if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x

A. find f(x)+g(x)

B. list all of the excluded values

C. classify each type of discontinuty


To receive​ credit, this must be done by Algebraic method​s, not graphing

Answer:

Step-by-step explanation:

3x3x3= 27

Answer:

Step-by-step explanation:

the answer is 69 the if we round of

Answer:

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x = 5/7,−3,3

Step-by-step explanation:

Both planes will reach the city at the same time again at 11 PM.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

As 5 and 3 are prime numbers, the least common factor is given as follows:

5 x 3 = 15.

15 hours after 8 AM is of 11 PM.

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The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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The length x in the similar triangles is given as follows:

x = 15 cm.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The proportional relationship for the side lengths in this triangle is given as follows:

x/25 = 9/15 = 18/30

Hence the value of x is obtained as follows:

x/25 = 9/15

15x = 25 x 9

x = 25 x 9/15

x = 15 cm.

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Hence the surface area of the given figure 168 km².

In the given prism contains

3 rectangular surface,

For rectangular surface 1:

Length = 6 km

Width = 7 km

Surface area = 6x7

                      = 42 km²

For rectangular surface 2:

Length = 8 km

Width = 7 km

Surface area = 8x7

                      = 56 km²

For rectangular surface 3:

Length = 10 km

Width = 7 km

Surface area = 10x7

                      = 70 km²

Hence total surface area of the given figure is,

⇒ 42 + 56 + 70

⇒ 168 km²

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The quotient of[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

To simplify the expression[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10)),[/tex] we can use the rule for dividing fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal.

Let's simplify the expression :

Simplify the numerator and denominator of the first fraction.

The numerator is 6x, and the denominator is (3x+15).

We can factor out a common factor of 3 from the denominator, which gives us 3(x+5).

So the first fraction simplifies to 6x / 3(x+5).

Simplify the numerator and denominator of the second fraction.

The numerator is (x^2+2x), and the denominator is [tex](x^2+7x+10).[/tex]

We can factor both the numerator and denominator:

Numerator: x(x+2)

Denominator: (x+5)(x+2)

Canceling out the common factor of (x+2), we are left with x / (x+5).

Multiply the two simplified fractions.

Multiplying the fractions, we get:

[tex](6x / 3(x+5)) \times (x / (x+5))[/tex]

Simplify the resulting expression.

Canceling out the common factor of (x+5) in the numerator and denominator, we are left with:

2x / 1

So the quotient simplifies to 2x.

Therefore, the quotient of [tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

The square inches of cardboard paper used is 56.8 square inches

From the question, we have the following parameters that can be used in our computation:

The prism

The square inches of cardboard paper is the surface area of the pyramid

And this is calculated as

Area = bh + L(Sum of side lengths)

Using the above as a guide, we have the following:

Area = 2 * 3.2 + 6 * (2 + 3.2 + 3.2)

Evaluate

Area = 56.8

Hence, the square inches of construction paper used to make the container is 56.8 square inches

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Answer:

189

Step-by-step explanation:

To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.

31.5 percent = 31.5/100 = 0.315

Multiplying 0.315 by 600 gives us:

0.315 * 600 = 189

Therefore, 31.5 percent of 600 is equal to 189.

The correct options are:

1) A, it is the midline.

2) D, the center is 35 meters above the ground.

The highlighted segment is the red dashed line that goes along with the graph of the sinusoidal function.

That line is called the midline of the function, which is the constant term of any sinusoidal function.

In this case, we know that this function represents the height of the blades, then that midline means that the turbine center is at 35 meters (the midline) above the ground.

So the correct options are A and D.

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Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Answer:

Step-by-step explanation:

The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.

Area of the rectangle = Length * Width

Plugging in the given values:

Area = 3 cm * 2 cm

Multiplying 3 cm by 2 cm gives us:

Area = 6 cm²

Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².

The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).

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These are the coordinates of the vertices of the transformed triangle.

Vertex A: (-15, 8)

Vertex B: (-4, 5)

Vertex C: (-9, 6)

To plot ΔABC and perform the given transformations, let's follow the steps:

Plot ΔABC:

Point A(10,4)

Point B(-1,1)

Point C(4,2)

Reflect ΔABC by multiplying the x-coordinates by -1:

Reflecting A: (-10,4)

Reflecting B: (1,1)

Reflecting C: (-4,2)

Translate the reflected triangle using the function (x,y) → (x-5, y+4):

Translating (-10,4): (-10-5, 4+4) = (-15, 8)

Translating (1,1): (1-5, 1+4) = (-4, 5)

Translating (-4,2): (-4-5, 2+4) = (-9, 6)

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Answer:

Set your calculator to degree mode.

x^2 = 4^2 + 10^2 - 2(4)(10)(cos 29°)

x^2 = 46.0304

x = 6.78

The number that belongs in the green box is 6.78.

The length of the arc can be obtained as follow:

Length of arc = 2πr × (θ / 360)

Length of arc = (2 × π × 7) × (210 / 360)

Length of arc = 49π / 6 ft (option D)

How do i determine the area of the sector?

i. The area of the sector can be obtained as shown below:

Area of sector = πr² × (θ / 360)  

Area of sector = (π × 19²) × (135 / 360)  

Area of sector = 1083π / 8 in² (option D)

ii. The area of the sector can be obtained as shown below:

Area of sector = πr² × (θ / 360)  

Area of sector = (π × 10²) × (165 / 360)  

Area of sector = 275π / 6 m² (option B)

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Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.

In order to answer your question accurately, I would need the specific values for Manuel's profit and cost functions. The information you provided is incomplete, as you mentioned Manuel's initial profit hill is plotted in green on a graph, but the graph itself is not available for reference.

To determine how a change in fixed costs affects the profit-maximizing quantity, we typically analyze the cost and revenue functions. Without these functions or the corresponding data, it is not possible to provide an exact numerical answer.

However, I can explain the general concept. Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.

When fixed costs decrease, it reduces the overall cost of production for each level of output. This means that Manuel can achieve higher profits or reduce losses for any given level of sales. Consequently, the profit-maximizing quantity may change as a result.

If we assume that the decrease in the price of the permit is the only change in fixed costs and all other factors remain constant, the new profit hill can be expected to shift upward. This is because the reduction in fixed costs increases the potential for higher profits at each level of output.

Without more specific information about Manuel's profit and cost functions, it is not possible to determine the exact profit-maximizing levels before and after the decrease in the price of the permit.

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Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

The restriction of a function f is when the domain of f is limited to a subset of its original domain.

The restriction of a function f can be demonstrated by considering a function f: R -> R, where R represents the set of real numbers.

Let u say f(x) = x^2. Now, if we restrict the domain of f to the interval [0, 5], the new function becomes f restricted: [0, 5] -> R and its expression would be f restricted(x) = x^2 for x in the interval [0, 5].

This means that the function f restricted only takes inputs from the interval [0, 5] and behaves the same way as the original function within that interval.

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The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

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4 will divide the 348 is 8 and 2 left, so you will write the two and move the 8 down, which is now 28, then divide the 28 by 4. It will be 7.

1) The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

2) Total area to be covered:

= 720 square feet.

3) You will need 1.8 gallons of paint to cover all four walls of the room.

Now, The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

And, The total area to be covered is:

For the two 20 feet long walls:

A = 20 feet x 8 feet

A = 160 square feet each.

And, For the two 25 feet long walls:

A = 25 feet x 8 feet

A = 200 square feet each.

Hence, Total area to be covered:

= (160 + 160 + 200 + 200) square feet

= 720 square feet.

For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:

Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint

Number of gallons of paint needed = 720 square feet / 400 square feet per gallon

Number of gallons of paint needed = 1.8 gallons

Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.

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The first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4

From the question, we have the following parameters that can be used in our computation:

The generalized Fibonacci sequence

In the sequence, we can see that the last two terms are added to get the new term

Also, we have

a(1) = -19

a(2) = 14

Using the above as a guide, we have the following:

a(3) = -19 + 14 = -5

a(4) = -5 + 14 = 9

a(5) = 9 - 5 = 4

Hence, the first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4

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