Can someone help me answer this?
Given the function f(x)= x^2+7x+10 / x^2+9x+20
Describe where the function has a hole and how you found your answer.
We need to simplify the function by factoring the numerator and the denominator. Plug the excluded values into the simplified function to find the hole.
Answers
Answer:
The function f(x) has a hole at point x = - 5.
Step-by-step explanation:
We are given a function as
[tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
Now, we have to describe where the function has a hole.
Now, [tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
⇒ [tex]f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}[/tex]
Therefore, the common factor of the numerator and denominator is (x + 5).
Now, (x + 5) = 0
⇒ x = - 5
Therefore, the function f(x) has a hole at point x = - 5. (Answer)
By factoring and simplifying the function f(x)=(x^2+7x+10)/(x^2+9x+20), we find a hole at x=-5. This is because -5 was an excluded value in the original function, but does not cause the denominator to be zero in the simplified function.
Explanation:The given function is f(x) = (x^2+7x+10) / (x^2+9x+20). To find where the function has a hole, we need to factor both the numerator and the denominator. We also must exclude any values of x that would cause the denominator to be zero as these are undefined in the function.
The numerator factors into (x+2)(x+5), and the denominator into (x+4)(x+5). If we simplify, the x+5 term will cancel out, leaving us with f(x) = (x+2)/(x+4).
Originally, x could not be equal to -4 or -5, as these would make the denominator zero. In the simplified function, only x=-4 causes the denominator to be zero. But since x=-5 was an excluded value in the original function, that indicates there is a 'hole' at x=-5 on the function.
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Related Questions
school starts at 8:55. one day katie was a quarter of an hour late. what time did she arrive
Answers
the answer is 9:10 hope it helps
Final answer:
Katie was a quarter of an hour, or 15 minutes, late to school which starts at 8:55 AM. So, she arrived at 9:10 AM.
Explanation:
If school starts at 8:55 AM and Katie was a quarter of an hour late, that means she was 15 minutes late because a quarter of an hour is 15 minutes (60 minutes divided by 4 equals 15 minutes).
To find out what time Katie arrived, we need to add 15 minutes to the starting time of school:
School starts: 8:55 AM
Time late: + 15 minutes
Time of arrival: 9:10 AM
So, Katie arrived at school at 9:10 AM.
A company makes four different types of candles. The ratio of fragrance to wax for each type of candle is shown in the tables below.
Answers
Answer:
the answer is type 2
Step-by-step explanation:
ok so you first have to find the ratio of all of them and for type 1 it is 40 to 1 for type 2 it is 50 to 1 type 3 is 25 to 1 and type 4 is 30 to 1 so there for type two has the biggest ratio of fragrance to wax
The required table that has a higher ratio of fragrance to wax is type 2.
As given in the question, a company makes four different types of candles. The ratio of fragrance to wax for each type of candle is shown in the tables.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
For Type 1
The ratio of Fragrance to wax.
= 20 / 0.5 = 40 / 1
For Type 2
The ratio of Fragrance to wax.
= 150 / 3 = 50 / 1
For Type 3
The ratio of Fragrance to wax.
= 250 / 10 = 25
For Type 4
The ratio of Fragrance to wax.
= 30 / 1
Now,
50 > 40 > 30 > 25
Type 2 > type 1 > type 3 > type 4
Thus, the required table that has a higher ratio of fragrance to wax is type 2.
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Benford’s law states that the probability that a number in a set has a given leading digit, d, is
P(d) = log(d + 1) - log(d).
State which property you would use to rewrite the expression as a single logarithm, and rewrite the logarithm. What is the probability that the number 1 is the leading digit? Explain.
Answers
Answer:
solutions
Step-by-step explanation:
use the quotient property to rewrite the expression.
write the difference of logs as the quotient log((d+1)/d).
substitute 1 for d to get log(2).
since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.
Answer:
Use the quotient property to rewrite the expression.
Write the difference of logs as the quotient log((d+1)/d).
Substitute 1 for d to get log(2).
Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.
Step-by-step explanation:
Four times a number,y,increased by eight
Answers
I'm assuming your teacher wants you to translate the given sentence into an algebraic expression.
y = some unknown number
4y = 4*y = four times a number y
4y+8 = four times a number, y, increased by 8
Answer: 4y+8Ethan says that the value of 40.7 is 10 times the value of 4.07 is be correct?
Answers
Answer:
He is correct
Step-by-step explanation:
multiplication and division are inverse operations so lets divide to see if he is correct
40.7/10=4.07
he is correct
Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.
According to Ethan, he assumed that the product of 10 and 4.07 is 40.7, we are to check if the calculation of Ethan is correct.
To do that, we will have to multiply 10 with 4.07 as shown below:
[tex]= 10 \times 4.07 \\= 10 \times \frac{407}{100}\\=\frac{4070}{100} \\=40.70[/tex]
Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.
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Solve for u.
3u+4u = 56
Answers
Answer:
8
Step-by-step explanation:
3u+4u=7u
7u=56
u=8 because you divide
Answer:
U=8
Step-by-step explanation:
3u+4u=56
7u=56
u=8
This is 6 grade homework please help me
Answers
Answer:
what is the problem?
Step-by-step explanation:
Answer:
What work do you need help with tag a photo or write it out.
A biology test is worth 100 points and has 36 questions
Answers
Answer:
whats the question?
Step-by-step explanation:
Label each pair of triangles with the postulate or theorem that proves the triangles are congruent.
Answers
Answer:
Δ MNO ≅ Δ PQR by ASA postulate
Step-by-step explanation:
Δ MNO and Δ PQR are congruents because:
1. Their included sides MN and PR are equal (22 units = 22 units)
2. Their angles ∠M and ∠P are equal (100° = 100°)
3. Their angles ∠N and ∠Q are equal (35° = 35°)
Now, we can conclude that Δ MNO ≅ Δ PQR by ASA postulate.
what is triangular number
Answers
Answer:
Theory
Step-by-step explanation:
A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...
Seniors at a high school were asked what color car they drive. The results were put in a circle graph. The measure of each central angle is shown. If a senior is chosen at random from this school, find the probability of each response.
What Color Is Your Car?
Car color is not red or blue.
options:
0.51
0.47
0.53
0.49
Answers
Answer:
P(The color of the car is red) is 0.32 .
P(The color of the car is white) is 0.34 .
P(The color of the car is silver) is 0.19 .
P(The color of the car is blue) is 0.15 .
P(car color is not red or blue) is 0.53 .
Step-by-step explanation:
We know that total angle subtended at the center by a complete circle is
360° .
According to the question,
P(The color of the car is red)
= [tex]\frac {115.2}{360}[/tex]
= 0.32
P(The color of the car is white)
= [tex]\frac {122.4}{360}[/tex]
= 0.34
P(The color of the car is silver)
= [tex]\frac {68.4}{360}[/tex]
= 0.19
P(The color of the car is blue)
= [tex]\frac {54}{360}[/tex]
= 0.15
So
P(car color is not red or blue)
= 1 - (0.15 + 0.32)
= 0.53
Answer:
0.53 is the correct answer.
Step-by-step explanation:
10. The area of Kaitlyn's square garden is 175 square feet. What is the measure of each side
of the garden to the nearest tenth? Support your answer.
Answers
Each side of garden measures 13.2 feet.
Step-by-step explanation:
Given,
Area of Kaitlyn's garden = 175 square feet
As the garden is in square shape, each side will have equal length.
Let,
a be the length of each side.
Area of square garden = A = a²
[tex]a^2=175[/tex]
Taking square roots on both sides
[tex]\sqrt{a^2}= \sqrt{175} \\a=13.22 \ feet[/tex]
Rounding off to nearest tenth,
Length of each side = 13.2 feet
Each side of garden measures 13.2 feet.
Keywords: area, square root
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Use the array to solve the problem 8x9
Answers
Answer:
72
Step-by-step explanation:
multiply
Answer:
72
Step-by-step explanation:
One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Find the two numbers.
Answers
One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7
Solution:
Given that one number is 7 less than a second number.
Twice the second number is 1 less than 5 times the first.
Need to determine two numbers.
Let assume first number be represented by variable x and second number be represented by variable y.
As first number is 7 less than a second number, adding 7 to first number will give us second number
=> x + 7 = y ------ (1)
[tex]\begin{array}{l}{\text { Twice of second number }=2 \times \text { second number }=2 \times y=2 y} \\\\ {\text { 5 times the first number }=5 \times \text { first number }=5 \times x=5 x}\end{array}[/tex]
As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,
=> 2y + 1 = 5x ------ (2)
On substituting value of y as x + 7 from equation 1 into equation 2 , we get
2(x + 7) + 1 = 5x
=> 2x + 14 + 1 = 5x
=> 2x – 5x = -15
=> -3x = -15
x = 5
Substituting x = 5 in equation (1) to get value of y
=> y = 5 + 7 = 12
Hence first number is 5 and second number is 12
(–x^2y^3m)^5 write the monomial in standard form
Answers
Answer:
-m^5*x^10*y^15
Step-by-step explanation:
remember alphabetical order
The standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (–x²y³m)⁵. The standard form of the number will be written as,
E = (–x²y³m)⁵
Solve the exponents and simplify.
E = -m⁵x¹⁰y¹⁵
Therefore, the standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
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Solve the following inequality. Show and explain your work
3(x-6)+2>5x-4
Answers
Answer:
x< (-6)
Step-by-step explanation:
If you have any questions about the way I solved it,don't hesitate to ask
It takes three painters 4 hours to paint 1 classroom.How many hour does it talk 1 painter to paint to classrooms?
Answers
It takes 1 painter 24 hours to paint two class rooms
Step-by-step explanation:
When some worker do a job together, then
The number of worker is varies inversely with the time to finish the job, because 2 workers take time less than 1 worker to finish the same jobWhen y varies inversely with x, then x y = k, where k is constantIf 5 workers finish a job in 2 hours, then 10 workers finish the same job is 1 hour because 5 × 2 = 10 × 1∵ It takes three painters 4 hours to paint 1 classroom
∵ It takes 1 painter x hours to paint 1 class room
- Equate 3 × 4 by 1 × x because they will do the same job
∴ 3 × 4 = 1 × x
∴ 12 = x
∴ It takes 1 painter 12 hours to paint 1 class room
We need to find it takes 1 painter to paint two class room
∵ The painter will paint 2 class rooms
∵ He takes 12 hours to paint 1 class room
- Multiply his time in one class room by 2
∵ 12 × 2 = 24
∴ It takes 1 painter 24 hours to paint 2 class rooms
It takes 1 painter 24 hours to paint two class rooms
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There are 4, 000 books in the towns library. Of these, 2, 600 are fiction. Write a percent equation that you can use to find the percent of the books that are fiction. Then solve your equation.
Answers
The percent equation showing the fiction books is y = 0.65x showing that among the 4,000 books in the library, 2,600 are fiction.
An equation is a mathematical representation of the equality of two expressions.
The number of books in the town's library = 4,000
The number of fiction books = 2,600
The number of nonfiction books = 1,400 (4,000 - 2,600)
The percentage of fiction books to the total number of books = 65% (2,600/4,000 x 100)
Let the total number of books in the library = x
Let the number of fiction books = y
Equation:
y = 0.65x
y = 2,600 (0.65 x 4,000)
3tenths - 3 twentieth
Answers
Answer:
0.15
Step-by-step explanation:
Given expression
3 tenths- 3 twentieth
⇒
[tex]=\frac{3}{10} -\frac{3}{20} \\=\frac{6}{20} -\frac{3}{20}\\=\frac{6-3}{20} \\=\frac{3}{20} \\=0.15[/tex]
Therefore value of given expression is 0.15
The drawing below has four lines . How many lines does it have
Answers
Answer: I think you answered your own question
Step-by-step explanation:
Micheal reads books that have at
most 400 pages in them. He reads around 20 books a year. What is the greatest amount of pages Micheal could have read this year?
Help please!!!
Answers
Answer:
8000
Step-by-step explanation:
you multiply 20 and 400
Answer: He could read at most 8000 pages this year.
4. If the expression 25y^2- 70y+d is a perfect square, where d is a constant, find the
value of d.
Answers
Answer:
d = 49
Step-by-step explanation:
Given that the expression is a perfect square of the form
(ay - b)² = a²y² - 2aby + b²
Then comparing like terms
a²y² = 25y², that is
a² = 25 ⇒ a = 5
and -2aby = - 70y, thus
2ab = 70, that is
2(5)b = 70
10b = 70 ⇒ b = 7
b² = 7² = 49
Hence
25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49
Thus d = 49
If on a scale drawing 75 feet are represented by 45 inches, then a scale of 1/5 inch represents how many feet?
Answers
Answer:
1/3 or 0.33 feet
Step-by-step explanation:
This question can be easily answered by using simple proportions.
If 75 feet are represented by 45 inches on a scale, then the scaling factor from feet to inches is 45/75, or from inches to feet is 75/45
If we have 1/5 inch and want feet, just multiply by 75/45 to get
1/5*75/45=1/3=0.33 feet
Answer:
1/3 feet
Step-by-step explanation:
We are given that
On a scale drawing
45 inches represented =75 feet
We have to find a scale of 1/5 inch how many feet represents.
To find the value in feet represented by a scale of 1/5 inch we will use unitary method.
Using unitary method
45 inches represents =75 feet
1 inch represents =[tex]\frac{75}{45}[/tex] feet
1/5 inch represents =[tex]\frac{75}{45}\times \frac{1}{5}[/tex] feet
1/5 inch represents=[tex]\frac{1}{3}[/tex] feet
Hence, a scale of 1/5 inch represents 1/3 feet
Domain and Range Mapping Diagrams
Determine whether each diagram depicts a function or not.
Function
VOON
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve for x: the quantity of x plus 4 over 3 = 2. (1 point)
Answers
For this case we must solve the following equation:
[tex]\frac {x + 4} {3} = 2[/tex]
We follow the steps below:
Multiplying by 3 on both sides of the equation we have:
[tex]x + 4 = 3 * 2\\x + 4 = 6[/tex]
Subtracting 4 from both sides of the equation:
[tex]x = 6-4\\x = 2[/tex]
Thus, the solution of the equation is[tex]x = 2[/tex]
Answer:
[tex]x = 2[/tex]
How do u solve 4(3x-1)=9-x
Answers
Answer:
x = 1
Step-by-step explanation:
Well the first step is to apply the distributive property:
4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.
And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.
Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.
Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.
[If there's no number in front of a variable, you can always just put 1 in order to make it easier]
12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13
Finally, 13x = 13. Divide 13 ÷ 13 to get 1.
x = 1
The length of a rectangle is three times width. If the perimeter of the rectangle is 40cm, find its length and width?
Answers
Answer:
width = 5
length = 15
Step-by-step explanation:
width: x
length : 3x
x + 3x + x + 3x = 40
8x = 40
x = 5
width = 5
length = 15
21 divided by 14 and checking with Multiplication
Answers
Answer:
21 divided by 14 is 1.5
and
1.5 x 4 = 21
The calculated division of the numbers 21 divided by 14 is 3/2
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
21 divided by 14
When represented as an equation, we have
21 divided by 14 = 21/14
Divide 21 by 14
So, we have the following result
21 divided by 14 = 3/2
Using the above as a guide, we have the following:
the result is 3/2
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The perimeter of a basketball court is 90 meters and the length is 6 meters longer than twice the width. What are the length and width?
Answers
The length of basketball court is 32 meters and width is 13 meters.
Step-by-step explanation:
Perimeter = 90 meters
Let w be the width
Length = l = 2w + 6
As basketball court are in rectangular shapes, therefore,
Perimeter = 2(length+width)
[tex]90=2(2w+6+w)\\90=2(3w+6)\\90=6w+12\\90-12=6w\\6w=78[/tex]
Dividing both sides by 6;
[tex]\frac{6w}{6}=\frac{78}{6}\\w=13\ meters[/tex]
Length = 2w+6
[tex]l=2(13)+6\\l=26+6\\l=32\ meters[/tex]
The length of basketball court is 32 meters and width is 13 meters.
Keywords: perimeter, rectangles
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Choose the correct solution and graph for the inequality-5y<_-15
Answers
For this case we have the following inequality:
[tex]-5y \leq-15[/tex]
To solve, we follow the steps below:
We divide between 5 on both sides of the inequality:
[tex]-y \leq \frac {-15} {5}\\-y \leq-3[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]y \geq3[/tex]
Thus, the solution is given by all values of "y" greater than or equal to 3.
Answer:
[tex]y \geq3[/tex]
See attached image
The vertical axis represents the "y" axis