Find the solution(s) to: LaTeX: \ln\left(x^2-30\right)=\ln\left(13x\right)ln ⁡ ( x 2 − 30 ) = ln ⁡ ( 13 x ) Check for extraneous solutions. Group of answer choices LaTeX: x=\ln15x = ln ⁡ 15 LaTeX: x=-2,\:x=15x = − 2 , x = 15 LaTeX: x=-2x = − 2 LaTeX: x=15x = 15

Answer: So the division between two persons is 1/6 and 1/2.

Step by step: First Person = 1*4/24= 4/24 = 1/6 (0.16)

Second Person = 3*4/24 = 12/24= 1/2 (0.5)

Answer: the division between two persons is 1/6 & 1/2.

Step-by-step explanation:

Just divide

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Based on the fact that the opposite sides are parallel and the diagonals are congruent, we can conclude that the parallelogram formed by the given vertices O, A, B, and C is indeed a rectangle.

To determine whether the parallelogram formed by the vertices O(0, 0), A(-4, 1), B(-3, 5), and C(1, 4) is a rectangle, we need to consider the properties of a rectangle.

A rectangle is a quadrilateral with four right angles (90 degrees each). We can examine the properties of the given parallelogram to determine if it satisfies these conditions.

First, we can calculate the slopes of the opposite sides of the parallelogram.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of AB and OC:

Slope of AB = (5 - 1) / (-3 - (-4)) = 4/1 = 4

Slope of OC = (4 - 0) / (1 - 0) = 4/1 = 4  

Since the slopes of the opposite sides AB and OC are equal, we can conclude that AB and OC are parallel.

Next, we can calculate the slopes of the other pair of opposite sides OA and BC:

Slope of OA = (1 - 0) / (-4 - 0) = 1/-4 = -1/4

Slope of BC = (4 - 5) / (1 - (-3)) = -1/4

Again, we find that the slopes of OA and BC are equal, meaning that OA and BC are parallel.

Since both pairs of opposite sides are parallel, this parallelogram satisfies one of the properties of a rectangle.

However, to confirm if it is indeed a rectangle, we also need to check if the diagonals are congruent (equal in length).

Let's calculate the lengths of the diagonals:

Length of diagonal \(AC = \sqrt{((1 - 0)^2 + (4 - 0)^2) }\)

\(= \sqrt{(1^2 + 4^2) }\)

= √17

Length of diagonal \(OB = \sqrt{((-3 - (-4))^2 + (5 - 1)^2) }\)

\(= \sqrt{(1^2 + 4^2) }\)

= √17.

Since the lengths of both diagonals AC and OB are equal, the parallelogram satisfies this additional property of a rectangle.

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Answer:

y = x - 7

Step-by-step explanation:

The equation can be found using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), you can use the formula: m = (change in y) / (change in x)

For the points (15, 8) and (16, 9), the change in y is 9 - 8 = 1 and the change in x is 16 - 15 = 1, so m = 1/1 = 1.

To find the y-intercept (b), you can use one of the points and the slope to solve for b. For example, using the point (15, 8), substitute x = 15 and y = 8 into the equation y = mx + b, and solve for b:

8 = 1 * 15 + b

8 = 15 + b

b = 8 - 15

b = -7

So, the equation from the relation is:

y = x + (-7)

y = x - 7

Answer: C and D are the correct answers

Step-by-step explanation:

Answer:

The total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Step-by-step explanation:

Circumference of ellipse = \(\pi(a+b)\)

Circumference of semi-ellipse = \(\frac{\pi(a+b)}{2}\)

we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.

So, \(a = \frac{6}{2}=3 , b = 2\)

Circumference of semi-ellipse =\(\frac{3.14(3+2)}{2}=7.85 feet\)

Distance from center =\(\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet\)

Hence the total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Answer:

The answer is -½.

✌ yeah it is ✌

Given:

Point P is the incenter of triangle HKM.

To find:

The measure of JP.

Solution:

In triangle MNP, using Pythagoras theorem, we  get

\(Hypotenuse^2=base^2+Perpendicular^2\)

\((MP)^2=(MN)^2+(NP)^2\)

\((25)^2=(24)^2+(NP)^2\)

\(625=576+(NP)^2\)

\(625-576=(NP)^2\)

\(49=(NP)^2\)

Taking square root on both sides, we get

\(\pm \sqrt{49}=NP\)

\(\pm 7=NP\)

Side cannot be negative. So,

\(NP=7\)

Point P is the incenter of triangle HKM.

\(JP=NP\)       [Incenter is equidistant from each side of triangle]

\(JP=7\)

Therefore, the value of JP is 7 units.

The time Billy should get up to be right on time for school is 6:52 am.

The formula to calculate the time Billy should get up to be right on time for school is as follows: Time Billy Should Get Up = School Start Time - (Time to Get Dressed + Time to Eat Breakfast + Time to Walk to School). In this case, the formula is: Time Billy Should Get Up = 8:35 am - (32 minutes + 13 minutes + 17 minutes). In order to solve this equation, first we must convert the minutes to hours. 32 minutes is equal to 0.53 hours and 13 minutes is equal to 0.22 hours. 17 minutes is equal to 0.28 hours. Thus, the formula is: Time Billy Should Get Up = 8:35 am - (0.53 hours + 0.22 hours + 0.28 hours). Now, we can solve for the time Billy should get up. 8:35 am minus 0.53 hours is 7:42 am. Then, 7:42 am minus 0.22 hours is 7:20 am. Finally, 7:20 am minus 0.28 hours is 6:52 am. Therefore, the time Billy should get up to be right on time for school is 6:52 am.

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 Therefore, Biren and Cemal get $(640 - $160) = $480. Let us find the share of Biren and Cemal in the ratio 15:9. Total ratio is 24. Share of Biren = (15/24) × $480 = $300  Share of Cemal = (9/24) × $480 = $180.

Therefore, Biren and Cemal receive $300 and $180 respectively.c) Aasha has $160 and she wants to buy books which costs $15. Therefore, she can buy a maximum of $160/$15 = 10.6 books.

Since she cannot buy a part of the book, she can buy a maximum of 10 books.d) Biren's share = 15/32 × 640 = $300Amount spent on clothes = 3/8 × $300 = $112.5

Amount spent on a computer = 1/3 × $300 = $100Left fraction = 1 - (3/8 + 1/3) = 1 - (9 + 8)/24= 1 - (17/24) = 7/24Therefore, Biren has 7/24 fraction of his share left. Answer:

So, the answer is:a) Aasha receives $160b) Biren and Cemal get $300 and $180 respectively.

c Aasha can buy a maximum of 10 books.d) Biren has 7/24 fraction of his share left.

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Answer:

so u have to shoe ur work right? so (-3,-1)=(-2,4-) there

Step-by-step explanation:

To generate a point, you plug in a number for x to get the corresponding y value.

If x = 0 for instance, then the y value is...

y = x^2 - 4

y = 0^2 - 4 ... x is replaced with 0

y = 0 - 4

y = -4

So x = 0 and y = -4 pair up to get the point (0,-4). This is the y intercept as the parabola crosses the y axis here. It turns out that this is also the vertex point as it is the lowest point on the parabola.

----------------

If x = 1, then,

y = x^2 - 4

y = 1^2 - 4

y = 1 - 4

y = -3

meaning (x,y) = (1,-3) is another point on this line.

----------------

Repeat for x = 2

y = x^2 - 4

y = 2^2 - 4

y = 4-4

y = 0

Since we got a y output of 0, we have found an x intercept located at (2,0). The other x intercept is (-2,0).

-------------------

The idea is to generate as many points as possible. Plot all of the points on the same xy coordinate grid. Then draw a curve through those points the best you can. You should get what you see in the diagram below. I used GeoGebra to make the graph. Desmos is another handy tool I recommend.

Note: the more points you generate, the more accurate the graph will be

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer: Here are three specific examples of public health problems that epidemiologists may investigate:

Obesity: Epidemiologists may investigate the causes and risk factors for obesity, as well as the prevalence and trends in obesity rates over time. They may also evaluate the effectiveness of interventions to prevent or treat obesity, such as diet and exercise programs, policy changes, or medical treatments.

Environmental exposures: Epidemiologists may investigate the health effects of exposure to environmental toxins, such as air pollution, lead, or pesticides. They may evaluate the risks associated with exposure to these toxins, identify populations that are particularly vulnerable, and assess the effectiveness of interventions to reduce exposure or mitigate health effects.

Injury prevention: Epidemiologists may investigate the causes and risk factors for injuries, such as motor vehicle crashes, falls, or firearm injuries. They may identify populations that are at higher risk for injuries, evaluate the effectiveness of injury prevention programs or policies, and develop strategies to reduce the incidence or severity of injuries.

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

27= 3 (3х - 6)

27 = 9x - 18

27 + 18 = 9x

45 = 9x

45/9 = x

5 = x

x = 5

The correct tests for a pairwise combination design of experiments are: Given 3 inputs: p1 with values v1 and v2; p2 with value v3, and p3 with values v4 and v5.

Pairwise testing is a popular black-box testing technique used for testing software applications. Pairwise testing is a software testing technique that is used to reduce the number of test cases while still ensuring that all combinations of input parameters are tested at least once. The correct tests for a pairwise combination design of experiments are : Test each input parameter individually.

Test every possible pair of input parameters. Test the interactions of three input parameters.

The technique of pairwise testing is a technique that involves testing every possible pair of input parameters in a system. When there are three or more input parameters, this technique may not be practical because it can lead to a large number of test cases. As a result, we can use the technique of pairwise combination design of experiments. Pairwise combination design of experiments is a technique that involves testing all possible pairs of input parameters. To be more specific, the correct tests for a pairwise combination design of experiments are: Test each input parameter individually. Test every possible pair of input parameters.

Test the interactions of three input parameters. Pairwise testing is a black-box testing technique that is particularly useful for testing software applications. It is based on the idea that most defects are caused by interactions between input parameters, rather than by individual parameters. By testing every possible pair of input parameters, the tester can identify and eliminate defects that are caused by these interactions. In addition, by using a pairwise combination design of experiments, the tester can reduce the number of test cases required to test all combinations of input parameters, thus saving time and resources.

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Answer:

50

Corresponding angles

The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.

Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.

We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.

All the other options are wrong because of this reason.

Therefore, option C is correct.

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Step-by-step explanation:

f(g(x)) simply means that you use the whole expression of g(x) as argument in f(x).

f(x) = 3x - 7/4

g(x) = 2x - 1

so,

f(g(x)) = 3(2x - 1) - 7/4 = 6x - 3 - 7/4

since 3 = 12/4, we get

f(g(x)) = 6x - 12/4 - 7/4 = 6x - 19/4

The sum of all the angles that are labeled in the given vertex is 294°

In a single vertex, the three angles around the vertex are given as 55°, 64°, and 175°

We have to find the sum of all the angles that are labeled in the given single vertex.

A vertex is a point two or more lines meets.

It is the corner of a geometrical shape.

Example:

A square has 4 corners so it has 4 vertexes.

A cube has 8 corners so it has 8 vertexes.

We will add all the different angles in the single vertex as shown in the figure below.

Let,

Angle A = 55°

Angle B = 64°

Angle C = 175°

The sum of all the angles that are labeled is:

= Angle A + Angle B + Angle C

= 55° + 64° + 175°

= 294°

The sum of all the angles that are labeled in the given vertex is 294°

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The correct formula to calculate inventory turnover is the first option:  Inventory turnover = Cost of goods sold / Average merchandise inventory

The correct formula to calculate inventory turnover is the first option: Inventory turnover = Cost of goods sold / Average merchandise inventory. Inventory turnover is a financial metric that measures how efficiently a company is managing its inventory.

It is calculated by dividing the cost of goods sold (COGS) by the average merchandise inventory. COGS represents the cost incurred by a company to produce or acquire the goods that are sold during a specific period. Average merchandise inventory is the average value of inventory held by the company over a certain time period.

By dividing COGS by average merchandise inventory, we can determine how many times the inventory is sold and replaced during that period, providing insight into inventory management efficiency.


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You can suggest that managers should avoid the quick-fix mentality that makes management by best-seller so tempting by implementing the following strategies:

1. Understand the Unique Nature of Your Business: Managers should take the time to understand the unique nature of their business. They should realize that what worked for another company may not work for their own company.

2. Avoid Short-Term Solutions: Managers should avoid short-term solutions that provide quick results. They should focus on long-term solutions that will benefit the organization in the long run.

3. Develop a Comprehensive Strategy: Managers should develop a comprehensive strategy that includes long-term goals and objectives. They should also have a plan in place to achieve those goals.

4. Invest in Employee Development: Managers should invest in employee development by providing training and development opportunities. This will help to build a strong workforce that is capable of handling complex challenges.

5. Encourage Collaboration: Managers should encourage collaboration among team members. This will help to create a culture of teamwork and cooperation.

6. Monitor Progress: Managers should monitor progress and adjust strategies as necessary. This will help to ensure that the organization is on track to achieving its goals.

By following these strategies, managers can avoid the quick-fix mentality that makes management by best-seller so tempting. They can focus on long-term solutions that will benefit the organization in the long run.

Hope this helped you...

Answer:

Sohan

Step-by-step explanation:

she was the one who made it faster to do the work!!

The reciprocal of the time it takes to do the work together is the sum of

the reciprocal of the time it takes to do the work individually.

Reasons

Let R represent the number of days it will take Rohan, S, the number of

days it would take Sohan, and M, the number of days it would take Mohan

to do the work alone, we have;

\(\displaystyle \frac{1}{30} = \mathbf{ \frac{1}{R} + \frac{1}{S}}\)...(1)

\(\displaystyle \frac{1}{24} = \mathbf{ \frac{1}{M} + \frac{1}{S}}\)...(2)

\(\displaystyle \mathbf{ \frac{1}{40}} = \frac{1}{R} + \frac{1}{M}\)...(3)

Subtract equation (1) from equation (2) and add the result to equation (3), we have;

\(\displaystyle \frac{1}{24} - \frac{1}{30} =\displaystyle \left( \frac{1}{M} + \frac{1}{S} \right) - \left(\frac{1}{R} + \frac{1}{S}\right) =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right)\)

\(\displaystyle \frac{1}{24} - \frac{1}{30} + \frac{1}{40} =\displaystyle \left( \frac{1}{M} - \frac{1}{R} \right) + \frac{1}{R} + \frac{1}{M} = \frac{2}{M}\)

\(\displaystyle \mathbf{\frac{1}{24} - \frac{1}{30} + \frac{1}{40}} = \frac{1}{30} = \frac{2}{M}\)

M = 2 × 30 = 60

\(\displaystyle \frac{1}{24} = \mathbf{\frac{1}{M} + \frac{1}{S}}\)

\(\displaystyle \frac{1}{24} = \frac{1}{60} + \frac{1}{S}\)

\(\displaystyle \frac{1}{24} - \frac{1}{60} =\frac{1}{40} = \frac{1}{S}\)

\(\displaystyle \frac{1}{S} = \frac{1}{40}\)

\(\displaystyle \frac{1}{40} = \frac{1}{R} + \frac{1}{M}\)

\(\displaystyle \frac{1}{40} = \mathbf{\frac{1}{R} + \frac{1}{60}}\)

\(\displaystyle \frac{1}{40} - \frac{1}{60} = \frac{1}{120} = \frac{1}{R}\)

Therefore;

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Answer: (0, 10) or 10

Step-by-step explanation:

plug 0 into y

(0) = 1/2x - 5

1/2x - 5 = 0

      + 5 + 5

1/2x = 5

* 2    * 2

x = 10

Function of a pencil: A pencil is a writing instrument used for creating marks on paper or other surfaces by applying graphite or a similar substance to leave a visible trace.

A pencil serves as a versatile tool for writing, drawing, and sketching. It consists of a cylindrical wooden casing that holds a graphite core, which is responsible for leaving marks on surfaces. The function of a pencil is to provide a convenient and easily controllable instrument for making various types of marks. Whether used for writing notes, solving mathematical equations, or creating intricate drawings, a pencil offers precision and flexibility to the user.

One of the key advantages of using a pencil is the ability to erase and correct mistakes. Unlike pens, which often leave permanent marks, pencils allow for erasure using an eraser located at the end of the instrument. This feature makes pencils ideal for tasks that require frequent revisions or adjustments.

Pencils are widely used in educational settings, offices, art studios, and everyday life. They are essential tools for students, professionals, artists, and individuals of all ages. Pencils are inexpensive, portable, and do not require any additional equipment to operate. Additionally, they come in various hardness grades, ranging from soft to hard, which allows users to adjust the darkness and texture of their marks.

In summary, the function of a pencil is to provide a reliable, versatile, and easily erasable tool for writing, drawing, and sketching on different surfaces.

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Answer:

1.2 x 10^8

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.