What are the coordinates of the point on the directed line segment from (1, 2)to(6,7) that partitions the segment into a ratio of 2 to 3?

The solution to the equation log_6 x + log_6 3 = log_6 (x+1) is x = 1/2.

Explain:

We can reduce the complexity of the left side of the equation by using the logarithmic identity log a + log b = log (ab):

Log6 x plus Log6 3 equals Log6 (3x)

When we add this to the initial equation, we obtain:

Log6 (3x) equals Log6 (x+1).

Because logarithms have the one-to-one property, we can drop the logarithm on both sides to get the following results:

3x = x + 1

When we simplify this equation, we obtain:

2x = 1

x = 1/2

As a result, x = 1/2 is the answer to the equation log 6 x + log 6 3 = log 6 (x+1).

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For the graph of given function, At x = 2, the graph crosses x axis At x = - 6, the graph touches x axis, At x = - 12, the graph crosses x axis.

What's an Equation?

The description of an equation in algebra is a fine statement proving the equivalency of two fine expressions.

The two equations 3x 5 and 14 are separated by the" equal" sign in the equation 3x 5 = 14, for illustration.

In mathematics, an equation is a relationship between two expressions that's equal on both sides of the equal to subscribe. An equation is commodity like 3y = 16.

Equation of a function f( x) = ( x − 2) 3( x 6) 2( x 12)

Lets find out the roots and dissect

lets set each factor = 0 and break for x

Exponent in each factor tell us the multifariousness. Using multifariousness we check whether crosses or traces x axis

When multifariousness is odd also graph crosses x axis.

when multifariousness is indeed also graph touches x axis.

f(x) = (x-2)^3(x+6)^6(x+12)

      ⇒(x-2)^3

      ⇒x-2 = 0

      ⇒ x = 2

Root is x = 2 with multifariousness 3. 3 is odd

At x = 2, the graph crosses x axis

⇒ (x+6)^2

⇒ (x+6)=0

⇒ x = -6

At x = - 6, multifariousness is 2 that's indeed.

At x = - 6, the graph touches x axis

x + 12 = 0

x = -12

x = - 12 with multifariousness 1. 1 is odd

At x = - 12, the graph crosses x axis.

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Answer:

Below

Step-by-step explanation:

L X W is area of rectangle ...this figure can be viewed as a rectangle on top of a rectangle

top rectangle is 3x-2   wide   and   (2x+5) - (3x-2)  length

   area =  (3x-2)(  (2x+5) - (3x-2) )

             = (3x-2) ( -x + 7)  = - 3x^2 + 23x -14     units^2

The bottom is then    (3x-2 + 2) * (3x-2)

                             area = (3x)(3x-2) = 9x^2 - 6x  units^2

Add the two areas together      (-3x^2+23x-14) + (9x^2 -6x)

                                                     6x^2 + 17x -14    and this = 25 cm^2  (given)

      6x^2 + 17x -14 = 25

      6x^2 + 17x - 39 = 0   Use Quadratic Formula to find x = 1.5

then find the longest side   using this value of x

        3x-2 + 2  = 4.5 cm

    2x+5 = 8  cm    <=====longest side

Based on the information provided, the storage space that will be required for 75 is 1,687 cubic feet in total.

To begin, let's determine the storage space for a single crate and to do this, let's calculate the volume:

Volume: Lenght x height x width

Volume: 3 x 2.5 x 3 = 22.5 cubic feet

Now, let's calculate the space for 75 crates:

volume of one crate x 75 crates

22.5 x 75 = 1,687 cubic feet

Based on this, it can be concluded that 75 crates will occupy 1,687 cubic feet.

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1. The function for this problem is defined as follows: y = 2x + 3.

2. The numeric value of the function at x = 2 is given as follows: y = 7.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define a function as follows:

y = 2x + 3.

At x = 2, the numeric value is found replacing the lone instance of x by 2, hence:

y = 2(2) + 3

y = 7.

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Exponential growth is a pattern of data that shows a rapid increase over time, while exponential decay is a pattern of data that shows a rapid decrease over time.

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The fundamental distinction between the two is that in an exponential decay relationship, the output values rise quickly as the input value rises, whereas in an exponential growth relationship, the output rises noticeably faster as the input value rises.

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At a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

The rectangle's area in square meters The area's width and length should be measured in feet. To calculate area, multiply your length by your width. Use our length converter to convert your measures if they aren't already in feet.

Area is length times breadth, or 12 feet by 16 feet, or 192 square feet. The cost of the carpet is $10 per square foot. By dividing the square footage of the room by the price per square foot, we can get the overall cost to carpet it.

Total cost is equal to Area. Cost per square foot is $1920 or 192 square feet (around 18 m2) times $10 per square foot.

Therefore, at a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

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Answer:

100

Step-by-step explanation:

I hate that I have to use 20 characterz

The number of hours that the prices of the two stocks be the​ same will be 4 hours.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Let 'x' be the number of hours and 'y' be the price of stocks. Then the equations are written as,

y = 13.52 + 0.05x           ...1

y = 14.27 - 0.14x             ...2

From equations 1 and 2, then we have

13.52 + 0.05x = 14.27 - 0.14x

0.14x + 0.05x = 14.27 - 13.52

0.19x = 0.75

x = 3.947 ≈ 4 hours

The number of hours that the prices of the two stocks be the​ same will be 4 hours.

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Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.

For example, if X = 2 and y = -7, then the equation becomes:

2 + (-7) = -5

-5 = -5

Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.

Step-by-step explanation:

Using the ratio formula the unknown numbers are found to be 6 and 9.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The original ratio value is 2 : 3.

Three is added to the ratio.

The new ratio value is 3 : 4.

Let the unknown numbers be 2x and 3x.

The equation will be -

2x + 3 / 3x + 3 = 3/4

Solve the equation -

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

8x + 12 = 9x + 9

8x - 9x = 9 - 12

-x = -3

x = 3

Substitute the value of x in the unknown numbers -

2x = 2(3) = 6

3x = 3(3) = 9

Therefore, the numbers are 6 and 9.

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The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.

Probability determines the likelihood of an event occurring.

P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.  

total number of teacher is 10

so number of ways total 10 teacher seat = 10!/(6!*4!)

= 210

and

the number of ways  the math majors are seated together

= 6

probability = 6/210 = 0.028

the number of ways the math majors are seated together and the computer science majors are seated together

= 1

probability = 1/210

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The range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.

What is Inequality?

An inequality is a mathematical statement that compares two values, expressing that they are not necessarily equal. It is often represented using one of the following symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

For example, "x > 5" is an inequality that states that the value of x is greater than 5. Similarly, "y ≤ 10" is an inequality that states that the value of y is less than or equal to 10.

Inequalities are commonly used in algebra and other areas of mathematics, as well as in many real-world applications, to express relationships between values that are not necessarily equal.

The inequality |t − 56| ≤ 3 represents all temperatures within 3 degrees of 56°F, including both those above and below 56°F.

We can represent this range graphically as a horizontal line segment centered at 56°F with a length of 6 units (3 units on either side of 56°F).

Thus, the range of possible temperatures in Steffi's storage room is between 53°F and 59°F, inclusive.

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As the university is sending out questionnaires, the data collection method the university is using is a survey

The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data. 

Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.

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Answer:

The down payment that Jordan made on the house was $300,000 x 10% = $30,000. So, he financed $300,000 - $30,000 = $270,000.

where

M = monthly payment

P = loan amount ($270,000)

r = monthly interest rate (3% / 12 months = 0.003)

n = number of payments (30 years x 12 months/year = 360)

This comes out to a monthly payment of approximately $1,173.38.

To simplify

The loan amount is- $270,000

Her monthly payment will be- $1,173.38

The amount of interest she will pay is- $8,100

When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.

To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.

Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.

The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.

Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.

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Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.

A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.

It is given that a phone sells for $230. It is now on sale for 30% off.

Now, Cost price = $230

sale percentage = 30%

so, the sale price = [tex]230 \times 30\%\\[/tex]

or  [tex]230 \times \frac{30}{100}[/tex] = $69

therefore, the money April will save if she buys the phone on sale is $69.

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Answer:

(x + 7)(x - 3) = 75 square feet.

Step-by-step explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.

Answer:

20.2%

Step-by-step explanation:

he relative difference between two values can be calculated using the formula:

Relative Difference = (|V1 - V2| / ((V1 + V2) / 2)) * 100%

where V1 is the first value and V2 is the second value.

For the U.S. per capita consumption of beef, we have V1 = 67.8 pounds in 2000 and V2 = 55.4 pounds in 2016. Plugging these values into the formula, we get:

Relative Difference = (|67.8 - 55.4| / ((67.8 + 55.4) / 2)) * 100%

Relative Difference = (12.4 / 61.6) * 100%

Relative Difference = 0.202 * 100%

Relative Difference = 20.2%

So the relative difference between the U.S. per capita consumption of beef in 2000 and 2016 is 20.2%.

According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.

To calculate how many hours we are going to have the cruising speed on we must carry out the following process:

To calculate the minimum we must subtract 35 from 215 and then divide by the speed:

So the minimum hours would be 3 hours.

On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:

So the maximum time would be 4.1 hours.

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Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.

Step-by-step explanation:

He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

A salesman earns a commission 40%

He sold yesterday 5 watches for $60 each

and, 4 watches for $40 each.

We have to find the how much he earn commission?

Now, According to the question:

Price of 5 watches = 60.00 × 5 = $300

4 watches = $40.00 each

Price of 4 watches = 40.00 × 4 = $160

Total sales made = 300 + 160 = $460

His commission is 40% of the sales = 40% × 460

                                                       = 0.40 × 460 = $184

Hence, He earns $184 in commission.

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the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.

To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:

dv/dt = -k*v

where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.

We can solve this differential equation to obtain the velocity of the boat as a function of time:

v(t) = v(0) * e^(-k*t)

where "v(0)" is the initial velocity of the boat (40 ft/sec).

Using the given information, we can set up two equations:

v(10) = 20 (velocity after 10 sec)

v(0) = 40 (initial velocity)

Plugging these values into the equation, we get:

20 = 40 * e^(-10k)

Solving for "k", we get:

k = ln(2)/10

Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:

d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]

Plugging in the values, we get:

d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft

To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.

Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.

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Complete question is:

Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?

Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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