This question is worth 100 points please answer now. Algebra 2. I will mark you brainliest.
Show all work to identify the asymptotes and zero of the function f of x equals 4 x over quantity x squared minus 16.
Answers
Answer:
The vertical asymptotes occur at x = 4 and x = -4
The zero of the function is (0, 0)
Step-by-step explanation:
The given function is [tex]f(x) = \dfrac{4\cdot x}{x^2 - 16}[/tex]
Therefore, we have;
[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = \dfrac{4\cdot x}{(x - 4) \cdot (x + 4)}[/tex]
The asymptote is given at the value of x for which the denominator = 0, therefore, the asymptote are the values of x that make the denominator of the equation equal to zero, which are given as follows
For the asymptote, the denominator = x² - 16 = (x - 4)·(x + 4) = 0
Therefore, the vertical asymptotes are the lines x = 4 and x = -4.
The zero of the function is given as follows;
[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = 0[/tex]
Therefore, 4·x = (x - 4)·(x + 4) × 0 = 0
x = 0/4 = 0
Therefore, when f(x) = 0, x = 0 and the zero of the function = (0, 0).
Related Questions
Geometry Question:
Find the value of x that makes N the incenter of the triangle (See attached)
Answers
Answer:
.5 or 1/2
Step-by-step explanation:
Y^2x 24^2=25^2
Y=7
7=14x
x=.5
The value of x is 0.5.
The calculation is as follows:Here we use Pythagoras Theorem
[tex]Y^2 - 24^2=25^2[/tex]
Y=7
Now
7 = 14x
So, x=.5
Therefore we can conclude that The value of x is 0.5.
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SOLVING SYSTEMS:
I just need the work for each equation.
Answers
+ 6 + 6
2x = x + 14
-x -x
x = 14
y = (14) + 8
y = 22
(14 , 22)
I. 2x - 5y = 16
-2x + 20y = -16
15y = 0
/15 /15
y = 0
x - 10(0) = 8
x = 8
(8 , 0)
F. 10x + 6y = -4
2x - 6y = -8
12x = -12
/12 /12
x = -1
2(-1) - 6y = -8
-2 - 6y = -8
+2 +2
-6y = -6
/-6 /-6
y = 1
(-1 , 1)
N. 24x - 3y = 15
2x + 3y = 11
26x = 26
/26 /26
x = 1
2(1) + 3y = 11
2 + 3y = 11
-2 -2
3y = 9
/3 /3
y = 3
(1 , 3)
T. 3x - 2y = -2
6x + 2y = 2
9x = 0
/9 /9
x = 0
-3(0) + 2y = 2
2y = 2
/2 /2
y = 1
(0 , 1)
O. -8x - 4y = 6
5x + 4y = -3
3x = -3
/3 /3
x = -1
-4(-1) - 2y = 3
4 - 2y = 3
-4 -4
-2y = -1
/-2 /-2
y = 1/2
(-1 , 1/2)
I. 8x - 9 = -2x - 4
+2x +2x
10x - 9 = -4
+9 +9
10x = 5
/10 /10
x = 1/2
y = -2(1/2) - 4
y = -1 - 4
y = -5
(1/2 , -5)
D. -6x - 4 = -3x + 5
+3x +3x
-3x - 4 = 5
+4 +4
-3x = 9
/-3 /-3
x = -3
y= -3(-3) + 5
y = 9 + 5
y = 14
(-3 , 14)
S. -9 = -3x - 3y
8 = 4x + 3y
-1 = x
3 = -1 + y
+1 +1
4 = y
(-1 , 4)
R. -5x - 5y = 25
5x - 4y = 2
-9y = 27
/-9 /-9
y = 3
-x - (-3) = 5
-x + 3 = 5
-3 -3
-x = 2
/-1 /-1
x = -2
(-2 , -3)
A. 8y + 3 = 3x
- 3 - 3
8y = 3x - 3
-3x -3x
-3x + 8y = -3
-3x + 8y = -3
Same equation = infinite solutions
K. 8x - 6y = -4
3x + 6y = 4
11x = 0
/11 /11
x = 0
4(0) - 3y = -2
-3y = -2
/-3 /-3
y = 2/3
(0 , 2/3)
T. -5x - 8y = 0
12x + 8y = 56
7x = 56
/7 /7
x = 8
3(8) + 2y = 14
24 + 2y = 14
-24 -24
2y = -10
/2 /2
y = -5
(8 , -5)
This is a test my sister made to see how smart I am plz help.
Answers
Answer:
16.) second choice: (5,-6)
17.) third choice: (-10) (-8) (-5) (0) (1)
18.) fourth choice: (.18) (0.4) (1/4) (227)
The vertices of the triangle in the diagram below are A(7,9), B(3,3), and C(11,3).
What are the coordinates of the centroid of triangle ABC?
Please Answer with work shown! I know that the answer is (7,5) But can some one show the work for it?
If you answer it and show the work for me then I will give you the brainiest question reward!
Please Help!
Answers
Answer:
(7 , 5)
Step-by-step explanation:
Add all the x-axis then divide by 3
7 + 3 + 11 = 21
21/3 = 7
Add all the y-axis then divide by 3
9 + 3 + 3 = 15
15/3 = 5
So answer will be (7,5)
The coordinates of the centroid of triangle ABC.
(x, y)
Where,
x = Sum all the x-coordinates of the vertices ÷ 3
y = Sum o
The coordinates of the centroid is (7, 5).
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The vertices of the triangle in the diagram below are:
A(7,9), B(3,3), and C(11,3).
Now,
The coordinates of the centroid of triangle ABC.
(x, y)
Where,
x = Sum all the x-coordinates of the vertices ÷ 3
y = Sum of the y-coordinates of the vertices ÷ 3
Now,
x = 7 + 3 + 11 / 3 = 21/3 = 7
y = 9 + 3 + 3 / 3 = 15/3 = 5
Now,
The coordinates of the centroid is (7, 5).
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Consider the following system of equations
-2x+5y=19
Y=-5/6x-1/6
Use this graph of the system to approximate its solution
A. (13/4,-5/2)
B. (-5/2,13/4)
C. (-13/4,5/2)
D.) (5/2,-13/4)
Answers
Answer:
C
Step-by-step explanation:
We have the system of equations:
[tex]\displaystyle -2x+5y=19 \\\\ y=-\frac{5}{6}x-\frac{1}{6}[/tex]
And we want to use the graph to approximate the solution to the system.
Remember that, graphically, the solution to a system of equations is where the two graphs intersect.
We can see that the point at which the two lines intersect is in QII.
Hence, x is negative and y is positive.
The only choices that satisfies these conditions are B or C.
However, for B, -5/2 is -2.5. As we can see from the graph, the x-coordinate of the point of intersection is less than -3.
Hence, the only choice left is C. -13/4 also is -3.25, fulfilling our condition.
So, our final answer is C.
A person standing 130 feet away from the foot of a tall building must look up at an angle of 30° to see the top of the building. There is a radio antenna on the top of the building. The angle of elevation of the top of the radio antenna is 45°.
Answers
Answer:
30 angels
Step-by-step explanation:
In a basketball game, the home team was down by 9 points at the end of the game. They only scored 6 points for every 7 points the visiting team scored. What was the final score of the game? Type both answers with a comma inbetween. Show your work below.
Answers
The final score of the basketball game is (54, 63).
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, They only scored 6 points for every 7 points the visiting team scored
and they differ by a total of 9 points.
Therefore, The final score would be 6×9, 7×9.
= (54, 63).
If we take the difference between 63 and 54 it would be 9.
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If you spend 3$ on 6 apples,what is the unit rate (in dollars) per apple?
Answers
Answer
2 apples per $1
Step-by-step explanation:
because 6 apples cost $3, so take 6 divided by 3 so you get 2 apples per dollar
The rainfall for the month of July was above average. The water level in a small lake measured 834 feet at the beginning of the month. Due to all the rainfall, the water level rose 35 of a foot per week for the first three weeks, then the lake dropped 12 foot in the last week of the month.
What was the water level of the lake at the end of July?
A
979ft.
B
101120ft.
C
10120ft.
D
71120ft.
Answers
Answer:
927 ft so A
Step-by-step explanation:
Answer:
Step-by-step explanation:
9 7/9
Given:x-8>-3
Chose the solution set.
1.{x|x€R,x>-5}
2.{x|x€R,x>14}
3.{x|x€R,x>5}
4.{x|x€R,x>-9}
Answers
Step-by-step explanation:
x - 8 > -3
x > -3 + 8 (add 8 to both sides)
x > 5
Hence 3.{x|x€R,x>5} is correct.
What is 23/24 as a decimal rounded to the nearest hundredth?
Answers
Answer:
95.80
Step-by-step explanation:
The number 23/24 rounded to the nearest hundredth is 0.96
What is rounding up numbers?
There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Given data ,
Let the number be A = 23/24
So , in order to round the number
First we need to find the decimal for of the number A
And ,
A = 23/24
A = 0.9583
And , rounding the number to its nearest hundredth is rounding the number to two decimal places
So ,
A = 0.9583
A = 0.96
Hence , The number 23/24 rounded to the nearest hundredth is 0.96
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8 more than a third of a number
Answers
Answer:
8 + 1/3n
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!
Answers
Answer:
882-28282=9191
Step-by-step explanation:
Which of the tables represents a function?
Table A
Input Output
5 3
5 2
4 1
Table B
Input Output
1 2
3 2
5 3
Table C
Input Output
0 0
1 2
1 3
Table D
Input Output
4 2
4 3
4 4
Table A
Table B
Table C
Table D
Answers
Answer:
table b i think
Step-by-step explanation:
6th grade math i mark as brainliest
Answers
Answer:
There are 5 terms
Step-by-step explanation:
each number is its own term
A Sweater That normally costs $25.00 is on sale for 10 percent Off.
What will the Discount be?
what will the cost of the Sweater be?
Can Someone Please PLEASE help me??
Answers
Answer:
15.00
Step-by-step explanati
the discount is 15% because you need to subtract it
There are 4,389 dogwood trees in the state park. The park workers are going to plant 342 more trees. How many trees will there be when they are done?
Answers
Answer:
4731
Step-by-step explanation:
4,389+342=4,731
using the elimination method to solve the system of equations.
3x+6y =36
3x-6y=0
a. 3,6
b. 6,-3
c. 6,3
d. 3,-6
Answers
Answer:
c. (6, 3)
Step-by-step explanation:
subtract
3x + 6y = 36
3x - 6y = 0
12y = 36, y = 3
3x + 6(3) = 36
3x + 18 = 36
3x = 18, x = 6
x = 6, y = 3
Answer:
the answer is b good luck
How much of earth surface by land
Answers
Answer:
GOOD AFTERNOON
UR ANSWER IS ::
Step-by-step explanation:
2
510.1 milion km
Mass: 5.972 × 10^24 kg
Distance from Sun: 92.96 million mi
I don’t understand so please HELPPPPPPPPPPPPPP
Answers
Answer:
C
Step-by-step explanation:
Okay so im going to gudie you thru So what it is asking you is to Count all the cubic squares looking things so what i can see is that You circled 169 aka C that would be correct because it cant be 11 cause it dosent look like 11 square units lol you get what im saying so the answer is C hope this HELPSS!!
By the way follow my insta. exotic. jaliyah if you need anymore help
843.5 x 10*2 =
I need help
Answers
Answer:
16870
Step-by-step explanation:
Answer: um 16870 I guess
Step-by-step explanation: I hope I help and can you plz give me a brainliest
Find the x- and y-intercepts of the graph of the linear equation 2x+3y=12.
Answers
Answer:
x-intercept= 6
y-intercept= 4
Step-by-step explanation:
Solve for x first then solve for y.
Answer: y= -2/3x+4
The X-Intercept is -2/3
The Y- Intercept is 4
Hope this helps!! Have a wonder day everyone!! (:
Step-by-step explanation:
Step one write out the equation 2x+3y=12
Then move the variable to the right hand side and change the sign. 3y=12-2x
Then divide both sides of the equation by 3. You get y=4-2/3x
Then: Use the Commentative Property to reorder the terms. y= -2/3x+4
Convert the Following: 5.4 oz=__________ mg
Answers
Answer:
153087 mg
Step-by-step explanation:
A.) what is the domain?
B.) what is the range?
C.) is this relation a function?
Answers
Answer:
The Domain is the set of all points over which a function is defined.
The range is the set of values the function takes on as output.
7 chocolate bars cost 19 dollars determine the cost per chocolate bar.
Answers
Answer: .368
Step-by-step explanation:
Answer:
$2.71
Step-by-step explanation:
to find the cost of each chocolate bar you must divide the total cost by the number of chocolate bars
19/7
= 2.714
≈ $2.71
Sara bought 12 apples, 24 oranges, and 18 bananas for fruit baskets. If Sara wants to create the greatest number of fruit baskets that all have the same amount of fruit without any left over, how many baskets can she create?
Answers
Answer:
Step-by-step explanation:
Apples- 2
Oranges-4
Bananas- 3
In each basket
Which expression is equivalent to 15x + 3?
15(1x + 1)
5(3x + 1)
3(5x + 1)
2(15x + 3)
Answers
A recipe requires 4 cups of
flour to make 3 dozen
cookies. How many cups of
flour are needed for 10
dozen cookies?
Answers
Answer:
13 1/3 cups
Step-by-step explanation:
The ratio of flour to dozens of cookies is 4:3 or 1 1/3:1
1 1/3 x 10 = 13 1/3
Answer:
13 1/3
Step-by-step explanation:
12 cups cover the first 9 cookies and than just divide 4 by 3 and you will get 1.3 which is 1 1/3 of a cup
The numbers 22 and 35 are relatively prime. TrueFalse
Answers
Answer: True
Step-by-step explanation:
Answer:
False They are coprime numbersStep-by-step explanation:
I hope it helps ❤❤Ahhff DF nfkemebebwjdbbdnsjwjxjdnddf
Answers
Answer:
0 is the surface of the sea
Step-by-step explanation:
Here, we want to know what zero represents
From the question, we are told that jumping 5 ft below the sea surface represents the depth
-5 ft is same as going 5 units below zero
So therefore, we can have zero representing the sea level
The zero in this case is the surface of the sea
Answer:
B. the surface of the sea
Step-by-step explanation:
have nice day