What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark

{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}

The solution of the inequality in set-builder notation is {p I p ≥ 1}.

The correct option is A.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

2(3p-11) ≥ -16

Solving the parenthesis,

6p-22 ≥ -16

6p  ≥ -16 + 22

6p  ≥ 6

p ≥ 1

Therefore, the solution is {p I p ≥ 1}.

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The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.

The number of minutes to read 6.25 pages will be given as,

⇒ 6.25 x 0.8

⇒ 5 minutes

The number of minutes to take the test will be given as,

⇒ 5.5 - 5

⇒ 0.50 minute

⇒ 0.50 x 60

⇒ 30 seconds

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

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The cost for one pound of birdseed should be $0.67. The solution has been obtained using the unitary method.

What is a unitary method?

In the unitary method, the value of a single unit is first calculated, and only then is the value of the necessary number of units calculated. The unitary technique, to put it simply, is used to calculate the value of a single unit from a given multiple.

We know that cost per pound = Total pounds/cost

So, for Mariela

15 pounds = $10.00      

1 pound = $0.67  

For Mark,

12 pounds = $8.00  

1 pound = $0.67

For Daryl,

18 pounds = $12.00    

1 pound = $0.67

Hence, the cost for one pound of birdseed should be $0.67.

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Since, the question is incomplete, the complete question has been attached below

Answer: X=-6

Step-by-step explanation: Since both logarithms have a base of 9, we can simply get rid of them. We could also do 9^(log9(8-2x))=9^(log9(-3x+2)). This would eliminate the logarithms.

Now we are just left with a simple algebraic equation: 8-2x=-3x+2.

We add 3x on both sides to get 8+x=2. We subtract 8 on both sides to get x=-6. There is no need to create a domain for the values of x since this is not an inequality problem.

The centroid of the region in the first quadrant bounded by the curves [tex]\(y = x^9\)[/tex] and [tex]\(x = y^9\)[/tex] is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

The centroid is given by the following formulas:

[tex]\[\bar{x} = \dfrac{\int_{a}^{b} x \cdot f(x) \, dx}{\int_{a}^{b} f(x) \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{c}^{d} y \cdot g(y) \, dy}{\int_{c}^{d} g(y) \, dy}\][/tex]

Where f(x) and g(y) are the functions that define the curves bounding the region.

Since we want to find the centroid of the region in the first quadrant, the intersection points of the two curves in the first quadrant.

The curves intersect at (1, 1).

Now, let's find the centroid of the region in the first quadrant.

First,  find the limits of integration:

1. For x:

The curve  [tex]\(y = x^9\)[/tex] is the upper curve, and it intersects the x-axis at x = 0  and the y-axis at x=1.

So, the limits of integration for x are [tex]\(0 \leq x \leq 1\)[/tex].

2. For y: The curve [tex]\(x = y^9\)[/tex] is the right curve, and it intersects the y-axis at y=0 and the x-axis at y=1.

So, the limits of integration for y are [tex]\(0 \leq y \leq 1\)[/tex].

Now,  set up the integrals:

[tex]\[\bar{x} = \frac{\int_{0}^{1} x \cdot x^9 \, dx}{\int_{0}^{1} x^9 \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{0}^{1} y \cdot y^9 \, dy}{\int_{0}^{1} y^9 \, dy}\][/tex]

1. [tex]\(\int_{0}^{1} x \cdot x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x \cdot x^9 \, dx = \int_{0}^{1} x^{10} \, dx[/tex]

                 [tex]= \left[\dfrac{x^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

2. [tex]\(\int_{0}^{1} x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x^9 \, dx = \left[\dfrac{x^{10}}{10}\right]_{0}^{1}[/tex]

             [tex]= \dfrac{1}{10}\][/tex]

3.[tex]\(\int_{0}^{1} y \cdot y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y \cdot y^9 \, dy = \int_{0}^{1} y^{10} \,[/tex] dy

                 [tex]= \left[\dfrac{y^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

4. [tex]\(\int_{0}^{1} y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y^9 \, dy = \left[\frac{y^{10}}{10}\right]_{0}^{1}[/tex]

            [tex]= \dfrac{1}{10}\][/tex]

Now, the centroid coordinates:

[tex]\[\bar{x} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

[tex]\[\bar{y} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

So, the centroid of the region is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

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The original cost for each concert ticket is given as follows:

$34.

The original cost for each concert ticket is obtained applying the proportions in the context of this problem.

The fee for a single ticket is divided as follows:

Hence the proportional relationship that models the cost of purchasing x tickets is given as follows:

y = (5 + n)x.

Alex purchased 3 concert tickets, meaning that x = 3, for a total of $117, meaning that y = 117, hence the original cost n is obtained as follows:

117 = (5 + n) x 3

Dividing by 3 on both sides, we have that:

5 + n = 39

n = 39 - 5

n = $34.

Which is the original cost for each concert ticket.

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Answer:

See attached graph.

Step-by-step explanation:

Given equation:

[tex]y+4=\dfrac{2}{5}(x-3)[/tex]

Expand the right side of the equation:

[tex]\implies y+4=\dfrac{2}{5}x-\dfrac{6}{5}[/tex]

Subtract 4 from both sides of the equation:

[tex]\implies y=\dfrac{2}{5}x-\dfrac{26}{5}[/tex]

Substitute x = 3 into the equation:

[tex]\implies y=\dfrac{2}{5}(3)-\dfrac{26}{5}[/tex]

[tex]\implies y=\dfrac{6}{5}-\dfrac{26}{5}[/tex]

[tex]\implies y=-\dfrac{20}{5}[/tex]

[tex]\implies y=-4[/tex]

Substitute x = -2 into the equation:

[tex]\implies y=\dfrac{2}{5}(-2)-\dfrac{26}{5}[/tex]

[tex]\implies y=-\dfrac{4}{5}-\dfrac{26}{5}[/tex]

[tex]\implies y=-\dfrac{30}{5}[/tex]

[tex]\implies y=-6[/tex]

To graph the given equation, plot the two found points on the given coordinate plane:

Draw a straight line through the points.

(See attachment).

The ratio of green to yellow marbles is 3/2.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given:

For every 3 green marbles James has, he has 2 yellow marbles.

We have to find the ratio of green to yellow marbles.

As for every 3 green marbles James has, he has 2 yellow marbles.

So, the the ratio of green to yellow marbles is 3/2.

Hence, the ratio of green to yellow marbles is 3/2.

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This year 71, 274 ounce cream used.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A French restaurant used 203,640 ounces of cream last year.

This, year 65% less cream used.

So, this year the amount of cream used

= 203640 - 203640 x 65%

= 203640 - 203640 x 0.65

= 203640 - 132366

= 71274 ounce

Hence, 71274 ounce cream used this year.

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Answer:

Should be Ones: 1, Tenths: 2, Hundredths: 5

Step-by-step explanation:

Answer:

53.333

Step-by-step explanation:

400/15 x 2 = 53.333

The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.

A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.

The information is given below.

PT = 3x + 6 and TQ = 5x - 6

T is the midpoint of PQ. Then the equation is given as,

PT = TQ

3x + 6 = 5x - 6

2x = 12

x = 6

Then the length of the line segment PT will be given as,

PT = 3(6) + 6

PT = 18 + 6

PT = 24 units

The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.

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The scale factor of the model to the real-life player is 6:76. This can be read as 6/76 or 0.0789 or 0.079(approximately)

The scale factor is a ratio that compares the size of the model to the size of the real-life object. In this case, the scale factor of 6:76 tells us that for every 76 inches of the real-life player, the model is only 6 inches. In other words, the model is 6/76 or approximately 0.0789 times smaller than the real-life player.

In general, a scale factor is a number used to multiply all the dimensions of an object to get a corresponding model or representation of that object, where the ratio of the corresponding dimensions between the real-life object and the model is represented by the scale factor.

It should be noted that the scale factor can also be represented in fraction or decimal form, but the colon notation gives a more meaningful representation of the comparison of the size between the model and the real-life object.

Answer: The scale factor for the basketball player to the model is 16 inches to 1 inch

Step-by-step explanation:

Answer:

y = -2x

Step-by-step explanation:

The equation is y = mx +b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,-4); we see the y decrease by 4 and the x increase by 2, so our slope is

m = -4/2 = -2

Y-intercept is when x = 0, y-intercept is located at (0,0)

So our equation is

y = -2x

Answer: 3/2

Step-by-step explanation:

Answer:

3/2 or 1 1/2

Step-by-step explanation:

[tex]2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}[/tex]

Answer:

9,000

Step-by-step explanation:

5(3)=15

3000(3)=9000

The better car is car A and Sam would pay $70.

We can see that we can only be able to judge the better car by the way that the gas is able to consume fuel. We can now see that the cars are two and we have the gas consumption of each as;

For car A = 75 miles / 5 gallons = 15 miles/gallon

For car B = 240 miles/ 20 gallons = 12 miles/gallon

As such car A is the better car.

Miles to be covered = 300 miles

If 1 gallon takes 15 miles

x galloons takes 300 miles

x = 20 gallons

If 14 gallons cost $49.42

1 gallon costs  49.42/14

=$3.5

Sam would pay; $3.5 * 20

= $70

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The number of people at the graduation party would be 57.5, so the quantity of food required for them is Food item A  = 65 piece, Food item B  = 14(1/6) pounds and Food item C  = 4(3/8) pounds.

What is fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Number of guests in the graduation party, a = 40

Number of drop in guests at the graduation party,  b = 35

Now, drop-in guests are counted as half a guest, so the number becomes b = 35/2.

Total number of guests = a + b

Total number of guests = 40 + 35/2

Total number of guests = (80+35)/2

Total number of guests = 115/2

Total number of guests = 57(1/2)...

The table shows amount of food -

Food item A 26 piece, Food item B  5(2/3) pounds and Food item C  1(3/4) pounds.

Also, it recommends amount of food to order for 23 party guests.

So, number of groups having 23 people -

= 2(23) + 11.5 group

= 2(23) + 1(1/2) group...

Therefore, there should be 2(1/2) times quantity of food mentioned in the table.

For Food item A  - 26 × 2(1/2)

= 26 × 5/2

= 65 piece

For Food item B  - 5(2/3) × 2(1/2)

= 17/3 × 5/2

= 85/6

= 14(1/6) pounds...

For Food item C  - 1(3/4) × 2(1/2)

= 7/4 × 5/2

= 35/8

= 4(3/8) pounds...

Therefore, the quantity of food for party should be Food item A  = 65 piece, Food item B  = 14(1/6) pounds and Food item C  = 4(3/8) pounds.

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Answer:

  a) 144°

  b) 90°

Step-by-step explanation:

You want the measures of the 2nd largest, and the smallest, of the angles in a hexagon whose ratios are 5:5:6:7:8:9.

The interior angles of a hexagon will have a sum of ...

  180°×(n -2) = 180°×(6 -2) = 720°

The sum of the numbers in the given ratio is ...

  5+5+6+7+8+9 = 40

This tells us that multiplying the ratio values by 720/40 = 18 will give the angle values:

  90:90:108:126:144:162

The second largest angle is 144°.

The smallest angle, 90°, is the one that is repeated.

Probability is the possibility that something will occur. The probability is computed by dividing the total number of outcomes by the number of possible ways the event could occur.

How do I calculate probability?

Adding the aforementioned figures in the third column yields a total of 2,598,960, which is the total number of potential hands.

The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability.

The 36 numbered cards go from 2 through 10, and there are 12 face cards (Kings, queens, and jacks). There will be 51 total cards left when the first face card is pulled, leaving 11 face cards.

Each of the four suits—Spades, Hearts, Diamonds, and Clubs—has 52 cards in a "normal" deck of playing cards. The 13 cards in each suit are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.

Here's one possible solution:

Let's start by assigning the numbers to the 5 cards:

Heart: 1

Spade: 2

Club: 7

Diamond: 8

Spade: 9

The sum of the numbers on the even-numbered cards (2, 8) is 10, which is equal to the sum of the numbers on the odd numbered cards (1, 7, 9). The sum of the black cards (7, 9) is 16, which is equal to the sum of the spades (2, 9). The sum of the red cards (1, 8) is 9, which is equal to 10.

So, the 5 cards are:

1 of Heart

2 of Spade

7 of Club

8 of Diamond

9 of Spade

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Answer:

An equivalent expression for (52 • 34)3 would be (52 • 34) • (52 • 34) • (52 • 34)

Another way to express this is (52)3 • (34)3

So it can also be written as (5^32^3) * (3^44^3)

It can be also expressed as 125 * (81*64)

This expression is the result of multiplying three times the product of 5^2 and 3^4

Answer:3 cm to 15 km

Step-by-step explanation:

The solution to the equation -3x - 6 = -4x + 5 is x = 11.

What is equation?

An equation is a mathematical statement that uses an equals sign (=) to show that two expressions have the same value.

To solve for x in the equation -3x - 6 = -4x + 5, we need to isolate the variable x on one side of the equation. We can do this by adding 4x to both sides of the equation to eliminate the negative 4x term on the right-hand side:

-3x - 6 + 4x = -4x + 5 + 4x

Simplifying the left-hand side by combining like terms, we get:

x - 6 = 5

Finally, to isolate x, we add 6 to both sides of the equation:

x - 6 + 6 = 5 + 6

Simplifying the left-hand side and the right-hand side, we get:

x = 11

Therefore, the solution to the equation -3x - 6 = -4x + 5 is x = 11.

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At 0 seconds and 12 seconds, the electric vehicle is not moving.

The most crucial scientific notion is measurement.

Base or physical fundamental units are used to quantify a wide range of quantifiable quantities.

One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

Since speed simply has a direction and no magnitude, it is a scalar quantity.

When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed.

Average speed is the constant speed determined by the ratio of the total distance traveled by an object to the total amount of time it took to travel that distance.

According to our question-

At the start of the test, x: represents the time in seconds.

Y: stands for the speed, expressed in miles per hour.

Then, we have this:

x = 0 —-> y = 0

x = 12 —-> y = 0

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The algebraic expression for "the result of subtracting j from 13" can be written as 13 - j.

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The 427 is in the sets of the whole number, real number, rational number, natural number, and integers.

What is set?

A set is a collection of clearly - defined +ique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 427

The number 427 is in the set of whole numbers

The number 427 is in the set of real numbers

The number 427 is in the set of rational numbers because it can be written as in the form of p/q.

The number 427 is in the set of natural numbers

The number 427 is in the set of integer numbers

Hence, the 427 is in the sets of the whole number, real number, rational number, natural number, and integers.

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Answer:

From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.

Step-by-step explanation:

From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.

Therefore, the linear function that relates y to x, using this table, is:

y = -7

It's a constant function, no matter what the x value is, the y value is always -7.

In the given word problem amount does Teresa spends is $16.50.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

The amount does Jayson Spends = $3.75

According to the question,

Myra spends 3times as much as Jayson . then

Amount does Myra spends = 3× 3.75 = $11.25.

Now Teresa spends $5.25 more than Myra then,

Amount does Teresa spends = 11.25+5.25 = $ 16.50.

Hence In the given word problem amount does Teresa spends is $16.50.

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Answer: 6

Step-by-step explanation:

12 ÷ 6 = 2

30 ÷ 6 = 5