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There are different ways to think about 2 2/3−2 1/3

Select three ways to find 2 2/3−2 1/3

The first five terms of the geometric sequence with a first term of 2 and a common ratio of 3 are 2, 6, 18, 54, 162.

A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a constant called the common ratio (r).

The general form of a geometric sequence is:

a, ar, ar^2, ar^3, ar^4, ...

Where:

- a is the first term,

- r is the common ratio.

To find the first five terms of a geometric sequence, you need the values of the first term (a) and the common ratio (r).

For example, let's assume the first term (a) is 2 and the common ratio (r) is 3.

The first five terms of this geometric sequence would be:

2, 2 * 3, 2 * 3^2, 2 * 3^3, 2 * 3^4

Calculating these terms, we get:

2, 6, 18, 54, 162

So, the first five terms of the geometric sequence with a first term of 2 and a common ratio of 3 are 2, 6, 18, 54, 162.

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you have to subtract from the $92.74 the $10 of the monthly fee, and then that is divided by the additional amount per minute, so that gives us the result I use it 1379 minutes

Answer:

-7y + 4x + 14

Step-by-step explanation:

We first need to simplify the expression removing parentheses

Simplify -7(y - 2):  Distribute the -7 to each term in (y-2)

-7 * y = (-7 * 1)y = -7y

-7 * -2 = (-7 * -2) = 14

Our Total expanded term is -7y + 14

Simplify x(9 - 5):  Distribute the x to each term in (9-5)

x * 9 = (1 * 9)x = 9x

x * -5 = (1 * -5)x = -5x

Our Total expanded term is 9x-5x

Our updated term to work with is -7y + 14 + 9x - 5x

Evaluate the y terms:

-7y  ← There is only one y term

Evaluate the x terms:

9x + - 5x

(9 - 5)x

4x

Evaluate the constants:

14  ← There is only one constant

Combining all like terms, we get:

-7y + 4x + 14

Analyze the 3 terms of the polynomial -7y + 4x + 14

Step-by-step explanation:

what is the problem ?

the solution of such a system of 2 equations is the point, where they cross.

this point has the same coordinates for both equations, and that is called the solution.

and we can clearly see that point in the graph :

(-1, 1)

formally we can solve that way

y = 2x + 3

y = -x

therefore,

2x + 3 = -x

3x + 3 = 0

3x = -3

x = -1

y = -x = - -1 = 1

so, we get

(-1, 1) as solution.

Using the law of cosines, the measures of the angles are given as follows:

The law of cosines states that we can find one of the sides or the angle C of a triangle according to the following equation:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters for the triangle are given as follows:

a = b = 12, c = 3.

We want to solve for the smallest angle C, hence:

c² = a² + b² - 2abcos(C)

9 = 288 - 288cos(C)

288cos(C) = 279

cos(C) = 279/288

C = arccos(279/288)

C = 14.36º.

The other two angles are congruent, and the sum of the internal angles of a triangle is of 180º, hence:

14.36 + x + x = 180

2x = 165.64

x = 165.64/2

x = 82.82º.

Then the measures of the angles are given as follows:

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Answer:

14

83

Step-by-step explanation:

i did it on edge

Answer:

The name of the solid with 20 faces that are congruent equilateral triangles is icosahedron.

The solid you are referring to is called an icosahedron. An icosahedron is a specific type of convex polyhedron that has 20 faces. In this case, all 20 faces are congruent equilateral triangles. Option d is correct answer.

To understand why this solid is called an icosahedron, let's break down the term. "Icosa-" comes from the Greek word for twenty, while "-hedron" means face. Therefore, an icosahedron is a polyhedron with twenty faces.

Each face of an icosahedron is an equilateral triangle, meaning that all three sides of the triangle are equal in length, and all three angles are equal to 60 degrees. Since all 20 faces are congruent, they have the same side lengths and angles.

The icosahedron has a total of 12 vertices and 30 edges. The vertices are the points where three edges meet, and the edges are the line segments connecting the vertices. The icosahedron has a symmetrical and regular structure, making it one of the five Platonic solids.

An icosahedron is a convex polyhedron with 20 congruent equilateral triangle faces, 12 vertices, and 30 edges.

Option d is correct answer.

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The value of P(0) and P(6) of The Polynomial Function above are 2 and 253/2 respectively.

Polynomial function refers to the algebraic expression that consists of several terms.

Polynomial function can be of different degrees, like linear polynomial (degree 1), quadratic polynomial (degree 2), cubic polynomial (degree 3), and so on.

The given polynomial function is P(w) = 6w² - 20w + 2.

To find P(6), substitute w = 6 in P(w).

Therefore,P(6) = 6(6)² - 20(6) + 2P(6) = 6(36) - 120 + 2P(6) = 216 - 120 + 2P(6) = 96

Adding P(6) = 349 to this equation, we get:2P(6) = 349 - 96 = 253

Therefore, P(6) = 253/2

Now, to find P(0), substitute w = 0 in P(w).

Therefore, P(0) = 6(0)² - 20(0) + 2 = 2

Therefore, P(0) = 2

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The amount of money that the person will have for a new bike by summer is $240.

From the information, the person opens a savings account and make a pact to deposit $30 a month. The person also has 8 months.

In this case, the total amount that will be in the account will be:

= Amount saved each month × Number of months

= $30 × 8

= $240

The person has $240.

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Answer:

(6, 9) (9, 13.5) (10, 15) and k = 1.5

Step-by-step explanation:

We can plug the given points into the equation y = kx

3 = k(2)

1.5 = k (constant of proportionality)

Then, we can use this to complete the other pints.

y = 1.5(6)

y=9, so (6, 9)

13.5 = 1.5(x)

9 = x, so (9, 13.5)

If we follow the pattern, the last point should be (10, 15)

Answer:

Sides: a = 9.165   b = 4   c = 10

Step-by-step explanation:

Is that check mark supposed to be square root?

Answer:

\((4^{2} +(\sqrt{84} ^{2} )\\=100\)

Step-by-step explanation:

After 2 weeks, the sunflowers in Class A and Class B will have the same height.

To find out after how many weeks the sunflowers in Class A and Class B will have the same height, we can set up an equation using the given heights and growth rates.

Let "x" represent the number of weeks.

For Class A, the sunflower starts at 6 centimeters and grows at a rate of 6 centimeters per week:

Height = 6 + 6x

For Class B, the sunflower starts at 12 centimeters and grows at a rate of 3 centimeters per week:

Height = 12 + 3x

To find the number of weeks when both sunflowers have the same height, we can set the two equations equal to each other:

6 + 6x = 12 + 3x

Now, solve for "x":

6x - 3x = 12 - 6

3x = 6

x = 2

So, the sunflowers in Class A and Class B will have the same height after 2 weeks.

Note: The question is incomplete. The complete question probably is: Class a was given a sunflower with a height of 6 centimeters that grows at a rate of 6 centimeters per week class b was given a sunflower with a height of 12 centimeters that grows at a rate of 3 centimeters per week. After how many weeks the sunflower the same height.

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The value of x for the nearest tenth in the given triangle is x = 41.30 degrees.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that occur and are defined on both sides of the equality. These are identities that, geometrically speaking, involve certain functions of one or more angles. They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

From the given figure we observe that, the lengths of the side corresponding to angle x are given.

Thus, using trigonometric identities we have:

tan x = 80/90

tan x = 8/9

x = arctan(8/9)

x = 41.34 degrees.

Hence, the value of x for the nearest tenth in the given triangle is x = 41.30 degrees.

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The final answers for the given problem without negative exponents are:

\(\(\frac{1}{16^{\frac{1}{8}}} = \frac{1}{4}\)\)

\(\(CA \cdot Db \cdot E = 36a^{11}b^9\)\)

\(\(GF = \frac{4}{x^{18}y^2}\)\)

\(\(GF = \frac{y^{10}}{x^{14}}\)\)

The given expressions, after simplification and rewriting without negative exponents, can be represented in LaTeX as follows:

\(\(\frac{1}{{16^{\frac{1}{8}}}} = \frac{1}{2^{\frac{8}{6}}} = \frac{1}{2^{\frac{4}{3}}} = 4 = \frac{1}{4}\)\)

\(\(CA \cdot Db \cdot E = (4a^7b^3)(3a^2b^3)^2 = 4a^7b^3 \cdot 9a^4b^6 = 36a^{11}b^9\)\)

\(\(GF = \left(\frac{x^6y^{-\frac{1}{2}}}{6x^{\frac{3}{2}}y^4}\right)^{-2} = \left(\frac{x^6}{y^{\frac{1}{2}}}\cdot \frac{2}{x^3y^2}\right)^2 = \left(\frac{x^6}{y^{\frac{1}{2}}}\right)^{-2} \cdot \left(\frac{2}{x^3y^2}\right)^2 = \left(\frac{y}{x^6}\right)^2 \cdot \frac{4}{x^6y^4} = \frac{y^2}{x^{12}} \cdot \frac{4}{x^6y^4} = \frac{4}{x^{18}y^2}\)\)

\(\(GF = \frac{1}{x^4y^{-10}} = \frac{y^{10}}{x^{14}}\)\)

Therefore, the final answers for the given problem are:

\(\(\frac{1}{16^{\frac{1}{8}}} = \frac{1}{4}\)\)

\(\(CA \cdot Db \cdot E = 36a^{11}b^9\)\)

\(\(GF = \frac{4}{x^{18}y^2}\)\)

\(\(GF = \frac{y^{10}}{x^{14}}\)\)

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Answer:

It's 84

Step-by-step explanation:

To calculate the area of a triangule you need to use this formula:

B * H / 2

So:

12 * 14 / 2 = 84

Hope this helps :)

Pls brainliest...

Answer:

12x^2; 21

Step-by-step explanation:

4x^2-3=4×1.5^2-3=6

4x^2-2=4×1.5^2-2=7

4x^2-1=4×1.5^2-1=8

6+7+8=p=21

Answer:

A ) 12x^2-6; 21 inches

Step-by-step explanation:

EDG2021

Answer:

use a net to fin surface area of a prism by multyplying 10 to the power of 50

Step-by-step explanation:

Answer:

To find the total surface area of a prism, you need to calculate the area of two polygonal bases, i.e., the top face and bottom face. And then calculate the area of lateral faces connecting the bases. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.

Step-by-step explanation:

There is only one way to pick a president from 1000 number of professors, and that is to select one of the professors.

1. There are 1000 number of professors to choose from

2. The board of trustees can only pick one of the 1000 professors

3. Therefore, there is only one way to pick a president - select one of the professors.

The board of trustees can pick a president from the 1000 professors by considering their qualifications, experience, and other criteria. They can also take into account the opinion of the faculty and students of the college. If applicable, the board may also take into account any applicable legal requirements. Finally, they can make their selection by majority vote.

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Answer:

A. y = x+0.25

Answer:

The value of x so f (x) = 7 is 5.

Step-by-step explanation:

Answer:

f(-1) = 12

Step-by-step explanation:

Using the graph for f(x)  let x=-1

Find the y value when x= -1

f(-1) = 12

The x-intercept of S(x), along with it's correct interpretation, is given by the following option:

A. (12, 0); After selling 12 items, Samuel will have a positive profit.

The x-intercept of a function S(x) is the value, or the values, of x, for which S(x) = 0. The point is given by (x,0).

In this problem, the function is given by:

S(x) = 25x - 300.

Hence the x-intercept is found as follows:

25x - 300 = 0.

25x = 300

x = 300/25

x = 12.

Hence the correct option is given by:

A. (12, 0); After selling 12 items, Samuel will have a positive profit.

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The correct option among the given choices is c. is often performed automatically, without awareness

A healthy habit is a behavior or action that people consistently engage in, usually without giving it any conscious thought.

These routines get established with these habits, which are frequently carried out automatically and unknowingly. frequently brushing your teeth, washing your hands before eating, using the stairs instead of the elevator, and exercising frequently are a few examples of healthy habits.

Therefore, option C is the most accurate description of a healthy habit.

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Given data:

The first given length is SL=4 units.

The second given length is LR=3 units.

The thi

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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The equation representing the ball's movement is given as follows;

To determine the value of t (that is, time), we shall now make the equation become;

This is because when the height is zero, then the ball has actually touched the ground. So making h equal to zero, we now have a quadratic equation and we shall solve it using the quadratic equation formula as follows;

The variables are,

We now have;

The quadratic equation now has two solutions.

Note however, that the question requires us to determine the time taken and we know this cannot be a negative value.

Therefore, we shall take t = 3.1896, and rounded to the nearest hundredth this becomes;

Answer: 3

Step-by-step explanation:

The required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)

For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.

The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi

\(z = 5\sqrt{3}/4 - 5/4i\)
the polar form complex numbner  can be given as
\(z = rcos\theta +rsin\theta i\)   - - - - - -(1)
where r = \(\sqrt{a^2+b^2}\)
and \(\theta=tan^-\frac{b}{a}\)

Since a = 5√3/4 and b = -5/4
\(r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}\)
r = 10/4
r = 5/2
Now,
\(\theta=tan^-\frac{b}{a}\)
\(\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30\)

Now the polar form is given by substituting the values of r and \(\theta\) in equation 1
Here,
\(z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i\)

Thus, the required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)

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Answer:

The correct option is;

69 cm

Step-by-step explanation:

The z-score, or standard score is a measure of how far a data is from the mean

The z-score, is given by the relation;

\(z = \dfrac{x- \mu}{\sigma}\)

Z = Standard score

x = Value observed

μ = The mean height of the plants = 52.5 cm

σ = Standard deviation = 7.2 cm

Given that the z-score = 2.25, we have;

\(2.25 = \dfrac{x- 52.5}{7.2}\)

Therefore, x = 7.2 × 2.25 + 52.5 = 68.7 cm ≈ 69 cm

Therefore, the minimum required height for this type of plant to be displayed in the main lobby is 69 cm.

Answer:

The width would be 8 inches

Step-by-step explanation:

50% of 16 is 8