given f (x)=x-4/x^2+13x+36 which of the following is true
Answers
The function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is a rational function
The simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is [tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
How to simplify the function?The function expression is given as:
f(x) =x - 4/x^2 + 13x + 36
Rewrite properly as:
[tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex]
Expand the denominator
[tex]f(x) =\frac{x - 4}{x^2 + 4x + 9x + 36}[/tex]
Factorize the denominator
[tex]f(x) =\frac{x - 4}{x(x + 4) + 9(x + 4)}[/tex]
Factor out x + 9
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
Hence, the simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
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Answer: f(x) is increasing for all x > -4
Proof of validity is shown below.
Related Questions
The length of a rectangle is three feet less than twice its width. Ifx represents the width of the rectangle, in
feet, which inequality represents the area of the rectangle that is at most 30 square feet?
O x(3 - 2.c) < 30
O <(2x - 3) < 30
O 2(3 – 23) > 30
O x(2x - 3) > 30
Answers
x(2x - 3) > 30
hope it helps...!!!
Academic Testing Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 50% of the seniors who do go on to a career in physics still fail the test. Further, 80% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics? (Round your answer to four decimal places.)
Answers
Answer:
ledsen jag vet inte din fråga väldigt ledsen vara vän med dig
What is the five-number summary of this data set?
{403, 276, 649, 786, 274, 189, 654, 652, 572}
Drag the numbers into the boxes to correctly complete the five-number summary.
Minimum
Q1
Q2
Q3
Maximum
(choices)
189 274 275 276 572 652 653 654 786
Answers
Answer:
Minimum: 189
Q1: 275
Q2: 572
Q3: 653
Maximum: 786
Step-by-step explanation:
I took the test, I got it wrong but I looked back at the answer I hope this helped. And I am sorry this is late.
Answer:
Minimum: 189
Q1: 275
Q2: 572
Q3: 653
Maximum: 786
Step-by-step explanation:
I took the test, I got it wrong but I looked back at the answer I hope this helped. And I am sorry this is
Explain why this comparison is either reasonable or not reasonable. 7.52 > 7.5
Answers
Answer:
Step-by-step explanation:
7.52 is greater than 7.5 because 7.52 has 2 hundredths more value as 7.5 is only 7.50.
Find an equation of the ellipse that has center (2,0), a major axis of length 12, and endpoint of minor axis (5,0).
Answers
The standard formula of the ellipse with center (2, 0), a major axis of length 12 and endpoint of minor axis (5, 0) described in the statement is (x-2)²/9 + y²/36 = 1.
How to derive the equation of the ellipse based on given information
The ellipse is a kind of conic whose formula in standard form is shown below:
(x-h)²/b²+(y-k)²/a² = 1 (1)
Where:
x, y - Orthogonal axes of the ellipse.h, k - Location of center of the ellipse.b - Length of the minor semiaxis.a - Length of the major semiaxis.In this question we are supposed to construct the standard equation the ellipse by replacing all the variables. If we know that b = 3, a = 6, h = 2 and k = 0, then the standard equation of the ellipse is:
(x-2)²/9 + y²/36 = 1 (2)
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Prism X is a dilation of Prism Y. The height of Prism X is 10 1/3 ft, and the volume of Prism X is 74 2/5 ft³. The height of Prism Y is 5 1/6 ft.
What is the volume of Prism Y?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer:
The volume of Prism Y which is dilated to form prism X is 981 1/3 ft³
Brainleist
help pls
10 points
Answers
Answer:
[tex]m \angle A = 100 \degree[/tex]
Step-by-step explanation:
Given:
[tex]m \angle A= (x-60) \degree \\ m \angle B= (x-40) \degree \\ m \angle C= 130\degree \\ m \angle D= 120\degree \\ m \angle E= 110\degree \\ m \angle F= (x-20) \degree[/tex]
Also, the given diagram is a perfect hexagon, having sum of all interior angles 720°
To find:
[tex]m \angle A= ?[/tex]
Solution:
[tex] \sf \: Sum \: of \: all \: interior \: angles = 720 \degree \\ \sf \: m \angle A + m \angle B + m \angle C + m \angle D + m \angle E + m \angle F = 720 \degree\\ \sf \: (x - 60) + (x - 40) +130 + 120 + 110 + (x - 20) = 720 \degree \\ \sf \: 3x - 120 + 120 + 240 = 720 \\ \sf 3x - \cancel{120}+ \cancel{120} + 240 = 720 \\ \sf 3x = 720 - 240 \\ \sf 3x = 480 \\ \sf x = \frac{480}{3} \\ \fbox{\sf x = 160 \degree}[/tex]
Substituting the value of x in,
[tex]m \angle A= (x-60) \degree \\ m \angle A= 160-60 \\ m \angle A = 100 \degree[/tex]
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Answer:
the answer is 100
Step-by-step explanation:
What is the value of x in the proportion below?
5/60=8/x
Answers
Answer:
x = 96
Step-by-step explanation:
5 = 8
__ __
60 x
*do cross multiply
5x = 8x60
5x = 480
x = 480/5
x = 96
Ryan is working on his first budget. He has placed all of the fixed expenses on the budget shown and then would like to use the information to evaluate his variable expenses. Ryan's take-home pay is 2,500 each month. Complete the table below the answer the questions below.
please help me
complete the table and answer the four questions below if you tell me how to do I'll be happy to mark you brainlest!!!
1) what percent of his monthly budget do his transport costs account for?
2) what percent of his monthly budget has he accounted for?
3) Ryan would like to save 10% of his take-home pay towards retirement. How much would he be able to save each month?
4) Assume that Ryan does save 10% for retirement. If he allocates the remainder of his take-home pay to entertainment compromise of the total monthly budget? How much will be budgeted towards entertainment?
Answers
The percent of his monthly budget that his transport costs account for will be 17.8%.
How to calculate the percentage?The percent of his monthly budget that his transport costs account for will be:
= 325/(800 + 450 + 125 + 325 + 125) × 100
= 325/1825 × 100
= 17.8%
The percent of his monthly budget has he accounted for will be:
= 1825/2500 × 100
= 73%
When he saves 10% of his take-home pay towards retirement, the amount saved will be:
= 10% × $2500
= $250
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The percent of Rayan's monthly budget that his transport costs account for will be 17.8%.
1. The proportion of his monthly budget that his transit expenses make up is:
= 325/(800 + 450 + 125 + 325 + 125) × 100
= 325/1825 × 100
= 17.8%
The proportion of his monthly budget that he has already accounted for is:
= 1825/2500 × 100
= 73%
He will save the following sum for retirement if he sets aside 10% of his after-tax income:
= 10% × $2500
= $250
The answer is $250.
2. To find the percentage of his monthly budget accounted for by transport costs, we add up the amounts for Car Payment and Gas:
$325 + $125 = $450.
Then we calculate the percentage: (450 / 2500) x 100% = 18%. Therefore, his transport costs account for 18% of his monthly budget.
3. To find the percentage of his monthly budget accounted for overall, we sum up all the amounts in the table:
$800 + $450 + $125 + $325 + $125 = $1,825.
Then we calculate the percentage: (1825 / 2500) x 100% = 73%. Therefore, he has accounted for 73% of his monthly budget.
4. To calculate how much Ryan can save each month for retirement, we take 10% of his take-home pay:
10% of $2,500 = $250.
Thus, he can save $250 each month for retirement.
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julia has 3/4 quart of ice cream. She gives 3/7 of it to her sister. How many quarts of ice cream does JULIA HAVELEFT?
Answers
3/4 = 21/28
4/7= 12/29
21-12=9
9/28
What is the approximate volume of the cylinder? Use 227 for π. Round to the nearest whole.
A cylinder with radius 3 centimeters and height 7 centimeters.
66 cm3
132 cm3
198 cm3
264 cm3
Answers
Answer:
The answer is 198cm3.
Step-by-step explanation:
Since the radius is 3 and the height is 7, use V=πr^2h
V=πr^2h=π·3^2·7=197.92034
round to the nearest whole and it gives you 198cm3
Answer:
C
Step-by-step explanation:
198 cm3
HOPE I WAS ABLE TO HELP!
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
Answers
Answer:
c
Step-by-step explanation:
I can do this so fast I know I am a high school
what numbers multiplied gives you -70 but added gives you -33
Answers
Answer:
-35, 2
Step-by-step explanation:
When you multiply -35*2 you will get -70
When you add a positive number to a negative number you will take the larger number and if it is negative you will add the positive and if it is positive you take away negative so -35+2 will be -33
PLEASE HELP ME IM LOSIN ALOT OF POINTS
Answers
Easy math pls help quick will give brainlest
Answers
Answer:Easy math pls help quick will give brainlest
Easy math pls help quick will give brainlest
Easy math pls help quick will give brainlestStep-by-step explanation:
is your correct answer
how do I find the area of composite figures
Answers
The area of the composite figure involving rectangle and trapezium is 810.5cm².
How to calculate the area?The area can be found by adding the area of the rectangle and trapezium. This goes thus:
Area of rectangle = Length × Width = 15 × 23 = 345cm²
Area of trapezium = 1/2(a + b)h
= 1/2(15 + 34) × 19
= 1/2 × 49 × 19
= 465.5cm²
The area will now be:
= 345cm² + 465.5cm²
= 810.5cm²
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what digit is in the one thousands place in 419,287
Answers
Answer:
9
Hope This Helps! :)
Answer:
9 is in the thousands place.
are the triangles similar? explain. please help
Answers
Answer:
The triangles are similar.
Step-by-step explanation:
The reason for this is because they both share two pairs of angles that are the same: 40 degrees and 60 degrees. If these are equal, then that must mean the third angle for both triangles is also the same, making both triangles equal in proportion. Therefore, they must be similar.
Answer:
Yes
Step-by-step explanation:
(i) By AA similarity
Both have two equal angles, 40° and 60°, therefore they can be defined as similar by AA similarity(ii) By SSS similarity
AB/DC = 32/40 = 4/5BC/EF = 24/30 = 4/5AC/DF = 36/45 = 4/5As the ratio of the sides of both triangles are equal, they are defined as similar by SSS similarityplsssssssss helpppppppppppppppppppp
Answers
Answer:
#1 B inferential
#2 A descriptive
Step-by-step explanation:
Hope this helps!
Write Down 3 numbers where the following are true:the total of the three numbers is 20.The product of the three numbers is 90
Answers
Answer:
1, 9 and 10.
Step-by-step explanation:
Let the 3 numbers be x, y and z, then
x + y + z = 20
xyz = 90
Assuming the numbers are whole numbers lets find the prime factors of 90:
90 = 2*3*3*5
So we need to combine these factors to fit the 2 eqautions.
Now 90 = 9 * 10
= 1 * 9 * 10
If we include 1 as one of the 3 numbers then 1, 9 and 10 will fit the bill.
Answer 1, 9 and 10
in the blanks below. Find the slope of the line passing through the points (-9, 2) and (9,2). slope:
Answers
I will assume that we are trying to find the slope between (-9,2) and (9, 2)
The slope's equation ⇒ [tex]\frac{y2-y1}{x2-x1}[/tex]
Let's set the variables:
(x1, y1) --> (-9, 2)
(x2, y2) --> (9, 2)
Now let's plug them in:
[tex]Slope = \frac{2-2}{9--9} =\frac{0}{18} =0[/tex]
Thus the slope of the line is 0.
Hope that helps!
What is the sum of the interior angles of this pentagon?
Answers
[tex]sum\ or\ interior\ angles[/tex]
[tex]ol\ pentagon\ is\ 540\textdegree.[/tex]
Step-by-step explanation:[tex]Given\ of\ Pentagon[/tex]
[tex]To\ hind\ o\ sum\ of\ Interiur\ angle\ of[/tex]
[tex]pentagon.[/tex]
[tex]solutiono[/tex]
[tex]sum\ of\ the\ interior[/tex][tex]angler\ of\ a\ pentajon[/tex]
[tex]can\ be\ round\ by\ 1\ st[/tex]
[tex]dividing\ it\ into\ triangler[/tex]
[tex]from\ 1\ verter.[/tex]
[tex]\therefore\ There\ are\ 3\ Triangles\ made.[/tex]
[tex]sum\ of\ interiar\ angler\ or\ Triangles\ is[/tex]
[tex]180\textdegree.\ Tmere\ are\ 3\ Triangles.[/tex]
[tex]\therefore \ \ \ \ \ 180\times 3=540\textdegree.[/tex]
[tex]Hence\ sum\ ot\ interior\ angles[/tex]
[tex]ol\ pentagon\ is\ 540\textdegree.[/tex]
I hope this helps you
:)
Find the next two terms in this sequence.
50,40,31,23,16,[???][???]
Answers
Answer:
10, 5.
Step-by-step explanation:
The differences are -10, -9, -8, -7,
so the next 2 terms are 16-6 and 10 - 5
= 10, 5
From the product of 3y and y^2 -4y +10, subtract y^3 + 7y2 -2y
Please help this is due tonight!
Answers
= 3y^3 -12y^2 + 30y - y^3 -7y^2 + 2y
= 2y^3 -19y^2 +32y,,
Hope I can help you!
write a quadratic function whose zeros are 7 and 2
Answers
Answer:
A quadratic function whose zeros are 2 and 7 is f(x) = x^2 - 9x + 14
If the zeros of a quadratic function are a and b, the quadratic function will be given as:
f(x) = (x - a)(x - b)
For the function f(x) whose zeros are 2 and 7:
f(x) = (x - 2)(x - 7)
Expand the equation
f(x)= x^2 - 7x - 2x + 14
f(x) = x^2 - 9x + 14
Therefore, a quadratic function whose zeros are 2 and 7 is
f(x) = x^2 - 9x + 14
what is the least common denominater of 1/2, 2/3, and 3/8?
Answers
Answer:
24
Step-by-step explanation:
2×12 =24
3×8 =24
8×3 =24
A point with a coordianates plane (-c -d) is shown on the coordinate grid
Answers
Ans The answer to the question is ###404 bad gateway Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST!!!
Which fraction has a value that's equal to 3/4?
A. 12/12
B.4/3
C. 12/16
D. 9/16
Answers
Answer:
C. 12/16
Step-by-step explanation:
If you multiply both the numerator AND the denominator by four you end up with the equivalent fraction of 12/16.
Select the best answer for the question.
7. What is 7/4 as a mixed number?
O A. 3/4
O B. 1914
O C. 1314
O D. 11/4
Answers
Answer:
[tex] 1 \frac{3}{4} [/tex]
Step-by-step explanation:
7/4 = [tex] \sf 1 \bold{R} 3 [/tex]
⇢ [tex] 1 \frac{3}{4} [/tex]
helppp!!!
Which expression is equivalent to 5a2+ 15a - 5?
A. 2042 - 5
B. 5a² + 10a
c. q2 + 3a - 1
D. 5a² + 20a - 5a - 5
Answers
Answer:
[tex]D)~~ 5a^2 +20a -5a -5[/tex]
Step-by-step explanation:
[tex]5a^2 +20a -5a -5 = 5a^2 +15a -5[/tex]
Answer:
D
Step-by-step explanation:
5a2 is same, -5 is same and 20a - 5a is same as 15a