Derive by means of the direct formulas the following functions

The required distance c between the point of marching formation is given as C = √61.

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,

The distance formula is given as,

C = √[[x₂ - x₁]² + [y₂+ - y₁]²]

Put the given point in the above equation,
C = √[[3 + 2₁]² + [4 + 2]²]
C = √25+36
C = √61

Thus, the required distance c between the point of marching formation is given as C = √61.

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Answer:

a

Step-by-step explanation:

|x|<a means -a<x<a

or x lies between -3 and 3

A function transformation is one that converts one function or graph into another, usually related function or graph.

Given function, f(x)

Transformed function is y = -3f(x + 2)

To find each points transformed function:

        After transformation the function becomes,

        y = -3(-4 + 2)

        y = -3 x -2

        y = 6

        Then the transformed points are (-4 , 6).

        After transformation the function becomes,

        y = -3(-2 + 2)

        y = 0

        Then the transformed points are (-2 , 0).

       After transformation the function becomes,

        y = -3(0 + 2)

        y = -3 x 2

        y = -6

        Then the transformed points are (0 , -6).

        y = -3(1 + 2)

        y = -3 x 3

        y = -9

        Then the transformed points are (1 , -9).

        y = -3(3 + 2)

        y = -3 x 5

        y = -15

        Then the transformed points are (1 , -15).

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The solution to the given linear equation is t = 14

From the question, we are to solve the given linear equation.

From the given information,

The given linear equation is

t - 5 = 9

To solve the equation, we will use the addition property of equality

Solving the equation

t - 5 = 9

Add 5 to both sides of the equation

t - 5 + 5 = 9 + 5

Simplify

t = 14

Hence, the solution is t = 14

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Answer: 300 ft

Step-by-step Explanation: You start by multiplying 4 by 3 to get 12 because each second is split into 3 parts. From there you just have to multiply 12 by 25 for foot per second to get 300.

Answer:

a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.

Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.

Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.

It means that the store will sell a maximum number of batteries when the price is at $5.00

And the maximum daily revenue will be $5 * 700 = $3500.

So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.

The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

The zeroes of the equation are the points at which the function crosses the x and y-axis.

The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)

The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)

Step-by-step explanation:

The mode is the most common value in a set of data and is typically used for categorical data such as eye color.

The mean and median, on the other hand, are measures of central tendency used for numerical data.

Since eye color is a categorical variable, the mode would be the appropriate measure to use to determine the most common eye color in Andrew's survey.

It can be seen that the mean, median, and mode are the most common measures of central tendency for a set of data, and typically, you use the mode with categorical, ordinal, and discrete data and this is the appropriate data collection that Andrew should use to find the most common eye color and not mean or median.

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Answer: y = 15

Step-by-step explanation:

Subtract both sides by 3

3 + y = 18

y = 15

Answer: Lauren's unit rate is 2.95 Miles per hour (MPH)

Step-by-step explanation:

divide the distance Lauren traveled by the time it took to travel said distance

112/38 hours=2.95 mph

Answer:

2.95 miles/hour or 2.95mph

Step-by-step explanation:

112/38 = 2.94736842 ⇒ 2.95 miles/hour

The rule for the graph changes form of the function is A)The graph is reflected across the x-axis.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Function is a relation that connects members of one set in a certain way to those of another set. Formally speaking, a function from to is an object such that each is specifically linked to an object. Therefore, a function is a many-to-one (or occasionally, one-to-one) relation.

Here Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let   h(x) = f(x)-c Shifting downward c units yields this graph of h from the graph of f.

We know that if the function reflected over x-axis then

g(x) = -f(x)

Here the given function f(x) = [tex]x^2-4[/tex] then reflection over x-axis then

=> g(x) = -f(x)

=> g(x) =-( [tex]x^2-4[/tex])

=> g(x) = [tex]-x^2+4[/tex]

Hence the correct option is A)The graph is reflected across the x-axis.

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Answer:

[tex] {h \: }^{2} + 6h + 10[/tex]

Answer:

$250

Step-by-step explanation:

because we have to do 5,000 of 5% = 250 in sale's tax or interest.

The solution is, $250 is the amount of interest.

Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.

here, we have,

Explanation:

given that,

A $5000 loan at 5% dated July 5 is due to be paid on November 10.

Since the borrower is to pay 5% of the money by  November 10(Due time)

so, we get,

5% of the principal is simply

(5/100)* 5000

= $250

Hence, The solution is, $250 is the amount of interest.

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A. The slope of the linear function is given as follows: m = 2.

B. The slope means that the number of races increases by two when the number of track meets increases by one.

C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.

D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The input and output variables for this problem are given as follows:

Two points in the function are given as follows:

(0,5) and (1,7).

Hence the slope and the intercept are given as follows:

Meaning that the function is defined as follows:

y = 2x + 5.

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Answer:

[tex]3.5\% = \frac{3.5}{100} = \frac{35}{10} (fraction) = 3 \frac{5}{10} (mixed)[/tex]

Answer:

Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.

Answer: To solve these simultaneous equations, we can substitute one equation into the other.

4x-3 = 3x + y.

3x+y =2y+5x-12

If we substitute the first equation into the second equation, we get:

3(4x-3) + y = 2y+5x-12

12x -9 + y = 2y+5x-12

Now we can solve the system of equations by isolating one of the variables and then substituting it back in one of the equations.

12x - 9 + y = 2y + 5x - 12

y = -9 + 2y + 5x -12

y = 2y + 5x -21

y - 2y = 5x -21 -9

-y = 5x -30

y = -5x + 30

Now we can substitute the value of y back into one of the original equations, we have:

4x-3 = 3x + (-5x + 30)

4x-3 = -2x + 30

4x-3+2x = 30

6x -3 = 30

6x = 33

x = 5.5

Now we can substitute the value of x back into one of the original equations to find the value of y:

4x -3 = 3x + y

4(5.5) -3 = 3(5.5) + y

22 - 3 = 16.5 + y

19 = 16.5 + y

y = 2.5

So the solution to the system of equations is x = 5.5 and y = 2.5.

Step-by-step explanation:

It is possible to find out the number of people who attended the event. Hence option B is correct.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.

Form about information, calculate the number of forks.

A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.

Form about information, calculate the number of spoons.

Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.

Form these we can get information that how many spoon used.

Since each guest will receive 2 forks and 3 spoons at the beginning of the event.

Using this information we can get the number of people who attend the event.

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If Margie has 64 rectangular steppingstones to arrange in an array in her backyard. The number of arrays that  Margie can  make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.

Given data:

Rectangular steppingstones to arrange in an array =64

In order to determine the number of arrays we have to find the number that will give us 64 when multiply.

The number that will gives us 64 as the answer when multiply are:

2 × 32 = 64

4 ×16 = 64

8 × 8 = 64

The arrays are 3 which are:

2 × 32

4 ×16

8 × 8

Therefore we can conclude that the  number of array that  Margie can  make with the 64 steppingstones is: 2 × 32, 4 ×16, 8 × 8.

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Answer:

a)

b)-4

Step-by-step explanation:

a) f(13) = 13-7=

b) f(3)= 3-7= -4

Answer: The area of the circle with a radius of 9 is approximately 253.94 square units.

Step-by-step explanation:

The area of a circle is given by the formula A = πr^2, where A is the area, r is the radius, and π is approximately 3.14.

Given that the radius of the circle is 9, we can substitute this value into the formula to find the area:

A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94

So the area of the circle with a radius of 9 is approximately 253.94 square units.

Note that the diameter of the circle is 18, which is twice the radius. If you knew the diameter you could also use the formula A = (π/4)*D^2 to calculate the area, where D is the diameter.

f(x) and g(x) are inverses using composition

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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The specialty fees will of the project will be $175,000.

What is specialty fee in a project?

Specialty fee of a project is associated with the cost or money that is given for some special task for e.g. hiring a architect or other specialist.

To calculate the amount of money that will be spent on specialty fees, we need to multiply the total amount of money raised (35,000,000) by the specialty fee percentage (0.5%).

specialty fees = 35,000,000 * 0.005 = 175,000

So, $175,000 will be spent on specialty fees.

Also, To calculate the amount of money that will be spent on service commission, we need to multiply the total amount of money raised (35,000,000) by the service commission percentage (2%).

service commission = 35,000,000 * 0.02 = 700,000

So, $700,000 will be spent on service commission.

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To raise $35,000,000 for a project's financing, a corporation will issue shares and bonds. The project's specialist fees will be $175,000 in total.

The cost or amount paid for a project's specialty work, such as employing an architect or another specialist, is known as the specialty fee. We must multiply the entire cash raised ($35,000,000) by the proportion of speciality fees ($0.5%) to determine the amount that will be used for fees.

35,000,000 * 0.005 = 175,000 in specialist fees.As a result, specialist fees will cost $175,000. Additionally, we must multiply the total sum of funds raised (35,000,000) by the service commission rate (2%), in order to get the amount that will be used for service commission. service commission: 35,000,000 * 0.02 = 700,000 , The service commission will therefore receive $700,000.

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Step-by-step explanation:

Possible values of the correlation coefficient range from -1 to +1, with -1 indicating a perfectly linear negative, i.e., inverse, correlation (sloping downward) and +1 indicating a perfectly linear positive correlation (sloping upward). A correlation coefficient close to 0 suggests little, if any, correlation

Step-by-step explanation:

(R○R)(x) = (5 - 2((5 - 2x)/x))/((5 - 2x)/x)

we simply put the original R function into the places of x.

so,

(R○R)(-6) = (5 - 2((5 - 2×-6)/-6))/((5 - 2×-6)/-6) =

= (5 - 2((5 + 12)/-6))/((5 + 12)/-6) =

= (5 - 2×17/-6)/(17/-6) =

= (5 + 17/3)/(17/-6) = (15/3 + 17/3)/(17/-6) =

= 32/3 / 17/-6 = -6×32 / (3×17) =

= -2×32 / 17 = -64/17

Answer:

-64/17

Step-by-step explanation:

Same person here who answered previous question.

(R · R)(-6)

This basically means R(R(-6))

Now, R(-6) = (5 + 12)/-6 = -17/6

Put that value again, in (5 - 2x)/x = (5 + 34/6)/(-17/6)

= (64/6)/(-17/6) = -64/17

So, the answer is correct.

If you have any questions, please leave a comment.

Otherwise, cheers

The correct classifications for these variables are a = numerical discrete, b= categorical, c= numerical continuous, d= numerical continous, e= categorical.

As indicated by their name, numerical variables can be measured using numbers; here are some examples:

On the other hand, categorical variables fit into categories, for example:

Female vs Male

Dog vs cat

Discrete variables differ from continuous variables because they are obtained by counting, for example, the number of students in a classroom, while continuous variables need to be measured, for example, the distance.

Based on this the correct classification is:

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a) The linear combination of v, w by finding scalars c₁, c₂ such that c₁v + c₂w = b is [v w | b]

b) The graph of the equation is attached below.

c) The matrix representation is a useful tool for finding linear combinations of vectors, but it becomes more complex as the number of dimensions increase.

A linear combination of two vectors is when a third vector is expressed as a sum of the two vectors multiplied by scalars.

In R2, this can be represented using a parallelogram, where the vectors are drawn and the third vector is the diagonal of the parallelogram.

To find the scalars, we use the matrix representation [v w | b]. If the matrix gives a consistent system, it means that the third vector b can be expressed as a linear combination of the two vectors v and w.

In R3, the matrix representation is still used but it becomes more challenging to find a consistent system because there are more variables involved.

The vectors are graphed in 3D, and the third vector is found as the diagonal of a parallelogram that is now a parallelepiped.

However, it may not always be possible to find a consistent system in R3, as the third vector may not lie in the plane formed by the two vectors.

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The number which is lesser than its square is 12/11

When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number as it is composed of 5 lots of 5, or 5 × 5. 

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.

The numbers are

9/10 , 12/11 , 15/16 and 13/13

The squares are

81/100, 144,121, 225/256, 1

here

81/100 < 9/10 abd

225/256 < 15/16

144/121 > 12/11

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[tex]-10w=-9[/tex]

Divide both sides by -10(to isolate the variable):

[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]

[tex]=0.9[/tex]

(a) -3,-11,-19, -27, -35,-43, -51, -59, -67, -75.

(b) -9,-18,-36,-72,-144,-288,-576,-1152,-2304,-4608.

(c) 2, 6, 12, 20, 30, 42, 56, 72, 90, 110.

In the provided sequence, we will find the difference between two consecutive integers.

The difference between the second and first numbers is 622=4.

The difference between the third and second numbers is 126=6.

The difference between the fourth and third numbers is =2012=8.

We can see that the difference between two consecutive integers starts at 4 and grows by 2 each time.

As a result, the supplied sequence is created by adding the difference between a number and the preceding number, as well as 2 to the number.

Using the rule, we can determine the following three words.

The difference between the fifth and fourth numbers is =8+2=10.

As a result, the fifth number of the series equals the fourth number of the sequence plus ten.

As a result, we get the fifth number from the series =20+10=30

The difference between the sixth and fifth numbers is 10+2=12.

As a result, the sixth number of the series equals the fifth number of the sequence plus twelve.

As a result, we receive the sixth number as the sequence's sixth number =30+12=42.

The difference between the seventh and sixth numbers is 12+2=14.

As a result, we get the sequence's seventh number = the sequence's sixth number + 14

As a result, we receive the seventh number as the sequence's seventh number =42+14=56.

As a result, the following three terms in the specified sequence are 30, 42, and 56.

The sequence is changed to 2, 6, 12, 20, 30, 42, 56.

The word 'prime numbers' was used in the answer. The numbers are known as prime numbers. It has just two variables, 1 and the number itself. For instance, 2 is the sum of 2 and 1. As a result, the components of 2 are 2 and 1. As a result, 2 is a prime number.

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