Answers
The sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x) and the type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.
To find f(x) + g(x), we need to add the two functions together:
f(x) + g(x) = (x+2)/(x²-9) + 11/(x²+3x)
To add these fractions, we need a common denominator.
The common denominator in this case is (x² - 9)(x² + 3x), which is the product of the denominators.
Rewriting the fractions with the common denominator, we have:
f(x) + g(x) = [(x+2)(x² + 3x)]/[(x²-9)(x² + 3x)] + [11(x²-9)]/[(x²-9)(x² + 3x)]
Combining the fractions, we have:
f(x) + g(x) = [(x+2)(x² + 3x) + 11(x²-9)]/[(x²-9)(x² + 3x)]
Simplifying the numerator:
[(x+2)(x² + 3x) + 11(x²-9)] = (x³ + 5x² + 6x + 11x² - 99)
= (x³ + 16x² + 6x - 99)
Therefore, the sum f(x) + g(x) is (x³ + 16x² + 6x - 99) / (x²-9)(x² + 3x).
The excluded values for the function f(x) are x = ±3, and for the function g(x), the excluded value is x = 0.
The type of discontinuity for f(x) at x = ±3 is a removable discontinuity, and for g(x) at x = 0, it is an infinite discontinuity or vertical asymptote.
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Related Questions
a survey found that in a city. 19 % of the population owned dogs, 14% of the population owned cats, and 6% of the population owned both a cat and a dog. find the probabililty that a randomly chosen member of the population ownns a cat or a dog.
Answers
The probability that a randomly chosen member of the population owns a cat or a dog is 33%.
How to determine the probabilityGiven information:
Percentage of population owning dogs (D): 19%
Percentage of population owning cats (C): 14%
Percentage of population owning both a cat and a dog (C ∩ D): 6%
To find the probability of owning a cat or a dog (C ∪ D), we use the principle of inclusion-exclusion:
P(C ∪ D) = P(C) + P(D) - P(C ∩ D)
Plugging in the given percentages:
P(C ∪ D) = 14% + 19% - 6%
P(C ∪ D) = 33%
Therefore, the probability that a randomly chosen member of the population owns a cat or a dog is 33%.
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PLEASE HELP. What is a coterminal angle of 31pi over 6?
Answers
The coterminal angle of 31π/6 is angle of 210 degrees.
To find a coterminal angle, we can add or subtract a full revolution (2π) or any multiple of it.
Let's calculate the coterminal angle:
31π/6 = (30π/6) + (π/6) = 5π + π/6
To simplify the angle, we can express it in terms of a common denominator:
5π + π/6 -2π
3π+ π/6
19π/6
570 degrees.
The other coterminal angle is 210 degrees which lies in the third quadrant.
Therefore, the coterminal angle of 31π/6 is 210 degrees.
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Select the correct answer.
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers.
Class A: (2, 5, 7,
6,4,3,8.7.4,5,7,6,3.5.4.2.4.6.3.5)
Class B (3, 7, 6, 4, 3,245,6,7,22,2,3,4,5,2,2,5,6)
Which statement is true for the data sets?
OA. The mean study time of students in Class A is less than students in Class B
OB. The mean study time of students in Class B is less than students in Class A
OC
The median study time of students in Class B is greater than students in Class A
OD. The range of study time of students in Class A is less than students in Class B
OE The mean and median study time of students in Class A and Class B is equal
Answers
The statement is true for the data sets is B. The mean study time of students in Class B is less than students in Class A.
How to explain the meanFor Class A, the mean is 5.3 hours. For Class B, the mean is 5.7 hours. Therefore, OB. The mean study time of students in Class B is less than students in Class A is the correct answer.
For Class A, the median is 5 hours. For Class B, the median is 5 hours. Therefore, OC.
The range is the difference between the largest and smallest values in the set. For Class A, the range is 8 hours. For Class B, the range is 21 hours.
The correct option is B.
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How do i simplify 2u-6u
Answers
Answer:
-4u
Step-by-step explanation:
Just subtract them!
2u-6u = -4u
2-6= -4u combing like terms and simplifying than solving and it turns into -4u so you’re answer is -4u
AREA AND PERIMETER OF SHAPES, HELP PLEASE!
Answers
Answer:
.
Step-by-step explanation:
please help! thank uu!~
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.
The given quadratic equation is x²+4x-9=-4x-7.
Here, x²+4x-9+4x=-7
x²+8x=-7+9
x²+8x=2 ------(i)
Choose coefficient of x, that is 8.
Half of coefficient of x is 4.
Take square of 4, that is 4²=16
Add 16 to both the sides of the equation, we get
x²+8x+16=2+16
(x+4)²=18
Therefore, the intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.
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How can you use the double number line diagram to find what percent 120 is of 150?
Answers
can you send a photo please
Triangle ABC was dilated using a center of dilation at (8, 0) to create image triangle A'B'C'. What scale factor was used to perform this dilation?
2
3
2/3
3/2
Answers
The scale factor that is used to perform the dilation is 3/2
What is dilation?Dilation is a transformation, which is used to resize the object.
Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.
Scale factor is the ratio of the dimension of the new imaged formed to the dimensions of old dimension.
The base of the original triangle is 4 units
The base of the new length = 6 units
Scale factor = 6/4
= 3/2
Therefore the scale factor in the dilation is 3/2.
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In this activity, you will graph systems of linear equations to find their solutions? Use the drawing tools to form the correct answers on the grid. Graph these equations: y = 3x - 5. y = =1/2x+5
Answers
The graph for the equation : y = 3x - 5 and y = =1/2x+5 is attached below.
Equation 1: y = 3x - 5
Choose some x values and calculate the corresponding y values:
For x = 0, y = 3(0) - 5 = -5
For x = 1, y = 3(1) - 5 = -2
For x = 2, y = 3(2) - 5 = 1
Plot the points (0, -5), (1, -2), and (2, 1) on the graph and connect them to form a line.
Equation 2: y = 1/2x + 5
Choose some x values and calculate the corresponding y values:
For x = 0, y = 1/2(0) + 5 = 5
For x = 1, y = 1/2(1) + 5 = 5.5
For x = 2, y = 1/2(2) + 5 = 6
Plot the points (0, 5), (1, 5.5), and (2, 6) on the graph and connect them to form a line.
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what is a number repeated as a term 3 times
Answers
A number repeated as a term three times can be expressed as a sequence or as a repeated multiplication.
A number repeated as a term three times means that the same number is used three times in a row. It can be expressed as a sequence or as a repeated multiplication.
For example, if the number is 5, the expression "5, 5, 5" represents the number 5 repeated three times in a sequence. It indicates that the number 5 is repeated consecutively as three separate terms.
Alternatively, the repeated multiplication of the number can also represent the concept. In this case, "5 x 5 x 5" would be equal to 125, which means that the number 5 is multiplied by itself three times.
In both cases, the idea is that the number is used three times in succession, either as a sequence or through multiplication, resulting in a repeated representation of the number.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
A restaurant Chef made 4 2/3 pints of mushroom soup. Each bowl of soup holds 2/3 of a pint. How many bowls of soup with the chef be able to fill
Answers
The restaurant chef made 4 2/3 pints of mushroom soup and each bowl can hold 2/3 of a pint.
To determine how many bowls of soup the chef will be able to fill, we need to find the quotient of the total amount of soup divided by the amount in each bowl.
First, let's convert the mixed number 4 2/3 to an improper fraction. Multiplying the whole number (4) by the denominator (3) and adding the numerator (2) gives us 14/3.
Now, we can divide the total amount of soup (14/3 pints) by the amount in each bowl (2/3 pint).
We divide a fraction by another fraction, we invert the second fraction and multiply.
We have:
(14/3) ÷ (2/3) = (14/3) × (3/2)
Canceling out the common factor of 3 in the numerators and denominators, we get:
(14/1) × (1/2) = 14/2
= 7
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Find the solutions for each system. x + y = 1, 3y=-3x+3
Answers
First we want to arrange the linear equations such that its in the form y=ax+ b
For the first equation we subtract x from both sides to get:
Y=-X + 1
For the second equation we divide by 3 to get:
y=-x+1
These two equations are the same line so there are infinitely many solutions
An artist's canvas has sides measuring 3x + 5 and 2x + 1 inches.
What is the area of the canvas? Show all work.
The artist laid the canvas flat on the floor and poured some paint in the center. The paint flows at a rate of r(t) = 2t where t represents time in minutes and r represents how far the paint is spreading on the canvas. The area of the paint can be expressed as A[r(t)]= rur?. What is the area of the circle created by the paint?
If the artist wants the circle to be at least 300 in?, will it be that large in 5 minutes? Support your answer with your work.
Answers
The area of the circle created by the paint is given by the expression 4πt².
The area of the circle is 100π, which is approximately 314.16 in².
The circle will be at least 300 in² in 5 minutes. Yes.
To find the area of the canvas, we multiply the lengths of its sides:
Area = (3x + 5) × (2x + 1)
Expanding the expression:
Area = 6x² + 3x + 10x + 5
Combining like terms:
Area = 6x² + 13x + 5
The area of the canvas is given by the expression 6x² + 13x + 5.
Now, let's find the area of the circle created by the paint.
The area of a circle is given by the formula A = πr², where r represents the radius.
The radius is given by the spreading of paint, which is r(t) = 2t.
Substituting the value of r(t) into the formula, we have:
A[r(t)] = π(2t)²
Simplifying:
A[r(t)] = π(4t²)
A[r(t)] = 4πt²
Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.
Substitute t = 5 into the area formula:
A[r(5)] = 4π(5)²
A[r(5)] = 4π(25)
A[r(5)] = 100π
Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.
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Rena, a pharmacy technician, is looking to make a 45%
solution. She has the alligation pictured below.
A.
20
45
Which solution can be used to fill in location A?
O 35
O 40
O45
O 55
Answers
The solution that can be used to fill in location A is 45%.
In this case, Rena is trying to make a 45% solution. The alligation diagram shows two solutions with concentrations of 20% and 45%. The concentration at location A represents the concentration of the final mixture.
To determine the concentration at location A, we can visually observe the positioning of the concentrations on the diagram. The closer a concentration is to location A, the more it contributes to the final mixture.
In this case, the concentration of 45% is closer to location A than the concentration of 20%.
This means that more of the 45% solution should be used in the mixture to achieve a 45% concentration.
Therefore, the solution that can be used to fill in location A is 45%.
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what is an example of ∈-minimal element?
Answers
An ∈-minimal element is an element in a set that is the smallest or least element in terms of a particular relation.
For example, if we have a set of integers {1, 2, 3, 4, 5} and define the relation "divides," where a divides b if b is a multiple of a, then the ∈-minimal element of this set would be 1.
This is because 1 divides every other integer in the set, and there is no smaller element that divides every other integer.
Another example could be a set of strings ordered by length. In this case, the ∈-minimal element would be the string with the smallest length.
In general, ∈-minimal elements are important in mathematical analysis and optimization problems, as they often provide a starting point or solution to larger problems.
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y= 3x-3
x -6 -3. 0 3
y
Answers
Answer:5y-3x
Step-by-step explanation: distributive
Which of the following number lines shows the solution to the inequality given below? 2x − 3 < -9 OR 2x − 3 > 3 A. -10-8-6-4-202468101214 B. -10-8-6-4-202468101214 C. -10-8-6-4-202468101214 D. -10-8-6-4-202468101214
Answers
The number line representation for the solution to the inequality 2x - 3 < -9 OR 2x - 3 > 3 is: -10-8-6-4-202468101214. Option A.
This number line correctly represents the solution to the given inequality. Let's break it down to see why this is the correct answer.
For the inequality 2x - 3 < -9:
Adding 3 to both sides, we get:
2x - 3 + 3 < -9 + 3
2x < -6
Dividing both sides by 2, we have:
x < -3
This means that x must be less than -3. Looking at the number line option A, we can see that it correctly represents the values less than -3 by having a solid line up to the point before -3, indicating that -3 is not included in the solution.
For the inequality 2x - 3 > 3:
Adding 3 to both sides, we get:
2x - 3 + 3 > 3 + 3
2x > 6
Dividing both sides by 2, we have:
x > 3
This means that x must be greater than 3. Looking at the number line , we can see that it correctly represents the values greater than 3 by having a solid line starting from the point after 3, indicating that 3 is not included in the solution.
Therefore, the number line -10-8-6-4-202468101214 correctly represents the solution to the given inequality, showing the values less than -3 and greater than 3. So Option A is correct,
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Find B: 6mi 9mi 5.3mi 8mi 10mi
Answers
The value of B by the given data is 8 mi.
We are given that;
Measurements= 6mi 9mi 5.3mi 8mi 10mi
Now,
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
To find B, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 10 mi and the other two sides are 6 mi and B. We can write:
10^2 = 6^2 + B^2
Simplifying, we get:
100 = 36 + B^2
Subtracting 36 from both sides, we get:
64 = B^2
Taking the square root of both sides, we get:
8 = B
Therefore, by Pythagoras theorem the answer will be 8 mi.
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Part B
If there are 205 students in the school, which is the best estimate of the number of students that are in 1st and 2nd grade?
1st grade: 19%
2nd grade: 14%
Answers
The best estimate of the number of students in the 1st and 2nd grade is approximately 39 students in the 1st grade and 29 students in the 2nd grade.
The best estimate of the number of students in 1st and 2nd grade, we need to calculate the percentages based on the total number of students, which is 205.
1st grade:
19% of 205 students.
To find the number of students in the 1st grade, we multiply the total number of students by the percentage:
19% of 205 = (19/100) × 205
= 0.19 × 205
= 38.95
≈ 39 students.
2nd grade: 14% of 205 students.
Similarly, we calculate the number of students in the 2nd grade:
14% of 205 = (14/100) × 205
= 0.14 × 205
= 28.7
≈ 29 students.
The percentages given represent the distribution of students across the grades accurately.
It is important to keep in mind that actual class sizes and grade distributions may vary.
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what is the inequality of this and step by step explanation please
Answers
The inequality graphed on the number line can be written as:
-3 ≤ x < 2
How to identify the inequality?Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3
A closed circle means that x = -3 is a solution.
And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.
Then the inequality thati is shown in the number line is written as:
-3 ≤ x < 2
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which operation results in a trinomial. (4x5-8x) (3x2-8x+9)
Answers
The operation that will result in a trinomial for the given expression is subtraction operator ( - ).
What is a trinomial?A trinomial is an algebraic expression that has three terms. It is also a polynomial consisting of three terms or monomials.
The given polynomial expression;
( 4x⁵ - 8x ) ? (3x² - 8x + 9 )
To simplify the given polynomial expression into trinomial, we will use the following operation.
The chosen operation will be such that, we will have only three terms left after simplification.
So we will choose subtraction operator "-"
( 4x⁵ - 8x ) - (3x² - 8x + 9 )
= 4x⁵ - 8x - 3x² + 8x - 9
simplify further; (-8x and +8x will cancel out)
= 4x⁵ - 3x² - 9
Finally, we have our desired trinomial as 4x⁵ - 3x² - 9.
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Simplify: x^2-2x-24/x^2+7x+12 * x^2-1/x-6
You must show your work and enter your answer below.
Answers
The expression [tex]\frac{x^2 - 2x - 24}{x^2 + 7x + 12} * \frac{x^2 - 1}{x-6}[/tex] when simplified is [tex]\frac{x^2 - 1}{x + 3}[/tex]
How to simplify the expressionFrom the question, we have the following expression
[tex]\frac{x^2 - 2x - 24}{x^2 + 7x + 12} * \frac{x^2 - 1}{x-6}[/tex]
When the factors of the expression are factorized, we have
[tex]\frac{(x + 4)(x - 6)}{(x + 4)(x + 3)} * \frac{(x - 1)(x + 1)}{x-6}[/tex]
Cancel out the common factors
So, we have
[tex]\frac{1}{(x + 3)} * \frac{(x - 1)(x + 1)}{1}[/tex]
Evaluate the products
[tex]\frac{x^2 - 1}{x + 3}[/tex]
Hence, the expression when simplified is [tex]\frac{x^2 - 1}{x + 3}[/tex]
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The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?
Answers
- g(7) - g(4) = 5/6
- g(x) is a linear function
- The slope of the tangent line to g(x) at x = 5.5 is 5/6
- The derivative of g(x) at x = 5.5 is 5/6
- The graph of g(x) is concave up on the interval [4, 7]
- The graph of g(x) has a local maximum at x = 5.5 and a local minimum at x = 6.5.
calcula el volumen de cada cuerpo
Answers
According to the information we can infer that the volume of the cube is 343cm³ and the rectangular prism is 105cm³.
How to calculate the volume of figures?To calculate the volume of the figures we must take into account the information of the measurements of each of its sides. Once we identify this information we can apply the following procedure. To find the volume of a figure we must multiply its sides, in the case of a cube it would be:
7*7*7=343cm³
On the other hand, to calculate the volume of the rectangular prism we must do the following multiplication:
7*5*3=105cm³
According to the above, the volume of these figures would be: 343cm³ the cube, and the rectangular prism 105cm³.
Note: Here is the question in English:
Calculate the volume of each figure
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What is (x³-8x² + 6x +41) ÷ (x-4)
Answers
Step 1: Write the dividend and divisor:
[tex]\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ [/tex]
Step 2: Divide the first term of the dividend by the first term of the divisor:
[tex]\sf\:\frac{{x^3}}{{x}} = x^2 \\ [/tex]
Step 3: Multiply the divisor (x - 4) by the result (x^2):
[tex]\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ [/tex]
Step 4: Subtract the result from the original dividend:
[tex]\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ [/tex]
Step 5: Bring down the next term from the dividend:
[tex]\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ [/tex]
Step 6: Repeat steps 2-5 with the new dividend:
[tex]\sf\:\frac{{-4x^2}}{{x}} = -4x \\ [/tex]
[tex]\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ [/tex]
[tex]\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ [/tex]
Step 7: Bring down the next term from the dividend:
[tex]\sf\:\frac{{-10x + 41}}{{x - 4}} \\ [/tex]
Step 8: Repeat steps 2-5 with the new dividend:
[tex]\sf\:\frac{{-10x}}{{x}} = -10 \\ [/tex]
[tex]\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ [/tex]
[tex]\sf\:(-10x + 41) - (-10x + 40) = 1 \\ [/tex]
Step 9: There are no more terms to bring down, so the division is complete.
Step 10: Write the final result:
The quotient is [tex]\sf\:x^2 - 4x - 10\\[/tex] and the remainder is 1.
Therefore, the division of [tex]\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\[/tex] is:
[tex]\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ [/tex] [tex]\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ [/tex]
Picture is below to the question
Answers
Answer:
Angle L
Step-by-step explanation:
Angle L is the obtuse angle, as it is the only angle with a measure greater than 90 degrees.
Is the following a statistical question?
) How many pounds are in one kilogram?
yes
No
Answers
No, The given question ''How many pounds are in one kilogram?'' is not a statistical question.
We have to given that,
The question is,
''How many pounds are in one kilogram?''
Since, We know that,
The given question is a straightforward conversion that can be answered with a simple fact or formula.
And, A statistical question is one that seeks to collect and analyze data in order to make inferences and conclusions about a population or sample.
Hence, The given question is not a statistical question.
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The algebraic expression for "the quotient of 42 and x" is
Answers
The algebraic expression for "the quotient of 42 and x" is 42/x.
The algebraic expression for "the quotient of 42 and x" can be represented as 42 divided by x, which is written as 42/x.
In this expression, 42 represents the dividend, which is the number being divided, and x represents the divisor, which is the number by which the dividend is divided.
The division symbol (/) is often used to represent the quotient or the result of the division operation.
So, the algebraic expression for "the quotient of 42 and x" is 42/x.
It's important to note that this expression assumes that x is not equal to zero, as division by zero is undefined.
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h(t) = -4.9t² +27.5t +7.8.
Answers
The graph of given quadratic function is plotted below.
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex: (2.80612244,46.38418367)
Focus: (2.80612244,46.33316326)
Axis of Symmetry: x=2.80612244
Directrix: y=46.43520408
Use the formula x=−b/2a to find the maximum and minimum.(2.80612244,46.38418367)
Therefore, the graph of given quadratic function is plotted below.
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