If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= ____
(Simplify your answer.)

(a) 250000 of this revenue was sales and $11250 much was sales tax. (b) $11250 of sales tax should be sent to the city and $3750 sales tax should be sent to the state.

Let us assume that the total sales are $X.

According to the given situation, 7% is the sales tax and an additional state sales tax of 1.5% will be charges on the sales.

The total revenue including sales tax is $271250.

(a) Total revenue = sales + total sales tax

So, we can write,

X + X(7+1.5)% = 271250

Solving further,

X + X(8.5%) = 271250

X + 8.5X/100 = 271250

108.5X = 271250×100

X = 250000

Total sales is $250000.

Total sales tax is $(2710250-250000)

Total sales tax is $21250.

(b) Total sales is $250000.

Tax charges by city is 7%.

Using percentage formula,

Percentage of tax = Total tax amount/Total sales amount × 100

Putting all the values,

7 = Total tax amount/250000 × 100

Total tax amount = 7 × 2500

Total tax amount = 17500 dollars.

Total amount to be sent to the city is 175000$.

(c) Total sales is $250000.

Tax charges by city is 1.5%.

Using percentage formula,

Percentage of tax = Total tax amount/Total sales amount × 100

Putting all the values,

1.5 = Total tax amount/250000 × 100

Total tax amount = 1.5 × 2500

Total tax amount = 3750 dollars.

Total amount to be sent to the city is 175000$.

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The second expression 1/(x^2 - 4x + 3) is equivalent to the given expression.

What are the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Consider the given expression,

((x + 3) / (x^2 - 2x - 3)) / ((x^2 + 2x -3)/ (x + 1))

We can write the expression as,

((x + 3) / (x^2 - 2x - 3)) x ((x + 1) / (x^2 + 2x -3))        

Rewrite the equation x^2 - 2x - 3 and x^2 + 2x -3 as,

x^2 - 2x - 3 = x^2 - 3x + x - 3 = (x - 3)(x + 1)

x^2 + 2x - 3 = x^2 + 3x - x - 3 = (x + 3)(x - 1)

plug these values in the above expression, we get

((x + 3) / ((x - 3)(x + 1)) x ((x + 1) / ((x + 3)(x - 1))

After solving this, we get

1 / ((x - 3)(x - 1) = 1 / (x^2 - 4x + 3)

Therefore, the second expression is equivalent to the given expression.

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Answer:

Step-by-step explanation:

Jenny is 20 years old

Lynn is 14 years old

Kim is 23 years old

The most appropriate choice for pattern will be given by

Option E is the correct option

What is pattern?

Repeated arrangement of number or shape is called pattern.

Here,

Let the boxes be counted row wise

The question is all about filling all the blank boxes with orange colour.

Let the pattern be solved column wise

In the first column,

In first figure

The 2nd, 3rd and 4th boxes are filled with orange colour

Then in the second figure 5th box is filled with orange colour

To complete filling all the boxes with orange colour, 1st, 6th, 7th, 8th and 9th boxes are left. That is shown in the third figure.

In the third column

In first figure

The 5th, 6th and 9th boxes are filled with orange colour

Then in the second figure

1st, 2nd, 4th, 7th and 8th boxes are filled with orange colour

To complete filling all the boxes with orange colour, only the 3rd box is left

That is shown in third figure

Now, in the second column,

In the first figure,

1st, 7th and 8th boxes are  filled with orange colour.

Then in the second figure 3rd, 6th and 9th are filled with orange colour

To complete filling all the boxes with orange colour, 2nd, 4th and 5th boxes are left.

That is shown in option E

So option E is correct

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Given:

The distance between two stations in map, D= 9cm.

The distance between two stations in real life, d=3 km.

Now, to find the scale of the map take the ratio of D/d .

So, the scale of the map is 1 km=3 cm.

Taking a look at the graph, we can notice that point (7000,2875.99) is highlighted.

Using this point, we can conclude that the cost of talking 7000 minutes is $2875.99

45 represents the slope while -900 is the y-intercept of the function

Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing

From the question, we are told that he averaged an elevation of 45 meters per hour

What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope

To get the y-intercept of the function, we can see this as a distance of -900 meters

The reason for this is that we can see the summit of the mountain as 0 m

So we can represent the equation as;

Answer:

y = [tex]\frac{5}{4}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{4}[/tex] , then

y = [tex]\frac{5}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, - 6 ) into the partial equation

- 6 = - 5 + c ⇒ c = - 6 + 5 = - 1

y = [tex]\frac{5}{4}[/tex] x - 1 ← equation of line

a. The company will break even in 6 years

b. The total profit with the newly developed line of business is:

c. The company will break even 3 years sooner

The projected profit is given as:

a. The company will break even when the profit is zero. That is;

6 is the realistic number of years (As we cannot have -3/2 years).

We conclude that they will break even in 6 years

b. The projected profit of a newly developed line of business is:

The total profit is now;

The company will break even with this new line of business as follows:

We choose t = 3 (because we cannot have -2 years or -3 years)

The difference between this and the previous time is 6 - 3 = 3 years

The company will break even 3 years sooner

A function is a relation that gives one input for every one output thus the value of g(10) is -31.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function,

g(x) = -3x - 1

The value of the function at x = 10

g(10) = -3(10) - 1

g(10) = -30 - 1 = -31

Hence "A function is a relation that gives one input for every one output thus the value of g(10) is -31".

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The given equation is

At first, we have to isolate x on one side and the numerical term on the other side, then

Add 1 to both sides

Subtract x from both sides

The solution of the equation is x = 8

Answer:

a. If the selection is made with replacement, they are NOT independent because they affect each other.

b. The probability of selecting TWO accurate orders is .7157 and the events ARE independent.

Step-by-step explanation:

Add the accurate orders:

315+273+248+125=961

Add the inaccurate orders:

38+56+37+17=148

148/961=0.1540 probability of getting ONE inaccurate order

1.0-0.1540=0.846 probability of selecting ONE accurate order

0.846 * 0.846 = 0.7157 the probability of selecting TWO accurate orders

Therefore, the probability is .7157 and the events ARE independent.

Determine the equation of line passing through two points.

So equation of line is,

From the given graph

The graph of g has an arrow with the left end it goes up, then

The absolute maximum of g is NONE

The graph of g has a minimum point (4, -4), then

The absolute minimum is -4

The graph of h has a maximum point (-4, 4), then

The absolute maximum is 4

The graph of h has a minimum point (-1, -4), then

The absolute minimum is -4

Answer:

g(x) + 4 = x

g(x) = x - 4 which is probably the answer you should submit.

Step-by-step explanation:

Givens

f(x) = x

g(x) +4 = f(x)  

Comment

f(x) and g(x) are forms of y or z. What they mean is that whatever x is on the left, it will be make the same on the right. It is just a short hand to help you in defining the y value.

If you want to move down, The y value is the one to notice. Notice that it is not intuitive. If you want to go down the sign on y + 4 = x is the equation you use. It is the exact opposite of what you think it should be. The graph below should help you.

The red line is f(x)  = x

The blue line is g(x) + 4 = x.

The blue line can be written as g(x) = x - 4 which would be more inetuitive.

The least positive number x for which cos x = 0 is 1.

The given trigonometric equation is cos x=0.

A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.

Now, cos x = 0

So, [tex]x=cos^{-1}(0)[/tex]

⇒ x = 1

Therefore, the least positive number x for which cos x = 0 is 1.

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Please provide the question.

We are asked to select the mathematical expressions that represent 40% of 84

We then recall that the mathematical form of 40% is in fact 40 / 100 = 0.4

Then, 40% of 84 can be written in math terms as:

40/100 times 84 = 40/100 * 84

or also

0.4 times 84 = 0.4 * 84

Therefore there are TWO options we can select in the list of possible answers:

Answer C and answer E

The smaller number = 27

The larger number = 119

Let the smaller number be x

Let the larger number be y

The sum of the two numbers is 146

x + y = 146..............(1)

The larger number is 16 less than five times the smaller number

y = 5x - 16.............(2)

Substitute equation (2) into equation (1)

x + (5x - 16) = 146

x + 5x - 16 = 146

6x = 146 + 16

6x = 162

x = 162/6

x = 27

Substitute the value of x into equation (2)

y = 5(27) - 16

y = 135 - 16

y = 119

The smaller number = 27

The larger number = 119

The current area of Mr. Milstein's kitchen table is:

The new width of Mr. Milstein's kitchen table = 5 feet

The area of the new kitchen table if the length is l is given by

Note that the area of the proposed kitchen table should be larger than the current one.

Therefore,

The correct option is F

Given

Jessie has 5 dogs

2 are male

3 are female

Procedure

What percent of the dogs are male?

Male dogs

40 % of dogs are male

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

hand-engraved watch bands:

total watch bands = 20

total profit = $105.00

Step 02:

ratio:

total profit (50 watch bands):

The answer is:

$ 262.50

Answer:

A. f(-2) = 13

B. f(0) = 1

C. f(7) = -41

Step-by-step explanation:

f(x) = 1 - 6x

A.

f(-2) = 1 - 6(-2)

f(-2) = 1 + 12

f(-2) = 13

B.

f(0) = 1 - 6(0)

f(0) = 1

C.

f(7) = 1 - 6(7)

f(7) = 1 - 6(7

f(7) = -41

I hope this helps!

The answer for this process of long division is, therefore:

To find the result for this long division, we needed to divide the first term of the polynomial by the x in the divisor. Then, if we see the first graph, we have:

Then, we need to multiply this term by the divisor (x - 3), and then, subtract the result from the first two terms of the dividend. We can see as follows:

The given inequalities are :

2x + 8 > 18

2c + 8 < 18

Inequality 1 : 2x + 8 > 18

Simplify

Subtract 8 from both side :

2x + 8 - 8> 18 - 8

2x > 10

Divide both side by 2

x > 5

Inequality : 2c + 8 < 18

2c + 8 < 18

Subtract 8 from both side:

2c + 8 - 8 < 18 - 8

2c < 10

Divide both side by 2:

2c/2 < 10/2

c < 5

So, the solution is x > 5 and c < 5

So, equation will be : c < x < 5

Answer:

Step-by-step explanation:

If I did the math right! The bill should be $400.00

How I did it, was I did 175+5x45.

seeing, it is $5 per mile! And the total miles you got was 45.

If I missed something, please let me know

Hello!

First, let me explain the difference between discrete and continuous.

Discrete: only some numbers of the interval are on the input. For example, in the interval 1 - 10, consider only the integers.

Continuous: all the numbers of the interval are on the input. For example: in the interval 1 - 10, all values are considered (integers and decimals).

Knowing it, let's analyze your exercise:

The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven.

We can represent miles as integers and also decimals, right?

• 2 miles

• 5.750 miles

So, it means that all values can be considered.

So, this is a continuous domain.

Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:

a verbal reasoning score,

a quantitative reasoning score,

an analytical writing score.

Let average verbal reasoning score represent by v

Let average quantitative reasoning score represent by q

Let average analytical writing score represent by a

In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points

i.e.,

Average quantitative reasoning score - average verbal reasoning = 1.3

q - v = 1.3 ...(1)

The average verbal reasoning score exceeded the analytical writing score by 150.5 points.

i.e.,

Average Reasoning score - average analytical writing = 150.5

v - a = 150.5 ...(2)

The sum of the three average scores was 305.9.

i.e.,

v + q + a = 305.9 ...(3)

Simplify the equation (1), (2) and (3) to get the value of q,v and a;

Add equation (1) and (2)

(q-v) + (v-a) = 1.3 + 150.5

q + a = 151.8 ....(4)

Substitute the value of (q+a=151.8) in the equation (3);

v + q + a = 305.9

v + 151.8 = 305.9

v = 305.9 - 151.8

v = 154.1

Substitute the value of v = 154.1 in the equation (2);

v - a = 150.5

154.1 -a = 150.5

a = 154.1 - 150.5

a = 3.6

Now, substitute the value of a = 3.6 in the equation (4)

q + a = 151.8

q + 3.6 = 151.8

q = 151.8 - 3.6

q = 148.2

Answer :

The average verbal reasoning score was 154.1

The average quantitative reasoning score was 148.2

The average analytical writing score was 3.6