Let f(x)= 1/x-2 and g(x)=5/x+2Find the following functions. Simplify your answers.F(g(x))=g(f(x))=

Let x be the quantity of flour used

Let y be the quantity of milk used

A pancake recipe asked for one and 2/3 times as much milk as flour:

If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?

Find x when y=2 1/2:

Write the quantities as fractions;

Solve x:

Write the answer as a mixed number:

1 day a cow can eat = 24 pounds

1 day 12 cows can eat = 24 x 12

2 weeks = 14 days

therefore:

12 cows can eat in two weeks = 24 x 12 x 14 or 12 ( 24x14 )

answer: A. 12(24x14)

Here, we proceed step by step, to obtain our answer,

[tex]\frac{1}{2}[/tex]  % of 36 can be written as ,

0.5 % of 36 , which means,

100 % refers to 36, then

0.5 % refers to what,  thus, by cross multiplication we get,

0.5 % of 36 =  [tex]\frac{0.5 X 36}{100}[/tex] = 0.18 ___(1), which can be expressed in whole numbers as 0.

Now, 30 % of 10 means,

100 % refers to 10, then

30 % refers to what,  thus, by cross multiplication we get,

30 % of 10 = [tex]\frac{30 X 10}{100}[/tex] = 3 __(2)

From equations (1)  and (2),

the whole numbers that we obtain are 0 and 3, respectively,

Thus the difference between these two whole numbers is,

= 3 - 0 = 3.

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Since there are 20 marbles and 12 of them are yellow; the marbles that are not yellow is not the same number as the marbles, and neither the number of Yellow marbles because they are yellow. So the answer is C.

Given function,

f(x) = 6x - 6

or

y = 6x -6

The inverse of a function is calculated by replacing the values of x and y

therefore

Inverse (y = 6x - 6)

x = 6y - 6

x + 6 = 6y

6y = x + 6

y = x/6 + 6/6

y = 1/6*x + 1

or

g(x) = 1/6*x + 1

Hence, both are inverse of each other.

By using polynomial rule we can get  6x^4-7x^3+3x^2+17x-14

What is polynomial rule?

All exponent in the algebraic expressions must be non-negative integer in order for the algebraic expressions to be a polynomial.

A polynomial is defined as per an expression which is the  composed of variables, constants and exponents, that are combined using the  mathematical operations are  such as addition, subtraction, multiplication and division.

Sol- (3x^2-5x+7).(2x^2+x-2)

(3x^2-2x^2+3x^2.x-3x^2.2)-5x.2x^2-5x.x+5x.2+7.2x^2+7.x-14

{polynomial multiplication rule}

=6x^4+3x^2-6x^2-10x^3-5x^2+1x+14x^2+7x-14

{Plus or minus with the same x coefficient}

We are get=

6x^4-7x^3+3x^2+17x-14

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NUMBER 5:

INFORMATION:

We have a trapeze and, we need to find the probability that a randomly chosen point is the figure lies in the shaded region

STEP BY STEP EXPLANATION:

To find the probability, we must divide the area of the shaded region by the total area of the trapeze

- Total area:

To calculate the total area, we must use the formula for the area of a trapeze

Where, b1 and b2 are the bases and h is the height

Then, analyzing the trapeze we can see that b1 = 20, b2 = 14 and h = 12

So, the total area is 204 square units

- Shaded area:

To find the shaded area, we must subtract the no shaded area from the total area.

We can see that the no shaded area is a rectangle with width = 14 and height = 12

Now, using the formula for the area of a rectangle

Then, subtracting the area of the rectangle from the total area

So, the no shaded are is 36 square units.

Finally, the probability would be

ANSWER:

the probability that a randomly chosen point is the figure lies in the shaded region is

Explanation:

Step 1. We are given the graph of a line and we need to find the equation of the line parallel to it that has an x-intercept of -3.

Since the new line will be a parallel line it means that it will have the same slope. Therefore, our first step is to find the slope of the current line.

Given any line, we find the slope as shown in the following example diagram:

Step 2. Using the previous method, the slope of our line is:

The new line will have the same slope of 2/3.

Step 3. We are also told that the x-intercept of the new line is -3, which means that the new line will cross the y-axis at x=-3, that point is:

(-3,0)

We will label that point of our new line as (x1,y1):

Step 4. So far, we know that the new line will have a slope of 2/3:

And that it includes the point (-3,0) where x1=-3 and y1=0.

To find the equation, we use the point-slope equation:

Step 5. Substituting the known values into the formula:

Solving the operations:

Answer:

Answer:

Step-by-step explanation:

fog(x)=3(-x+1)^2+5

         =3(x^2+2x+1)+5

        =3x^2+6x+3+5

fog(x)   =3x^2+6x+8

gof(x)=-(3x^2+5)+1

        =-3x^2-5+1

gof(x)=-3x^2-4

gof(-1)=-3(-1)^2-4

         =-3-4

gof(-1) =-7

Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

As given in the question,

Interest rate = 5%

Types of account = Saving account

Pays the interest in two forms :

Compounded semiannually and Compounded daily

Saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

Reason :

Frequency of interest given on compounded daily is much higher and increase the amount much faster as compare to compounded semiannually.

When interest compounded daily generate 365 compounding periods a year, where as compounded semiannually generates two times in a year.

Therefore, saving account that pays 5% interest compounded daily is much better than the account that pays 5% interest compounded semiannually.

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Solution

- The solution steps are given below:

Final Answer

The answer is 16

Given: The points a line intersects as shown below

To Determine: The slope of the line in its simplest form

Solution

The formula for finding the slope of two points is as shown below

Let us apply the formula to the given points

Hence, the slope of the line in simplest form is -6

For this type of problems we use the formula for the volume of a pyramid:

Substituting h=12 yd and knowing that the area of a square is side*side we get that:

Notice that XZ = XY + YZ

where XY = 5m

YZ = m and XZ =25

Thus,

25 = 5m + m

25 = 6m

Hence,

But YZ = m

Therefore, YZ =

option B

The cost of renting per hour = $2

For 1 hour = $2

For each additional hour, it is $1

For 2 hours = First hour + 1(additional hour)

For 2 hours = $2 + $1(1) = 2+1 = $3

For 3 hours = $2 + $1 (2) = 2+2 = $4

For 4 hours = $2 + $1(3) = 2+3 = $5

The graph which shows this rental cost as 2, 3, 4, 5 is option B

There are different graphs of polynomial functions. In terms of shape, it can go from a straight line, slanting line, parabola, to curvy graphs especially when we are graphing polynomial functions with degrees 3 or higher.

See examples below:

However, what is similar to these graphs is that each graph is continuous or has no breaks and the domain of every polynomial function is the set of all real numbers.

ANSWER

EXPLANATION

We want to find the derivative of the function:

The quotient rule states that:

where u = the numerator of the function

v = the denominator of the function

From the function, we have that:

Now, we have to differentiate both u and v:

Therefore, the derivative of the function is:

We know that the tax rate is 7.3% and it corresponds to $12.41. We want to find the total price of the table saw without taxes, it is to say the 100%. We have the following equivalence:

100% ⇔ ??

7.3% ⇔ $12.41

If we divide both parts of the equivalence we will have the same result:

Multiplying both parts of the equation by 12.41:

Now, we can find the total price of the table saw without taxes:

Answer A. the purchase price is 170

The total price of the table saw (it is to say, including taxes, $12.41), is

170 + 12.41 = 182.41

Answer B. the total price is 182.41

Given:

There are given that the data for x and y are in the form of a table.

Explanation:

According to the concept of function:

The function is not defined when the value of x will be repeated.

That means if the input value is repeated again and again then the given relation will not function.

In the given relation, we can put 7 into the input box.

Final answer:

Hence, the value is 7.

The density of the cube is equal to ρ = m / L³.

The density of the plastic cube (ρ), in grams per cubic centimeter, is equal to the mass of the cube (m), in grams, divide to the volume of the cube. The volume is equal to the cube of the side length (L), in centimeters. Then, the density of the plastic cube is:

ρ = m / L³

By using the definition of density, the density of the element is equal to ρ = m / L³.

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We know that

1 quarter gallon of paint ⇄ 1/12 wall

?? ⇄ 1 wall

Now we just divide both sides of the equivalence

We clear the equation in order to find the unkown value

[tex]\frac{4}{5}[/tex].

[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]

A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:

[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]

[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]

[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].

[tex]\frac{4}{5}[/tex].

[tex]1+\frac{2}{5} -\frac{6}{10}[/tex]

A common denominator is just a number that can be used as a denominator all fractions when we convert them through multiplications. A common denominator is usually found just by multiplying all denominators of all fractions. In this case, we don't need to go that far, since 5 could be a common denominator.This is how you do it:

[tex]1=\frac{1}{1} *\frac{5}{5}=\frac{5}{5} \\ \\\frac{2}{5}= \frac{2}{5}\\\\\frac{6}{10} =\frac{6/2}{10/2}=\frac{3}{5}[/tex]

[tex]\frac{5}{5} +\frac{2}{5} -\frac{3}{5} =\frac{5+2-3}{5} =\frac{4}{5}[/tex]

[tex]1+\frac{2}{5} -\frac{6}{10}=\frac{4}{5}[/tex].

It is desired that the domain and range of the function should, respectively, be

Observe the given choices of function.

It is evident that all the functions are exponential functions, so their domain must be the set of all real numbers,

Now, we have to check the range of each of the 4 given functions.

Option A:

The function is given as,

Consider the following,

Thus, we see that the range of the function is,

Since this does not match with the desired range. This is not a correct choice.

Option B:

The function is given as,

Consider the following,

Thus, we see that the range of the function is,

Since this does not match with the desired range. This is not a correct choice.

Option C:

The function is given as,

Consider the following,

Thus, we see that the range of the function is,

Since this exactly matches with the desired range. This is a correct choice.

Option D:

The function is given as,

Consider the following,

Thus, we see that the range of the function is,

Since this exactly matches with the desired range. This is also a correct choice.

Thus, the we see that the functions in option C and D possess the desired domain and range.

Therefore, option C and option D are t

The numbers are given to be:

This is written in Interval notation.

In "Interval Notation" we just write the beginning and ending numbers of the interval, and use:

a) [ ] a square bracket when we want to include the end value, or

b) ( ) a round bracket when we don't.

Because the interval given uses round brackets, the inequality will contain all real numbers between negative infinity and -5, but not including negative infinity and -5.

Therefore, the inequality will be:

Answer:

D.

Explanation

We know that g(x) = f(1/2x)

Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).

It means that f(-2) = 0 and f(2) = 0

Then, g(-4) = 0 and g(4) = 0 because

Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.

If the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.

Let the tangent function be f(z) = tan (Bz)

The period exists [tex]$P=\frac{\pi}{|B|}$[/tex]

The frequency exists [tex]$F=\frac{1}{P}=\frac{|B|}{\pi}$[/tex].

The period exists inversely proportional to B, therefore, as B increases, the period decreases.

Frequency exists inversely proportional to the period, therefore, as the period decreases, the frequency increases.

When B is negative, we get f(z) = tan -Bz = f(-z), therefore, the function exists reflected over the y-axis, as the graph at the end of the answer shows, with f(z) exists red(B positive) and f(-z) exists blue(B negative).

As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B exists negative, the graph of the function reflects over the y-axis.

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From the information provided we will have that the predictions will be:

*Line of best fit:

So, the extrapolation from the line of best fit is 4.9 sold.

*Curve of best fit:

So, the extrapolation for the curve of best fit is 32.2 sold.

After solving the system of equations we get the values as:

Given the equations are as follows, we need to solve them using multiplication method:

take c+3t=7

rearrange the terms.

c = 7-3t

substitute c value in other equation.

3(7-3t)-2t=-12

21-9t-2t=-12

21-11t=-12

-11t = -12-21

-11t=-33

t=33/11

t=3

now substitute t value in c = 7-3t

c = 7-3(3)

c=7-9

c=-2

hence t and c values are 3 and -2.

take 5x – 4z = 15

5x = 15+4z

x=15+4z/5

substitute x value in other equation.

-3(15+4z/5)+2z=21

-45-12z+10z=105

-45-2z=105

-2z=105+45

z=-75

substitute z value in x=15+4z/5

x=15+4(-75)/5

x=-57

hence x and z values are -57 and -75.

consider, -4m+3n=50

3n = 50+4m

n=50+4m/3

substitute n value in other equation.

2m+n=10

2m+50+4m/3 = 10

6m+50+4m=30

10m=30-50

10m=-20

m=-2

substitute m value in n=50+4m/3

n = 50+4(-2)/3

n = 50-8/3

n = 42/3

n = 14

hence m and n values are -2 and 14.

consider 2p - 4q = 18

2p = 18+4q

p = 9+2q

substitute p value in other equation.

-3p+5q=22

-3(9+2q)+5q=22

-27-6q+5q=22

-27-q=22

-q = 22+27

q = -49

now p = 9+2q

p = 9+2(-49)

p = 9-98

p=-89

hence p and q values are -89 and -49.

consider 3a + 4b = 51

3a = 51-4b

a=51-4b/3

substitute a value in other equation.

2(51-4b/3)+3b=37

102-8b+9b=111

102+b=111

b=111-102

b=9

now, a=51-4(9)/3

a = 51-36/3

a = 15/3

a = 5

hence a and b value are 5 and 9.

Therefore, we solved the required system of equations.

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The number of words of the book Jimmy reads os 21,356, and the number of words of the book Bob reads is one-and-a-half times (that is, 1.5x) as many words, so to find the number of words Bob reads, we just need to multiply the number of words of Jimmy's book by the factor of 1.5: