if f(x) = 1/x and g(x) = x+1/x find(fog)(x).a) x +1/ x squared b) x / x + 1 c) x squared (x + 1)d) x + 1 / x cubed

We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.

Hello there. To solve this question, we'll have to remember some properties about unit conversions.

We want to convert 90 meters per minute to meters per second.

Remember 1 minute is equal to 60 seconds, therefore we can write

90 meters per 60 seconds

Simplify it by a factor of 30

3 meters per 2 seconds

Which is the same as

1.5 meters per second

The unit multiplier was divide the number by 60, in order to get minutes to seconds and, therefore, find the value in m/s.

The given system is

First, we multiply the first equation by -3/10.

Then, we sum the equations

Given

First : They assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones

Let's represent regular wreaths with r

and

Let's represent deluxe wreaths with d

Second: They assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones

We now have

we can now solve simultaneously, by subtracting the equation 1 and 2

We can subsitute d=5 in equation 1 or 2

The final answer

5 pinecones on the deluxe wreath and 3 pinecones on the regular wreath

Given:

Linear equation in x and y:

An equation of the form y = mx + c or ax + by +c =0 is a linear equation as the degree of both variables x and y is one.

(a) 2x = 5 + y:

The equation can be written as:

This is of the form of ax+by+c=0 so it is linear.

Here, a=2, b= 1, c= - 5

(b) y = 5x + 3:

This is already in the form of ax + by+ c=0 so it also linear.

Here, a= 5 , b = - 1, c= 3

We want to know the maximum value for f(x). In this case, we have that when f(x) = 10, x =6. Then, the ordered pair (6,10) represents the maximum from the table

We have the following equation:

where x denotes the number of years after 1998.

By substituting the given information, we have that

and we need to find x. Then, by dividing both sides by 1.8208, we get

then by taking natural logarithm to both sides, we obtain

which gives

then, the number of years after 1998 is:

which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.

Given the values shown in the table, let be "x" the Vehicle weight (in hundreds of lbs.) and "y" the City MPG (Miles per gallon).

1. Given the points:

You can plot them on a Coordinate Plane:

2. Notice the following line:

Notice that the points are closed to the red line that has a negative slope. Therefore, you can identify that when one of the variables increases, the other variable decreases. Hence, you can conclude that the data describes a negative correlation.

3. You need to follow these steps to find the equation of the line of best fit:

- You need to find the average of the x-values by adding them and dividing the Sum by the number of x-values:

- Find the average of the y-values:

- Find:

Where this represents each x-values in the data set:

You get:

- Find:

You get:

- Find:

You get:

- Find:

You can find it by squaring each Difference of the x-values and the Mean. you get:

- Find the slope of the line

- Find the y-intercept with this formula:

Therefore, the line in Slope-Intercept Form:

is the following:

4. If:

You can predict the vehicle weight by substituting that value into the equation found in Part 3, and solving for "x":

5. If a vehicle weighs 1500 pounds, then:

Then you can determine the expected city MPG of the vehicle by substituting this value into the equation and evaluating:

Hence, the answers are:

1.

2. It describes a negative correlation.

3.

4.

5.

The first thing we have to do is find the pascal coefficients of the triangle for this we use the following image

From our exercise we know that

Then our coefficients of Pascal's triangle are 1 - 3 - 3 - 1

Using the right triangle we get:

We substitute the values of a and b in our new expression to find our solution

So the solution is:

We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,

Applying this property to the presented case, we obtain that

Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.

Thus, the answer to the exercise is a= 2 and b = 13.

A) It's a function because each point of x has a point on y.

B. It's a discrete functions because you can't see a continuous line.

C. Domain (-3,6)

D. Range (0,3)

* C and D if each square is equivalent to 1 unit.

step 1

Find out the slope of the given line

we have

y+1=-(1/2)x

The slope is m=-1/2

Remember that

If two lines are perpendicular

then

their slopes are negative reciprocal

so

The slope of the perpendicular line is

m=2

step 2

Find out the equation of the line in slope-intercept form

y=mx+b

we have

m=2

point (-8,7)

substitute and solve for b

7=2(-8)+b

7=-16+b

b=23

therefore

the equation of the line is

For the given vector  v=7i - 5j and w=-i+j,

        projwv =  6i - 6j

                   v1 = 6i -6j

                     v2 = i +j

Vector:

              A quantity that has both magnitude and direction are called vector. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.

a) projwv is the projection of v onto w. Use the following equation:

projwv = [(v•w)/((magnitude(w))2)] w

v•w = (7*-1) + (-5*1) = -12

(magnitude w)^2 = ([tex]\sqrt{1^{2} + 1^{2}}[/tex])^2 = 2

projwv = ((-12)/2)(-i + j)

            =  6i - 6j

b) The two components of the decomposed v will add to create the original vector v. v1 that is parallel to w will be the same as the projection of v onto w.

v = v1 + v2

v2 = v - v1 = (7i - 5j) - (6i -6j) = i +j

You can check that v2 is orthogonal by taking the dot product (v2•w). This equals 0.

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Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.

Given,

The selling cost of shelving units that are 10 years old = $800

Original cost of shelving units = $6400

Estimated residual value for 10 years = $400

Assets = Liabilities +Stockholders equity

Accumulated depreciation for 10 years=[(Original cost of the equipment-Residual value) / Useful life] ×10 years

=[($6400-$400)/10 years]×10 years

=$600×10 years

=$6000

Book value equipment=Original cost of the equipment-Accumulated depreciation for 10 years

=$6400-$6000

=$400

Calculate gain on sale of equipment.

Gain on equipment sale equals selling price minus book value of equipment

=$800-$400

=$400

Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.

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Let x be the unknown value.

Therefore we have

So we can inform from the first term that the denominator is double the numerator, since this term is equal to second term with the unknown x, same applies there also.

So,

This can be further confirmed by applying cross multiplication,

Given the function c(x) = 50x where c (x) is the number of words. In 6.5 minutes, the number of words that can be typed is

= 50 * 6.5

= 325 words

Vertical angles are opposite angles that also are congruent angles.

Then, due to the given figure, you can conclude that the vertical angles are:

angle FGD and angle of 15° are vertical, then

Given the coordinates of L and M

To get the length between the two coordinates, we will follow the steps below

Step 1: List out the coordinates of L and M

step 2: calculate the distance

Since they both have the same x coordinates, we can simply subtract the y-coordinate of L from M

Therefore, the distance LM is 7 units

Explanation:

This function is C(n) which means it's a function of n. It is said that n is the number of observed vehicles in a specified time interval. It cannot be negative and it has to be an integer. Therefore the domain is all integers greater or equal than zero.

Answer:

4) {0, 1, 2, 3...}

Given the equation system:

To solve the system and determine the value of x, first step is to write one of the equations in terms of y:

Then replace this expression in the second equation

Now that you have an expression with only one unknown, x, you can calculate its value.

Solve the parenthesis using the distributive property of multiplication

EXPLANATION:

We are given an exponential function as shown below;

When shifted one unit right we have the following;

We also are given the quadratic function;

When shifted one unit right and one unit up, we would have;

The equations for both functions after the transformations would be;

The graphs of both equations is now shown below;

The two points where m(x) and n(x) intersect are;

ANSWER:

Answer:

√52 feet

Step-by-step explanation:

5 - -1 = 6

-2 - 2 = -4

6 = change in y

-4 = change in x

a² + b² = c² (pythagoras theorem)

6² = 36

-4² = 16

36 + 16 = 52

c² = 52

c = √52

Answer: square root of 52 feet

Reason:

When we cube the (r^2) in the numerator, we're multiplying it by itself 3 times

(r^2)^3 = (r^2)*(r^2)*(r^2) = r^(2+2+2) = r^6

or a shortcut is to say

(r^2)^3 = r^(2*3) = r^6

That explains how we get r^6 in the numerator of the final answer.

The s^3 in the denominator is simply the result of cubing the 's' in the original expression.

Answer:

r2x3 / s1x3

Step-by-step explanation:

Raise both the numerator and denominator to the third power. Multiply by the exponents in the numerator (2x3). Multiply the exponents in the denominator (1x3). PF.

The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

The given parameters are

Degree = 5

Zero = 1, i, 1 + i

There are complex numbers in the above zeros

This means that, the other zeros are

Zeros = 1 - i and -i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)

This gives

P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)

Solving further, we have

P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)

P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)

Evaluate the products)

P(x) = (x³  - x² + x - 1) * (x² - 2x + 2)

This gives

P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2

Express in standard form

P(x) = x⁵ - 2x⁴ - x⁴ + 2x³  + 2x³ + x³ - 2x²  - 2x²  - x² + 2x + 2x - 2

Evaluate the like terms

P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

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Given:

A recipe has a ratio of 6 cups of flour to 2 cups of water.

We need to find the number of cups of water for each cups of flour

So, let the number of cups of water = x

We have the following ratio:

Solve for x:

so, the answer will be:

There are 1/3 cups of water for each cup of flour.

William, this is the solution:

An= -2n - 4

A1 = -2 * 1 - 4

A1 = -6

A2 = -2 * 2 - 4

A2 = -4 - 4

A2 = -8

A3 = -2 * 3 - 4

A3 = -6 - 4

A3 = -10

A4 = -2 * 4 - 4

A4 = -8 - 4

A4 = - 12

A5 = -2 * 5 - 4

A5 = -10 - 4

A5 = - 14

Given:

Given the equation

Required: Rewrite the given equation.

Explanation:

Take the common coefficients of p and add the constants.

Final Answer: The given equation can be rewritten as 4.19p+6.1 = 0

10% = 10/100 = 0.10

therefore:

answer: 2.5

[tex]\framebox{Slope intercept: -$\dfrac{5}{3}$x+3}[/tex]

The slope intercept form of  [tex]5x+3y=9[/tex] would be written as:

[tex]-\frac{5}{3} x+3[/tex]

So,

We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation: