Simplify (5n4)−3. Assume n ≠ 0.

The potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

The product of the log rule says that the sum of number of logarithm functions is equal to the log function of product of all the numbers, given  that base is same.

The given logarithmic function in the problem is,

\(\log_6x+\log(6x+5)=2\)

Using the product rule of logarithmic function, the above equation can be written as,

\(\log_6(x\times(x+5))=2\\\log_6(x^2+5x))=2\)

Using the equality rule of logarithmic function, the above equation can be written as,

\(x^2+5x=6^2\\x^2+5x=36\)

Take all the terms one side of the equation as,

\(x^2+5x-36=0\)

Find the factors of above equation using the split the middle term method as,

\(x^2+9x-4x-36=0\\x(x+9)-4(x+9)=0\\(x+9)(x-4)=0\)

By equating these factor to the zero one by one, we get the potential solution as -9 and 4.

Thus, the potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

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Answer:

-9 and 4

Step-by-step explanation:

Did it on edge :)

To solve this system, we can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation to solve for the other variable.

Using the second equation, we can solve for y:

y = x - 7

Next, we can substitute this expression for y in the first equation:

y = 3x - 1

x - 7 = 3x - 1

Now we can solve for x by simplifying the equation:

x - 3x = -1 + 7

-2x = 6

x = -3

Now that we have solved for x, we can substitute this value back into either of the original equations to solve for y. Let's use the second equation:

y = x - 7

y = -3 - 7

y = -10

Therefore, the solution to the system is (-3, -10).

Answer:

will you go out with me

Step-by-step explanation:

i will make pumpkin pie

Therefore, the value of q(α) is 0.

Let p(x) = x³ + ax² + bx + c be a polynomials with distinct roots α, β, and γ, where α, β, and γ are real numbers and α, β, and γ are also roots of another polynomial q(x)

.To find: the value of q(α).

Given:p(x) = x³ + ax² + bx + c

has three distinct roots α, β, and γ such that α, β, and γ are real numbers and α, β, and γ are also roots of q(x).

The root of p(x) are:

α, β, and γThe root of q(x)

are:α, β, and γ

Since α, β, and γ are the roots of q(x),

we have:q(x) = (x - α) (x - β) (x - γ) ... (1)

Let's evaluate q(α) using equation (1)

q(α) = (α - α) (α - β) (α - γ)q(α) = 0

(Since α, β, and γ are distinct)

Therefore, the value of q(α) is 0. Hence, the correct option is (D).

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Answer:

c is the answer

Step-by-step explanation:

Answer:

D. 400 cu ft/

Step-by-step explanation:

1620 - 1180

= 440.

Answer:

c

Step-by-step explanation:

C=2πr=2·π·2≈12.56637

Answer:

25.14

Step-by-step explanation:

formula is 2πr^2.

Given,

The diagram of the angles is shown above in the question.

Required

The incorrect statement for the angles.

The angles are of 90 degree as it is given.

So, statement b, c and d is correct.

Here, angles are not perpendicular, sides can be perpenicular to each other.

Hence, statement a is incorrect.

Answer:

B

Step-by-step explanation:

The answer is B because we can estimate by seeing that: 3 x 3 = 9, so henceforth the answer must be between 3 and 4, so it must be B.

\(4x=8\\\frac{4x}{4} =\frac{8}{4} \\x=2\)

simplified it is x=2

Answer:

x = 2

Step-by-step explanation:

4 x 2 = 8

Answer:

y = 28

Step-by-step explanation:

Given that y varies directly as x and inversely as z then the equation relating them is

y = \(\frac{kx}{z}\) ← k is the constant of variation

To find k use the condition y = 4 when x = 2 and z = 7, then

4 = \(\frac{2k}{7}\) ( multiply both sides by 7 )

28 = 2k ( divide both sides by 2 )

14 = k

y = \(\frac{14x}{z}\) ← equation of variation

When x = 6 and z = 3 , then

y = \(\frac{14(6)}{3}\) = 14 × 2 = 28

To find the equation of the line, we need to figure out the slope and y-intercept.

To find the y-intercept, look at the number where the line intersects the y-axis. The number is 5. The equation so far is y = ?x + 5.

We still didn't figure out the slope yet. To figure out the slope, pick two points. Use the rise over run method. It is in the image below. The line is going up to the left, so the slope will be negative. Now we know the slope is -1/3. The equation now that we figured out the slope is y = -1/3x + 5.

I hope this helps you! Let me know if I got something wrong.

The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let \(Wi\) and \(Li\) denote whether the game '\(i\)' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [\(W1W2\)] + P [\(W1L2W3\)] + P [\(L1W2W3\)]

        = \(p(1-p)\) + \(p3\) + \(p(1-p){2}\)

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

Answer:

Company "A"

Step-by-step explanation:

its the highest line on the graph from the 300 point.

Answer:

Amount of grass needed (In square meter) = 34 meter²

Step-by-step explanation:

Divide given shape into rectangle and trapezium

Given:

Width of rectangle = 2 m

Length of rectangle = 5 m

Height of parallelogram = 9 - 5 = 4 m

Base of parallelogram = 10 m

Opposite site of parallelogram = 2 m

Find:

Amount of grass needed (In square meter)

Computation:

Amount of grass needed (In square meter) = Area of rectangle + Area of parallelogram

Amount of grass needed (In square meter) = (l x b) + (1/2)(sum of parallelogram)(height)

Amount of grass needed (In square meter) = (5 x 2) + (1/2)(2 + 10)(4)

Amount of grass needed (In square meter) = 10 + (1/2)(12)(4)

Amount of grass needed (In square meter) = 10 + 24

Amount of grass needed (In square meter) = 34 meter²

Answer:

The variable is usually the unknown part of the whole.

The equation that represents this parabola in standard form is y = x²

From the question, we have the following parameters that can be used in our computation:

(0,0) , (1,1) and (-1, 1)

A parabola in standard form is represented as

y = ax² + bx + c

Using the points, we have

(0)²a + (0)b + c = 0

c = 0

Next, we have

(1)²a + (1)b + 0 = 1

a + b = 1

(-1)²a + (-1)b + 0 = 1

a - b = 1

Add the equations

2a = 2

a = 1

So, we have

1 + b = 1

b = 0

This means that the equation is y = x²

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Question

Given three points that lie on the parabola, find the equation that represents this parabola in standard form

(0,0) , (1,1) and (-1, 1)

The statement given is False. Any segment with both endpoints on the circle is not the radius of the circle. It is called chord.

The radius of the circle is the line segment with one endpoint at the centre of the circle and another endpoint on the circle.

If both endpoints of the line segment are on the circle, it is called a chord.

A special case of a chord is called diameter. If both endpoints of the line segment lie on the circle and the line passes through the centre of the circle, the line segment is called diameter of the circle.

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Answer:

ion kno gang ask a teacher

So, your first move should be to remove a number of sticks that is less than or equal to 21, but also leaves your opponent with 4 sticks or more. This will set you up for success in the game.

The first few numbers in the Fibonacci sequence are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. To determine the number of sticks a player can remove, they look at the previous two numbers in the sequence and add them together. For example, if the previous two numbers were 3 and 5, the player could remove 8 sticks.

To start, we need to find the largest number in the Fibonacci sequence that is less than or equal to 500. Looking at the sequence, we see that 21 is the largest number that fits this criteria. Therefore, on your first move, you can remove up to 21 sticks from the pile.

But should you remove all 21 sticks? Not necessarily. In Fibonacci nim, it is often advantageous to leave your opponent with a certain number of sticks that will force them to make a move that is disadvantageous. One such number is 4. If you can leave your opponent with 4 sticks, they will be forced to remove all 4 and you willbe left with a favorable position.

So, your first move should be to remove a number of sticks that is less than or equal to 21, but also leaves your opponent with 4 sticks or more. This will set you up for success in the game.

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Answer:

t = 5

Step-by-step explanation:

20t + 5 + 15t = 180

35t + 5 = 180

35t = 175

t = 5

Hopefully this helps!

Brainliest please?

Answer:

264

Step-by-step explanation:

220-22=198

198/3=66 (which is 1/4)

66x4=264

Rolle's theorem:

If a function \(f\) is continuous on the closed interval \( [a, b] \) and differentiable on the open interval \((a,b)\) such that \(f(a) = f(b)\), then [tex)f′(x) = 0\) for some \(x\) with \( a \leq x \leq b\).

Tangent:

A tangent is parallel to the x-axis if the slope of the tangent is 0. So, using Rolle's theorem, if we consider \(x=-\pi/2\) and \(x=\pi/2\), then \(f(-\pi/2)=f(\pi/2)=-1\).

Since \(f(x)\) is continuous on \([-\pi/2, \pi/2]\) and differentiable on \((-\pi/2, \pi/2)\), \(f'(x)=0\) for some \(-\pi/2 \leq x \leq \pi/2\), and thus there is a point in this interval which is parallel to the x-axis.

The distance from the point (2, -4, 1) to the line defined by x = 3 + t, y = -3 + 4t, z = -5 + 3t is √41.

To find the distance from a point to a line, we can use the formula of the distance between a point and a line in 3D space. Let P be the given point (2, -4, 1) and L be the line defined by x = 3 + t, y = -3 + 4t, z = -5 + 3t.

The formula for the distance between a point (x0, y0, z0) and a line in vector form (x = a + mt, y = b + nt, z = c + pt) is given by:

Distance = |(P - L) × v| / |v|,

where P - L is the vector from any point on the line to the given point P, v is the direction vector of the line, and × represents the cross product.

Substituting the given values, we have:

P - L = (2 - (3 + t), -4 - (-3 + 4t), 1 - (-5 + 3t)) = (-1 - t, -1 - 4t, 6 - 3t),

v = (1, 4, 3).

Calculating the cross product:

(P - L) × v = (-1 - t, -1 - 4t, 6 - 3t) × (1, 4, 3)

           = (-1 - 4t - 12 + 3t, -3 + t - 18 - 3t, -4 + 4 + t + 4)

           = (-13 - t, -21 - 2t, t).

Taking the magnitude of (P - L) × v:

|(P - L) × v| = √((-13 - t)^2 + (-21 - 2t)² + t²)

             = √(169 + 26t + t² + 441 + 84t + 4t² + t²)

             = √(6t² + 110t + 610).

Calculating the magnitude of v:

|v| = √(1²+ 4² + 3²) = √26.

Finally, the distance is given by:

Distance = |(P - L) × v| / |v|

        = √(6t² + 110t + 610) / √26

        = √(6/26)(t² + (110/6)t + 610/6)

        = √(3/13)(t² + (55/3)t + 305/3).

Since t can take any value along the line, the expression inside the square root represents a quadratic equation. The distance is therefore √41.

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Based on Amy's survey, 632 people are most likely to have never visited the library in the summer.

You need to determine the percentage of people who did not visit the library from Amy's survey in order to determine the number of people who were most likely not to do so.

Male percentage:                                          Female percentage:

= 14 / 25                                                               =17 / 25                                                                                                                  

= 56 %                                                                  = 68%

The number of men:                                          Female percentage:

= 56 percent x 400                                               = 68% of 600

= 224 men                                                            = 408 females      

224 plus 408 equals 632 people.

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(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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The researcher could use statistical analysis to compare the proportion of accidents that occur among older employees (e.g., those over 50 years old).

The proportion that occurs among younger employees (e.g., those under 30 years old).

If the proportions are similar, then the data would suggest that older and younger employees are equally prone to having accidents.

To determine whether older and younger employees are equally prone to having accidents.

The researcher at the light manufacturing plant would need to analyze the data collected on accident types and age of the employees involved in the accidents.

If the proportions are different, then the data would suggest that one age group is more prone to accidents than the other.

It is important to note that other factors, such as job type, experience level, and physical condition, could also influence the likelihood of accidents. Therefore, the researcher should also consider these factors when analyzing the data.

to ascertain if employees of different ages are similarly prone to accidents.

The light manufacturing plant researcher would have to examine the information gathered on accident kinds and the ages of the personnel involved in the incidents.

The data would indicate that one age group is more prone to accidents than the other if the proportions were different.

It is significant to remember that additional elements, such as work kind, amount of expertise, and physical condition, may also affect the chance of mishaps.

As a result, when the researcher analyses the data, they should also take these things into account.

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By collecting data, calculating and comparing percentages, and analyzing accident types, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant for random sample.

We will look at the data from the researcher's investigation at the light manufacturing plant. They classified a random sample of accidents by type and age of the employee.

Step 1: Collect data on the total number of accidents involving older and younger employees, as well as the types of accidents they were involved in.

Step 2: Calculate the percentage of accidents involving older employees and the percentage involving younger employees.

Step 3: Compare the percentages and determine if there is a significant difference between the accident rates for older and younger employees.

Step 4: Analyze the types of accidents each group is involved in to see if there are any patterns or trends that may suggest a higher risk for either age group.

By following these steps, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant.

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Answer: C, 7s + 3t and 3t + 7s.

Step-by-step explanation: Nothing is changing between the expressions except for their position. In addition, position does not matter though, so these two are the SAME EXPRESSION