What is the twentieth term in the sequence 23, 43, 63, 83 …?

Answer:

I think it should be A.

Step-by-step explanation:

8-1 is 7 which is very close to 6, and it says they are similar so this could work.

The surface area of this figure is made by 1 rectangle in the bigger base, 1 rectangle in the smaller base, 2 lateral rectangles and 2 trapezoids.

In order to calculate the total surface area, let's calculate each individual area and sum them.

So we have:

Now, calculating the total area, we have:

Therefore the total surface area is 648 cm².

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = \(\frac{1}{2} bh\)

        = \(\frac{1}{2}\) × 3 × 4

       = 6 units²

For triangle BCD

Area = \(\frac{1}{2}bh\)

        = \(\frac{1}{2}\) × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = \(\frac{1}{2} (a + b) h\)

        = \(\frac{1}{2}\) × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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The derivative of the function f(x) = ln(e^(4x) + 6), is f'(x) = 4e^(4x) / (e^(4x) + 6)  To find the derivative of the function f(x) = ln(e^(4x) + 6), we can use the chain rule.

The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is ln(x) and the inner function is e^(4x) + 6.

To find the derivative, we can follow these steps:

1. Find the derivative of the outer function:

  The derivative of ln(x) with respect to x is 1/x.

2. Find the derivative of the inner function:

  The derivative of e^(4x) + 6 with respect to x is 4e^(4x).

3. Apply the chain rule:

  Multiply the derivative of the outer function (1/x) by the derivative of the inner function (4e^(4x)).

So, the derivative of f(x) = ln(e^(4x) + 6) is:

f'(x) = (1 / (e^(4x) + 6)) * (4e^(4x))

Simplifying further, we can write:

f'(x) = 4e^(4x) / (e^(4x) + 6)

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Rich will incur interest totaling $1,525.095 throughout the course of the 4.5-year non-payment period.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Given that he is aware that he has the option to start loan payback in 4.5 years at the current interest rate of 4.29% on a $7,900 loan, the following will apply:

4.29% of 7900 after the first year

\(4.29/100*7900\)

=338.91

So, after the tenure of 4.5 years, to find total interest, the interest will be multiplied by 4.5:

=338.91*4.5

=1525.095

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The distance from the base of the stand to the campfire is 285.6 feet.

The angle of depression of 35 degrees.

Let's denote the distance from the base of the stand to the campfire as "x."

Since we know that,

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

Using the tangent function, we have:

tan(35 degrees) = opposite/adjacent

tan(35 degrees) = 200/x

To find the value of x, we can rearrange the equation:

x = 200 / tan(35 degrees)

x ≈ 200 / 0.7002

x ≈ 285.6 feet

Therefore, the distance from the base of the stand to the campfire is 285.6 feet.

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The co-terminal angle to 5π/6 in the unit circle is C. 17π/6

Co-terminal angles in a unit circle are angles that share the same terminal point

Given the angle 5π/6, we desire to find the angle that shares the same terminal point in the unit circle. We proceed as follows.

We know that x = 5π/6 + 2π

Taking the L.C.M which is 6, we have that

x = (12π + 5π)/6

x = 17π/6

So, the angle is C. 17π/6

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To solve the given quadratic equation, we need to factorize the given expression.

To do it, the first step is to multiply all terms in the equation by the coefficient of the first term (7):

Now, re write the equation in terms of 7x:

Now, factorize the expression, look for 2 numbers whose product equals 84 and whose sum equals 31. Those numbers are 28 and 3.

Now, divide the expression by the coefficient of the first term in the original equation (7):

Now, for the expression to be equal to 0, one of the factors must be 0. Use this information to find the values of x:

The solutions are x=4 and x=3/7.

Answer:

3x + 3(-8x - 24) = 12

3x - 24x - 72 = 12

-21x - 72 = 12

-21x - 72+72 = 12+72

-21x = 84

-21x/-21 = 84/-21

x = -4

(-4,-24)

The required solution to the given system of equations is (-4,8).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The system of equations is given in the question

y = -8x – 24   ....(i)

3x + 3y = 12   ....(ii)

Substitute the value of equation (i) in equation (ii), and solve for x

3x + 3(-8x - 24) = 12

3x - 24x - 72 = 12

-21x - 72 = 12

-21x - 72+72 = 12+72

-21x = 84

x =  -84/21

Apply the division operation,

x = -4

Substitute the value of x = -4 in equation (i), and solve for y

y = -8(-4) – 24

y = 32 - 24

y = 8

Therefore, the required solution to the given system of equations is (-4,8).

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Answer:

22%.

Step-by-step explanation:

7/25 = 28%

0.09 = 9%

2/5 = 40%

29% + 9% + 40% = 78%

100% - 78% = 22%

And you have your answer. Hope this helped.

The given equations of planes are: 15x - 3y + 12z = 2  & 2y = 10x - 8z

To determine whether these planes are parallel, perpendicular or neither, we need to compare the normal vectors of the planes. The normal vector of a plane is given by the coefficients of x, y and z in the equation of the plane.

The normal vector of the first plane (1) is [15, -3, 12] and the normal vector of the second plane (2) is [10, 2, -8/2] = [10, 2, -4].

Now, to check if the planes are parallel or perpendicular, we can take the dot product of the normal vectors. If the dot product is 0, then the planes are perpendicular, and if it is non-zero, then the planes are parallel.

The dot product of the normal vectors of the given planes is:

[15, -3, 12] · [10, 2, -4] = (15)(10) + (-3)(2) + (12)(-4) = 0

Since the dot product is zero, the planes are perpendicular to each other.

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Answer:2693

Step-by-step explanation:

Answer:

2x+6 +x-4 +4+4

Step-by-step explanation:

Hi There!!

Here's the answer below.

Step-by-step explanation:

Well, The Part A

The area is...

\((x +4)\) \((2x+6+ x-4)\)

\(=\) \((x+4) (3x+2)\)

\(=\) \(3x^{2} + 14x + 8\)

Now, We finish Part A.

We got to do Part B.

The length is \(x-4\) and it's \(12\)

\(x-4 = 12\)

\(x = 12 +4\)

\(x = 16\)

Now, We got to the area.

\(3(16)^{2} + 14(12) + 8\)

\(= 3(256) + 168 + 8\)

\(= 768 + 176\)

\(= 994\)

So, Your best answer choice is \(994\)

#\(Be\) \(Bold\)

\(_{Loserbrazts}\)

The distance from the car to the gate to magic kingdom is 1 1/12 miles.

From the information given, it was stated that get from their car in the parking lot to the gate at the magic kingdom they walk 1/4 mile take a tram for 1/3 their total distance and take a monorail for 1/2.

Therefore, the distance from the car to the gate to magic kingdom based on the information will be the addition of the fractions given. This will be:

= 1/3 + 1/2 + 1/4

= 4/12 + 6/12 + 3/12

= 13/12

= 1 1/12

The distance is 1 1/12 miles.

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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Answer:

33.92

Step-by-step explanation:

40 x .2= 8

40-8= 32

32x.06=1.92

32+1.92= 33.92

Answer:

16-1=15

Step-by-step explanation:

decreased means subtraction

(a) The required rate of return on the stock is 21.9%. (b) This decrease occurs because the increase in the risk-free rate reduces the equity risk premium and, consequently, the required rate of return on the stock.

The risk-free rate, denoted as "T F​," is 5%, and the equity risk premium, denoted as "Tk," is 13%. Additionally, the beta of the stock, represented as "b," is 1.3. The first part of the question requires determining the required rate of return, while the second part explores the effects of changes in the risk-free rate on the required rate of return and the slope of the Security Market Line (SML).

a. To calculate the required rate of return on the stock (nu), we can use the Capital Asset Pricing Model (CAPM). According to CAPM, nu = T F​ + (Tk * b). Substituting the given values, we have nu = 5% + (13% * 1.3), which simplifies to nu = 5% + 16.9% = 21.9%. Therefore, the required rate of return on the stock is 21.9%.

b. When the risk-free rate (T F​) increases to 6% while keeping the slope of the SML constant, it affects the required rate of return (ry) and the market risk premium (n). In this case, both the market risk premium (n) and the required rate of return (ry) will decrease by 1 percentage point. This decrease occurs because the increase in the risk-free rate reduces the equity risk premium and, consequently, the required rate of return on the stock.

If the risk-free rate (T F​) decreases to 4% while keeping the slope of the SML constant, it affects the risk-free rate (T F​) and the required rate of return (ry). In this scenario, the risk-free rate (T F​) will decrease by 1 percentage point, while the required rate of return (ry) will remain the same. The decrease in the risk-free rate does not directly affect the required rate of return on the stock, as it is primarily driven by the equity risk premium and beta.

In conclusion, the required rate of return on the stock is determined using the Capital Asset Pricing Model (CAPM) formula. Changes in the risk-free rate impact the required rate of return and the market risk premium. Increasing the risk-free rate decreases both the market risk premium and the required rate of return, while decreasing the risk-free rate affects only the risk-free rate itself, without directly impacting the required rate of return.

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Step-by-step explanation:

12 degrees is 1 person

360÷30people=12

12 for 1 person

thanks for the ez question im doing a challenge TvT

Answer:

(4 1/2) / (2/3) =

(9/2) / (2/3) =

9/2 * 3/2 =

27/4 =

6 3/4 (or 6.75) calories per minute

Step-by-step explanation:

Answer:

The half life of a radioactive substance is 10 days. If you start with 50 grams of the substance, how many grams will be left after 30 days?

First point. Your question is worded fine. As usual, there are folks answering this question saying that “radioactive decay doesn’t reduce mass”. PFUI folks. When an atom decays, it becomes ANOTHER element. THEREFORE, if you started with 50 grams of substance X, after decay you have LESS mass of substance X.

Second point. There is an “easy” way to do this problem, and you got several answers about that. (first half life you drop to 25 gm. Second half life you drop to 12.5 gm. Third half life, and you have 6.25 gm. You can do this one on your fingers.

Now. There is a “hard” way, but it allows you

If you had 16 grams of an element with a half life of 15 minutes would you have 1 gram of mass left after an hour or would its radioactivity only be 1/16th?

Its mass would remain virtually unchanged (diminished very slightly by radiation), but only 1/16 of that mass would still be the original isotope; 15/16 of that mass would now be the daughter isotope (or a granddaughter isotope, or some other descendant, depending on the daughter isotopes' half-lives), which may be either more or less radioactive than the original isotope in question.

The half-life of a certain radioactive element is 35 hours. If there are 904 grams of this element, how much will be left after 70 hours?

If we do your homework for you, you won’t learn anything.

This is a simple problem. Think it through. 35 hours is the half-life so after 35 hours how much is left of the 904g?

P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.

Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.

2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.

3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

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Answer:

Cheetah A ran at a faster speed than Cheetah B, as it ran 18 miles in 16 minutes while Cheetah B ran 54 miles in 50 minutes.

Step-by-step explanation:

Answer: its A

Step-by-step explanation:

Answer:

Complex and imaginary number

Step-by-step explanation:

First, let's write the number\(-16.2i\) in the form of \(a+bi\).

\(0+ (-17)i\)

Since \(-16.2i\) can be written in the form of \(a + bi\), where \(a\) and \(b\) are real numbers, it is a complex number.

Also, since \(a=0\), it is also an imaginary number.

\(-16.2i\) is complex and imaginary.

Answer:

  (c)  x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

Step-by-step explanation:

The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.

The last step shown in the derivation so far is ...

  \(x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}\)

The left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.

  \(\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}\)

Answer: \(x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}\)

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

\(\left(x+\frac{b}{2a} \right)^2\)

So, taking the square root of both sides,

\(x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}\)

Answer:

2

Step-by-step explanation:

+3 to both sides then

/2 from both sides

18 triangles area unit required to compose a vicinity that's one square meters.

A square with a locality of one square metre is rotten into nine identical little squares. every little sq. is rotten into 2 identical triangles.

1 square metre is rotten into nine identical little squares.

So there area unit nine little squares in one square metre.Each little sq. is rotten into 2 identical triangles therefore nine little squares is rotten into 9(2) = eighteen identical triangles

Hence, one square metre is rotten into eighteen identical triangles.

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Answer:

2,712.96 yd³

Step-by-step explanation:

The formula for finding the volume of a cylinder:

πr²h

π (in this case) = 3.14

r = radius

h = height

In this picture, we are given all of the values we need to set up and solve this equation.

r = 12 yd

h = 6 yd

3.14(12)^2 · 6

3.14(144) · 6

452.16 · 6

2,712.96

Step-by-step explanation:

by using the pythagoras theorem,

the height of the ladder touching the wall =

√(20²- 4²)

=√ (400-16)

=√384

= 8√6 feet

or 19.6 feet

Using Pythagorean theorem

\(\\ \rm\longmapsto P^2=H^2-B^2\)

\(\\ \rm\longmapsto P^2=20^2-4^2\)

\(\\ \rm\longmapsto P^2=400-16\)

\(\\ \rm\longmapsto P^2=384\)

\(\\ \rm\longmapsto P=\sqrt{84}\)

\(\\ \rm\longmapsto P=19.6ft\)

Answer:

D. h(x) = 4(x - 5)² - 18

Step-by-step explanation: