed that are possible areas of the square quilts Garrett can make will be 0.25, 0.81, etc.

Your information is incomplete as your didn't give the areas listed. Therefore, an overview will be given.

It should be noted that the area of a square is simply gotten by multiplying the side by itself. For example, if a side is 4cm, the area will be 4 × 4 = 16cm².

In this case, we are told that each patch has an area of 1 ft. Therefore, the square of the area gotten should not be more than 1 feet. Possible values include:

0.5 × 0.5 = 0.25

0.9 × 0.9 = 0.81

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Garrett is cutting square patches from old sports jerseys. Each

patch has an area of 1 ft?. He wants to put some of the

patches together to make square quilts.

Which areas listed below are possible areas of the square

quilts Garrett can make? What side length will each of

those square quilts have? Show your work.

Answer:

The least number of packages of balloons he can buy in order to have one balloon per person is 8.

Step-by-step explanation:

;)

The difference of two polynomials is just another polynomial that represents the result of subtracting one polynomial from another.

Let's say we have two polynomials: f(x) and g(x). We're told that their difference is 2x² - 8.

This means we can write:

f(x) - g(x) = 2x² - 8

Now, we just need to come up with two polynomials that satisfy this equation.

f(x) = 3x² - 2x + 1

g(x) = 3x² + 2x + 9

Now, let's check that their difference is indeed 2x² - 8

:f(x) - g(x) = (3x² - 2x + 1)  

Let's try:- (3x² + 2x + 9)= 3x² - 2x + 1 - 3x² - 2x - 9

= -4x - 8

= 2(x² - 4)

= 2x² - 8

So we see that these two polynomials do indeed have a difference of 2x² - 8.

When we subtract two polynomials, we simply subtract the corresponding coefficients of each term.

For example, if we have:

f(x) = 4x³ + 2x² - x - 5

g(x) = 2x² - x + 3

Then the difference between these two polynomials is:

f(x) - g(x) = (4x³ + 2x² - x - 5) - (2x² - x + 3)

= 4x³ + 2x² - x - 5 - 2x² + x - 3

= 4x³ + x² - 8

So the difference of two polynomials is just another polynomial that represents the result of subtracting one polynomial from another.

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The complete question is:

Come up with your own example that satisfies the following statement:

Give an example that satisfies the following:

The difference of two polynomials 2x²-8

The required additional information for a quadrilateral ABCD is a parallelogram with AB ∥ CD is given by AB ≅ CD.

In quadrilateral ABDC,

AB ∥ CD

Additional piece of information for a quadrilateral ABCD to be a parallelogram if and only if it satisfies any of the following conditions,

Opposite sides are parallel,

If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram.

Opposite sides are equal in length,

If both pairs of opposite sides of a quadrilateral are equal in length, then it is a parallelogram.

Opposite angles are equal,

If both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram.

Diagonals bisect each other,

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

One pair of opposite sides is both parallel and equal,

If one pair of opposite sides of a quadrilateral are both parallel and equal in length, then it is a parallelogram.

Here AB ∥ CD

Additionally if we have ,

AB ≅ CD

⇒ Quadrilateral ABCD is a parallelogram.

Therefore, the additional information for quadrilateral ABCD to be a parallelogram is AB ≅ CD.

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The above question is incomplete, the complete question is:

In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? AB ≅ CD AC ≅ BD AB ⊥ BD CD ⊥ BD.

Answer:

You can't get an answer to this unless you know what x is. The reason you can't solve is because it is factored down to the lowest form, but if you need to make an equation. Here is one: x^2 + 5x

Answer:

(x+4)

Step-by-step explanation:

Since area is width times length, you can just factor the area to get the width and length

You factor to get (x+4)(x+7)

Since (x+7) is the length, (x+4) must be the width

Answer:

(x + 4) m

Step-by-step explanation:

\(Area \: of \: rectangle = length \times width \\ \\ width = \frac{Area \: of \: rectangle}{length} \\ \\ = \frac{ {x}^{2} + 11x + 28 }{x + 7} \\ \\ = \frac{ {x}^{2} + 7x + 4x + 28}{x + 7} \\ \\ = \frac{ x({x} + 7) + 4(x + 7)}{x + 7} \\ \\ = \frac{ ({x} + 7) (x + 4)}{x + 7} \\ \\ = (x + 4) \: m \\ \\ \red{ \boxed{\bold {\therefore \: width \: = (x + 4) \: m}}} \)

Answer:

A=3.14⋅16⋅12V=3.14⋅16⋅12

Step-by-step explanation:

The equation to find the volume of a cylinder is h(3.14r^2), where h is the height of the container and r is the radius of the circle base. This works because for all regular prisms, the volume can be found by finding the area of the base x the height of the prism. 3.14r^2 = area of the base circle and 12 is the height, so therefore, we have found the volume. Additionally,3.14 is substituted for pi, most of the time in these equations the pi symbol is used.

Hope this helps!

Answer:

Step-by-step explanation:

Question 6)

sin Y= m

sin Y = m/1

So, hypotenuse is 1

Since sine is opposite over hypotenuse

So XZ= m and YZ = 1

Similarly, cos Y = k

cos Y = k/1

So adjacent side of angle Y is k

So XY = k

cos z - sin z = \(\frac{XZ }{YZ } - \frac{XY}{YZ}\)

cos z - sin z = \(\frac{m }{1 } - \frac{k}{1}\)

cos z - sin z = m - k

Question 7)

the relationship between sine, cosine, and tangent.

tan(x) = sin(x)/cos(x) = (11/61)/(60/61)

tan(x) = 11/60

Question 8)

Start with where the shorter leg is. It must be opposite the smallest angle.

In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it. 

That being said, if the shortest side is x, the hypotenuse will be 2x.

Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22

The answer is 22

Answer:

11 degrees

Step-by-step explanation:

The bottom triangle has 2 given angle, therefore we know the 3rd angle has to be 29 degrees. Given that the 2 lines are parallel, we know that the upper triangle has 140, 29, and x degrees. 180-140-29=x=11 degrees

Hope this helped, feel free to leave a comment if you still have any questions!

Cheers!

The price of the most expensive house sold is 3.112 millions of dollars.

What is algebra ?

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division.

The stem-and-leaf plot shows house sale prices over the last week in Tacoma. The stem is in hundreds of thousands of dollars and the leaf is in tens of thousands of dollars.

The most expensive house is represented by the number 3|0001122.

The stem is 3 which means the house price is in hundreds of thousands of dollars and the leaf is 001122, which means the house price is 1,122 thousands of dollars.

So the price of the most expensive house sold is ,

3 (hundreds of thousands of dollars) + 1,122 (tens of thousands of dollars) = 3.112 (millions of dollars)

So the price of the most expensive house sold is 3.112 millions of dollars.

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Answer:

20.

Step-by-step explanation:

We need to setup a proportion. We want the result to be 40% out of 50, meaning that we are solving for x:

4/10=x/50.

Cross-multiplying, we have 200 = 10x, and x = 20.

The requried function among the expressions is y = 4x - 19. Option A is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the question,

We have given four expressions, there is only an equation that represents a function y = 4x - 19.

Thus, the requried function among the expressions is y = 4x - 19. Option A is correct.

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Answer:

c=3√5

Step-by-step explanation:

it appears the vertices of the inscribed quadrilateral,cuts the edges of the square at certain points that form right angles,with C being the hypotenuse.

c=√3²+6²

c=√9+36

c=√45=3√5

The number of total parts in the ratio, given the ratio the line is divided into is a total of 7 parts .

When a line is divided in the ratio 3 : 4 , it means that the line is divided into 3 parts and 4 parts. The total number of parts is 3 + 4 = 7.

For example, if a line segment is 7 units long, then the part that is in the ratio of 3 : 4 would be 3 / 7 of the line segment and the other part would be 4 / 7 of the line segment.

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Full question is:

A line is divided in the ratio 3/4. How many total parts in the ratio?

Answer:

A

Step-by-step explanation:

i just know :)

Answer:

1/ $ 4.08

2/ $675.92

Step-by-step explanation:

Take 68 times 0.06% = $4.08

680 - 4.08= 675.92

Answer:

Step-by-step explanation:

40.80 it told me the answer

To approximate the value of f(1) using Taylor series, we first need to find the derivatives of the function f(x). The approximate value of f(1) using the Taylor series expansion is 4

Let's denote the nth derivative of f(x) as f⁽ⁿ⁾(x).

Then the Taylor series expansion of f(x) around x = 0 is given by:

f(x) = f(0) + f'(0)x + f''(0)x²/2! + f'''(0)x³/3! + ...

Since f(0) = 1 and f'(x) = ex(1 + x), we can evaluate the derivatives at x = 0:

f(0) = 1

f'(0) = e0(1 + 0) = 1

f''(0) = e0(1 + 0) + e0 = 2

f'''(0) = e0(1 + 0) + 2e0(1 + 0) = 3

Now we can plug these values into the Taylor series expansion and approximate f(1):

f(1) ≈ 1 + 1(1) + 2(1²)/2! + 3(1³)/3!

Simplifying the expression, we have:

f(1) ≈ 1 + 1 + 1 + 1 = 4

Therefore, the approximate value of f(1) using the Taylor series expansion is 4.

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Answer:

54√2

Step-by-step explanation:

3√3 . 6√6 = (3 . 6)√(3 . 6)

= 18√18

= 18√9 . √2

= 18 . 3√2 = 54√2.

Answer:

40 + 25 = 65

49 + 63 = 112

63 + 15 = 78

7×16 =112

26 × 3 =78

5×13=65

so the answer is

40 + 25 -------- 5 × 13

49 + 63 -------- 7 × 16

63 + 15 --------- 26 × 3

i hope this help you

Hence, the two triangles have the same side length so they are congurent triangles.

What is the congurency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

Here given triangles are

In Δ\(FGH\) and Δ\(JKL\) are congruent. If they are, give the reason, if they aren't choose "not congruent".

\(F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)\)

We know the distance formula

ie., \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Length in between \(FG\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}\)

Length in between \(GH\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-9-(-2))^2+(-7-2)^2}\\\\d=\sqrt{(-9+2)^2+(-7-2)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}\)

Length in between \(HF\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}\)

Length in between \(JK\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}\)

Length in between \(KL\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}\)

Length in between \(LJ\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(0+8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}\)

Therefore, \(FG\)≅\(LJ-GH\)≅\(JK-HF\)≅\(KL\)

Hence, the two triangles have the same side length so they are congurent triangles.

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Answer:

Step-by-step explanation:

See ratios and step changes below

Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)

The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.

We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)

As we parabola is quadratic function,

f(x) = a(x-8.4)(x-7.3)

It is passing through the point (0, 8.2)

8.2 = a(-8.4)(-7.3)

a = 8.2/61.32 =7.5 (approx)

Now, equation of parabola is

F(x) = 7.5(x-8.4)(x-7.3)

f(x) = 7.5(x^2-7.3x-8.4x+61.32)

F(x) = 7.5(x^2-15.7x+61.32)

Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).

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Answer:

1.56

Step-by-step explanation:

Don't forget your decimal placement. other than that you are correct I believe