It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.

The required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression.
= x ² + 8x + 12 / x² - 2x -8
= (x + 6)(x + 2) / (x + 2)(x  - 4)

Since, if we put x = -2 and x = 4, the expression will we undefined.

And,
= x + 6 / x -4

Thus, the required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

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The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.

The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.

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Answer:

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]

Answer: z = 280

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.

The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be

z = kx

When x is 10, z has the value 140. It means that

140 = 10k

k = 140/10

k = 14

The equation becomes

z = 14x

the value of z when x = 20 is

z = 14 × 20

z = 280

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Vertex = (-5, -2)

Point = (-4, 2)

This is a vertical parabola the opens upwards.

The equation is

                             (x - h)² = 4p(y - k)

Substitution

                             (-4 + 5)² = 4p (2 + 2)

Simplification

                                      1² = 4p(4)

                                      1 = 16p

                                      p = 1/16

Equation of the parabola

                          (x + 5)² = 4/16(y + 2)

                          x² + 10x + 25 = 1/4y + 1/2

Conclusion

The coefficient of the squared expression is 1

Answer:

 22.19 feet

Step-by-step explanation:

You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

Using these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.

Referring to the attached diagram, we have ...

  CE = 8/sin(63°) ≈ 8.9786

  FC = 6/cos(63°) ≈ 13.2161

Then the total length of the ladder is ...

  FE = CE +FC

  FE = 8.9786 +13.2161 = 22.1947

The length of the ladder is about 22.19 feet.

Answer:

This is the volume of cube V = 729 [tex]in^{3}[/tex]

Step-by-step explanation:

Surface area of cube = 486 [tex]in^{2}[/tex]

Surface area of the cube is given by A = 6 × [tex]a^{2}[/tex]

⇒ 6 × [tex]a^{2}[/tex] = 486

⇒ [tex]a^{2}[/tex] = 81

⇒ a = 9 in

This is the value of side of the cube. so volume of the cube is given by

⇒ V = [tex]a^{3}[/tex]

Put the value of a in above formula w get,

⇒ V = [tex]9^{3}[/tex]

⇒ V = 729 [tex]in^{3}[/tex]

This is the volume of cube

To find the volume of a cube with a surface area of 486 in², calculate the side length using the formula A=6s², leading to a side length of 9 inches, and then calculate the volume as V=s³, resulting in 729 cubic inches.

The volume of a cube with a given surface area using the formula A=6s², where A is the surface area and s is the side length of the cube. First, find the side length by dividing the given surface area by 6, then take the square root. After finding the side length, calculate the volume using the formula V=s³.

Given the surface area A=486 in², the side length s can be found as follows:

Answer:

Each boy will get 25 marbles.

Step-by-step explanation:

Given:

William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.

Now, to write an expression using parentheses to find number of marbles each boy get.

Let the number of marbles each boy get be [tex]x.[/tex]

Total number of boys = 2.

Number of marbles first jar holds = 12.

                          Second jar holds = 21.

                        And third jar holds = 17.

As given, William shares marbles equally with his brother.

Now, we write the expression to find the number of marbles each boy get:

[tex]x=\frac{(12+21+17)}{2}[/tex]

[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]

[tex]x=6+10.5+8.5[/tex]

[tex]x=25.[/tex]

Therefore, each boy will get 25 marbles.

Answer:

The plant makes 34,802,178 ball bearings in a single day

Step-by-step explanation:

The total output of a plant in a 5-day week is 4335 pounds

Each ball bearing weighs 0.0113g

We are to calculate the number of ball bearings made per day

First, we ensure both mass are in the same unit

Now 1 pound =453.5924 grams

4335 pounds=453.5924 X 4335 =1966323.054 grams

Number of bearings made in a week therefore

= 1966323.054 /0.0113=174010889.7

≈174010890 (to the nearest whole number)

Since there are 5 days in a week of production,

Daily Production=174010890/5

=34802178

The plant makes 34,802,178 ball bearings in a single da

Answer:

I have a feeling its B

Step-by-step explanation:

Vicky's Gross Monthly Income for the job at Southside High School is $3708.33.

Gross income of an individual is the income he/she receives before deduction and taxes.

Given that,

Base salary per year = $43,600

Income for coaching JC softball = $900

Free life insurance coverage = $15,000

Health & dental or medical premiums = $78/month

Gross income is the income an employee receives before all the deductions.

Insurance premiums are deducted from the base salary. So it is not included in gross income.

Annual Gross income = $43,600 + $900 = $44,500

Monthly Gross Income = $44,500 / 12 = $3708.33

Hence the monthly gross income is $3708.33.

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Answer:

Option B is correct.

Stephanie should add Jim to her health care plan.

Step-by-step explanation:

Let's take the options one by one.

Option 1

If Jim's employers insure him and his wife.

Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.

It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.

Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09

Option 2

If Stephanie's employers insure both of them.

Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.

It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.

Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2

Option 3

If each of them does an insurance plan with their respective employers

Jim’s employer pays 42% of his $378 monthly premium.

Stephanie’s employer pays 35% of her $298 monthly premium

Jim would pay (0.58 × $378) for himself = $219.24

Stephanie would pay (0.65 × $298) for herself = $193.7

Total they would pay in this option = $219.24 + $193.7 = $412.94

Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.

Hope this Helps!!!

Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.

An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.

The correct answer is option B.  Stephanie should add Jim to her health care plan.

The evaluation of each and every option is as follows:

Option 1

If Jim and his wife are covered by Jim's employer's insurance.

Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.

Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.

Jim's payment = = $471.09

Option 2

If both of them are protected by Stephanie's company's insurance.

Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.

Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.

Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).

Option 3

If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.

Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.

For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24

Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.

Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.

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Answer:

36 π square feet

Step-by-step explanation:

so the formula for area of a circle is  πr^2

so the radius is 6, which we can just plug in

π(6)^2

36π

so option 3

Answer:

(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]

Step-by-step explanation:

If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]

Using Pythagoras,

Opposite=5, Hypotenuse =6, Adjacent=?

[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]

In the Second Quadrant,

[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]

(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]

[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]

Answer:

Each of these is based on the principle of difference of two squares where:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Step-by-step explanation:

1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]

[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]

2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]

[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]

3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]

[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]

4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]

[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]

Answer:

The bottom answer

Step-by-step explanation:

Answer:

B. [tex](1,-5)[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.

[tex]y=-7x+2...(1)[/tex]

[tex]y=9x-14...(2)[/tex]

To solve our given system, we will equate both equations as:

[tex]9x-14=-7x+2[/tex]

Combine like terms:

[tex]9x+7x-14+14=-7x+7x+2+14[/tex]

[tex]16x=16[/tex]

[tex]x=\frac{16}{16}=1[/tex]

Upon substituting [tex]x=1[/tex] in equation (1), we will get:

[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]

Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.

Answer:

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b

Step-by-step explanation:

Answer:

Therefore the shortest man of 65.6 cm was more extreme.

Step-by-step explanation:

A z-test is a statistic test. It is used to determine whether two population mean are different when the variances of the population are known and the sample size large.

[tex]z=\frac{x- \mu}{\sigma}[/tex]

z= the standarized z score

x = the height of sample

μ = mean  = 172.27 cm

σ = standard deviation = 8.82 cm

For tallest

x = 259

[tex]z= \frac{259-172.27}{8.82}[/tex]

  ≈9.83

For shortest

x= 65.6

[tex]z= \frac{65.6-172.27}{8.82}[/tex]

  ≈ - 12.09

The most extreme value has a z score that the furthest from 0.

Since -12.09 is further from 0 than 9.83.

Therefore the shortest man of 65.6 cm was more extreme.

Answer:

10.7°

Step-by-step explanation:

1 mile = 5280 feet

Tan(X) = 1000/5280 = 25/132

X = (tan^-1)(25/132)

X = 10.72444854

Answer:

Step-by-step explanation:

The movement of the forms a right angle triangle with the ground. The vertical distance which the plane moves represents the opposite side of the right angle triangle. The horizontal distance covered by the plane represents the adjacent side of the right angle triangle.

1 mile = 5280 feet

To determine the angle of elevation, θ, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan θ = 1000/5280 = 0.189

θ = Tan^-1(0.189)

θ = 10.7°

Answer: it will take 1.8 hours

Step-by-step explanation:

The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes

t = k/s

The journey takes 1.5 h when the average speed is 54 miles per hour. This means that

1.5 = k/54

k = 54 × 1.5 = 81

The equation becomes

t = 81/s

Therefore, when the average speed is 45 miles per hour, the time taken would be

t = 81/45

t = 1.8

Answer:

24p8 - 36p6 + 36p2 = 48p

Step-by-step explanation:

I hope this helps!

Answer: last option.

Step-by-step explanation:

There are several transformations for a function f(x). Some of them are shown below:

1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.

2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.

3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.

4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.

In this case you have the following function:

[tex]h(x)=log_6x[/tex]

And the function m(x) is obtained by transformating the function h(x). This function is:

[tex]m(x)=log_6(x+3)[/tex]

Then, based on the transformatios shown before, you can identify that:

[tex]m(x)=h(x+3)[/tex]

Therefore, you can determine that you could graph the function  [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.

Answer: The answer should be C!

Step-by-step explanation:

I took the quiz

The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).

The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.

In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.

This is so because it doesn't fall under the shaded area.

This is due to the broken horizontal line; y < 3.

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Answer:

Step-by-step explanation:

Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14

They bought a movie for $12. The amount that they have left is

14 - 12 = $2

They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is

2/1 = 2

If they split the containers evenly between themselves, then each person would get

2/2 = 1 container of fruit salad

Answer:

PR² = PQ² + QR²

Step-by-step explanation:

Since the triangle PQR is a right triangle, according Pythagorean theorem:

So:

as

Answer:

PR² = PQ² + QR²

Step-by-step explanation:

When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.

To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:

So, the result of the subtraction is 12a^2 - 9a - 36.

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Answer:

Therefore the length of aluminum surrounding the pool is 88 feet.

Step-by-step explanation:

Circle:

Given that the circular swimming pool has walls made of aluminum.

To find out the length of the of aluminum, we need to find out the circumference of the pool.

The radius of the circular pool is = 14 feet.

Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]

                                                                       [tex]=2\times \frac{22}{7} \times 14[/tex]  feet

                                                                     =88 feet

Therefore the length of aluminum surrounding the pool is 88 feet.

Answer:

Step-by-step explanation:

#using java

Double result;

public Double half(Double number){

return number/2;

}

result=half(number);

Final answer:

The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.

Explanation:

The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.

Example of a half function in C++:

double half(double number) {
   return number / 2.0;
}

This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.

To use this function, you would write the following code in your main program:

double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0

Understanding the code:

When invoked, the function will return half of the input value, effectively operating as number / 2.0.

Sure, what do you need help finding?

Answer:

to find a percentage of a number u multiply/divide 100

Step-by-step explanation:

[tex]y = - 2x + 3[/tex]

The slope of the above line = -2

slope of the line perpendicular to the above line = 1/2

If it passes through point (4,-3) , it's equation

[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]

[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]

[tex]2(y + 3) = x - 4[/tex]

[tex]2y + 6 = x - 4[/tex]

[tex]x - 4 - 2y - 6 = 0[/tex]

[tex]x - 2y - 10 = 0[/tex]

A = 1, B = -2 and C = -10

A+B+C= 1+(-2)+(-10)

= 1-2-10

= 1-12

= -11

Answer:

A = 1, B = -2 and C = -10

Step-by-step explanation: