Find the gradient of the line segment between the points (2,4) and (4,6)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{6}}} \implies \cfrac{ 2 }{ 1 } \implies 2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{6}) \\\\\\ y-5=2x-12\implies {\Large \begin{array}{llll} y=2x-7 \end{array}}\)

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Option B, Justice is one of four ethical concepts. The definition states that there must be fairness in all medical judgments.

Four ethical principles: autonomy, benevolence, harmlessness, and justice. Each of these principles serves a specific purpose, but all four work together to empower you as healthcare professionals and ensure that your patients receive high-quality, ethical care.

The literal concept of autonomy and the medical concept of autonomy diverge and intersect. Charity is an act of compassion or mercy. The activities of all healthcare workers should always be positive. Of the four principles of medical ethics, harmlessness is the most important.

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Answer:

B

Step-by-step explanation:

If you multiply 8 times 3 you’ll get 24

The sum of this infinite series 80 +60 +45 +... is 320 after applying the formula of the sum of the infinite series.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an infinite series

80 +60 +45 + ...

It is the geometric sequence

The common ratio r = 60/80 = 0.75

We know the sum of the infinite series is given by:

S = a/(1-r)

a is the first term.

S = 80/(1-0.75)

S = 320

Thus, the sum of this infinite series 80 +60 +45 +... is 320 after applying the formula of the sum of the infinite series.

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The radical form  ∛ is 1/3.

The radical form of the expression \(15^{\frac{1}{3}\) is ∛15.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

Example: 3 + x, 3x, √4, ∛27 are all expressions.

We have,

\(15^{\frac{1}{3} }\)

We need to write it in radical form.

This means we must remove the power 1/3 in the given expression.

Some of the expressions in the radical form are:

∛ = 1/3

√ = 1/2

We know that,

∛ = \(\frac{1}{3}\)

So,
Since ∛ is 1/3 we can write the expression as ∛15.

\(15^{\frac{1}{3} }\) = ∛15.

Thus,

The radical form of the expression \(15^{\frac{1}{3}\) is ∛15.

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The sample space as Feechi makes three attempts at a basket in a basketball game is BBB, BMB, MBM, MMM).Option A

The sample space represents all possible outcomes of Feechi's three attempts, where each attempt can either result in a basket (B) or a miss (M).

Option A lists the following four outcomes: BBB, BMB, MBM, and MMM. Each outcome is a sequence of three letters, where B represents a basket and M represents a miss.

Therefore, the correct answer IS (BBB, BMB, MBM, MMM).

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The sample space for Feechi's result would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM). That is option D.

The various moves to make a successful attempt at the basket was done 3 times.

When she gets a B = Basket

When she gets an M = Miss

The possible outcome of the sample space would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM).

This is because only 8 unique arrangements can be gotten from the list of possible outcomes.

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answer:

9 po

explanation:

:)

Answer:

\(3+2\left(2+1\right)\)

\((2+1)=3\)

\(3+2\times \:3\)

\(3+6\)

\(9\)

Answer:

This is super simple! No need to worry.

Step-by-step explanation:

Just add the two results from the aquarium and amusement park for both the teacher and the students!

Soooo it'd look something like this lol

8 + 32 = 40 students were polled

5 + 5 = 10 teachers were polled

Answer:

Step-by-step explanation:

The problem as stated asks for the limit as x approaches 2 of (0/x) -2.

As written, the limit is (0/2) -2 = -2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/x -2 is defined as -2 everywhere except x=0. So, the value at x=2 is 0/2 -2 = -2.

__

If you mean (f(2) -f(x))/(x -2), that limit is the limit of 0/(x-2) = 0 as x approaches 2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/(x-2) is zero everywhere except at x=2. The left limit and right limit are both 0 as x approaches 2. Since these limits agree, the limit is said to be 0.

__

If you mean f(x) = ln(x) and you want the limit of (f(2) -f(x))/(x -2), that value will be -1/2.

Explanation: The value of the ratio is 0/0 at x=2, so we can find the limit using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

  lim = (-1/x)/(1)

The value is -1/2 at x=2.

The range for the following sets is:

{9.12, 9.33, 9.18, 9.12. 9.24} = 0.21

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.54

{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26

The range is the difference between the highest value and the lowest value of a given set of data.

We have,

{9.12, 9.33, 9.18, 9.12. 9.24}

Range = 9.33 - 9.12

Range = 0.21

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}

Range = 33.4 - 3.8

Range = 29.6

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}

Range = 0.65 - 0.11

Range = 0.54

{6, 2, 14, 11, 28, 10, 19, 15, 11}

Range = 28 - 2

Range = 26

Thus,

The range of the given sets is as follows:

0.21, 29.6, 0.54, and 26.

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To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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The measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.

Based on the problem description, we can see that the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA. Therefore, we need to find the measure of the exterior angle at vertex A.

We know that the sum of the measures of the angles in a triangle is 180 degrees. So, we can find the measure of angle BAC by subtracting the measures of angles BCA and ABC from 180 degrees:

angle BAC = 180 - angle BCA - angle ABC

We can find the measure of angle ABC by subtracting the measure of angle A from 180 degrees:

angle ABC = 180 - angle A

Similarly, we can find the measure of angle BCA by subtracting the measure of angle C from 180 degrees:

angle BCA = 180 - angle C

Substituting these expressions into the equation for angle BAC, we get:

angle BAC = 180 - (180 - angle A) - (180 - angle C)

         = angle A + angle C

Therefore, the measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

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The equation for a rational function with vertical asymptotes at x = -3 and x = 2, x-intercepts at x = -1 and x = -5, and a y-intercept at y = 9 is f(x) = (x + 1)(x + 5) / (x + 3)(x - 2). To construct a rational function that satisfies the given conditions, we need to consider the behavior of the function at the vertical asymptotes and the x-intercepts, as well as its y-intercept.

First, let's consider the vertical asymptotes at x = -3 and x = 2. Vertical asymptotes occur when the denominator of the rational function is equal to zero, so we can include factors in the denominator that will result in these specific values as zeros.

One possible form for the denominator is:

(x + 3)(x - 2)

Now, let's address the x-intercepts at x = -1 and x = -5. X-intercepts occur when the numerator of the rational function is equal to zero, so we can include factors in the numerator that will result in these specific values as zeros.

One possible form for the numerator is:

(x + 1)(x + 5)

Combining the numerator and denominator, we have the rational function in the form:

f(x) = (x + 1)(x + 5) / (x + 3)(x - 2)

Finally, let's consider the y-intercept, which occurs when x = 0. To find the y-intercept, we substitute x = 0 into the function and solve for y:

f(0) = (0 + 1)(0 + 5) / (0 + 3)(0 - 2) = 5 / (-6) = -5/6

Therefore, the equation for a rational function with vertical asymptotes at x = -3 and x = 2, x-intercepts at x = -1 and x = -5, and a y-intercept at y = 9 is f(x) = (x + 1)(x + 5) / (x + 3)(x - 2)

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Answer:

k = 5/6

Step-by-step explanation:

The √ can be rewrite as a power, and this power is 1/2

So √a = a^1/2, and it is multiplying a, so we add the powers: a¹•a^1/2 = a^(1+1/2) = a^3/2

And the ³√ can be rewrite as the power 1/3, but the a inside the ³√ is to the power of 2, so we can rewrite it like this: (a²)^1/3

And to evaluate this we have to multiply the powers, so we will have: a^2/3

Now we have this fraction:

\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } \)

A fraction with powers in the same base can be rewrite like a subtraction of the powers, so let's do that:

\( \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } = {a}^{ \frac{3}{2} - \frac{2}{3} } = {a}^{ \frac{5}{6} } \)

Answer:

The given expression is not a complete equation or function. It seems like a linear function, but it is missing an input variable and an equal sign.

A linear function in the form of y = mx + b, where y is the output, x is the input, m is the slope, and b is the y-intercept.

Without the input variable, we cannot evaluate the function. Can you please check if you have provided the complete equation or function?

Step-by-step explanation:

53. tan2x - 1 = 0  

x = 0, 180  

54. tan x + 1 = 0  

x = -1  

55. 2 cos x + V3 = 0  

x = -V3/2  

56. 2 cos x - V3 = 0  

x = V3/2  

57. cot x = 1  

x = 0, 180

58. cot x = -1  

x = 90, 270

59. sin x(1 + 2 cos x) = 0  

x = 0, 180, 360  

60. cos x(1 - 2 sin x) = 0  

x = 0, 90, 270  

61. tan x cos x = tan x  

x = 0, 90, 180, 270  

62. cot2x = 1  

x = 0, 90, 180, 270

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Answer:36.53

Step-by-step explanation: Subtract them the two numbers.

Answer:

36.53 is the correct answer

Radius of convergence for the new power series is R' = R¹/³

To determine the radius of convergence of the power series ∑cn x³ⁿ, we can use the ratio test. The ratio test states that limit as n approaches infinity of the absolute value of consecutive terms, |a_(n+1) / a_n|, exists and is less than 1, then the series converges.

For the given power series ∑cn xⁿ, the radius of convergence is R. Apply the ratio test to this series:

lim (n→∞) |(cn+1 xⁿ⁺¹) / (cn xⁿ)| = lim (n→∞) |(cn+1/cn) * (x)| < 1

Since the radius of convergence is R, we know that:

|x| < R

Now, let's apply the ratio test to the new power series ∑cn x³ⁿ:

lim (n→∞) |(cn+1 x³ⁿ⁺¹) / (cn x³ⁿ)| = lim (n→∞) |(cn+1/cn) * (x³)| < 1

To make a comparison, we can rewrite the inequality as:

|x³| < R'

where R' is the radius of convergence of the new power series.

Taking the cube root of both sides, we get:

|x| < (R')¹/³

Since we know that |x| < R for the original power series, we can deduce that the radius of convergence for the new power series is:

R' = R¹/³

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Answer:

$4.50

Step-by-step explanation:

You would divide 6 by 4 to get 1.5 being $1.50 and then muiltpy it by 3 to get 4.50.

Answer:

Step-by-step explanation:

Answer:

M= 3/4

Step-by-step explanation:

Take what is before the x and that is you're slope.

Answer:

As a decimal: 0.13

As a fraction: 5/36

Step-by-step explanation:

Answer: 5

Step-by-step explanation: hope this helps!

Total time = 2 hours

Time playing video games = 50 minutes

We have to write an equation:

Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes

Time must be in the same unit ( minutes)

since 60 minutes =1 hour

2 hours = 2 (60) =120 minutes

Back with the equation:

120 x = 50

Solving for x

x = 50/120

x = 0.42

In percentage form:

0.42 x 100 = 42%

Answer:

Step-by-step explanation:

4 + 6z - 15 = 6z - 11

2(3z -4) = 6z - 8

Here's the tricky part. You are only taking 8 away from 6z

The result is going to be larger than when you take away 11 from 6x

Try it

suppose z = 7

6*7 - 8 = 42 - 8 = 34

6*7 - 11 = 42 - 11 = 31

34>31

Answer:

Step-by-step explanation:

1).

Answer:

350 dollars

Step-by-step explanation:

We're given:

First, find the total cost for student tickets:

Therefore, the total cost for student tickets was 170 dollars.

Now, find the total cost for adult tickets:

Therefore, the total cost for adult tickets was 180 dollars

To find the total cost for the museum tickets, find the sum:

180 + 170 = 350 dollars

Therefore, the museum tickets cost 350 dollars in total.

Answer:

I have attached as an image. Kindly check.

Step-by-step explanation:

Answer: 44\(\pi\)

Step-by-step explanation:

khan academy

The volume of a given cylinder is 113.04 cubic units.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a cylinder with base radius 2 units and height units.

We know that, the volume of a cylinder is πr²h.

Now, volume = 3.14×2²×9

= 113.04 cubic units

Therefore, the volume of a given cylinder is 113.04 cubic units.

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Answer:

I don't think so

Step-by-step explanation:

the length of the newspaper page=36cm

the advert will take 1/3 of the page=1/3*36=12

so the advert takes12 cm and he says it has to be 11 cm which is not right .

I hope this helps

You can rent time on computers at the local copy center for 35 minutes with $25.

To find out how much time you can rent for $25 at the local copy center, follow these steps:

1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.

So, you can rent time on computers at the local copy center for 35 minutes with $25.

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