The graph of a rational function f is shown below.
Assume that all asymptotes and intercepts are shown and that the graph has no "holes".
Use the graph to complete the following.
Answers
We have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The y-intercept of a function is determined by the intersection of its graph with the y-axis. The value of y on the y-axis at which the considered function crosses it is called the y-intercept.
Assume the following equation: y = f (x)
We have x =0- 2 and y+2 = 0,The x and y intercept of the given function is -2 and +2.
The vertical asymptote is none. The horizontal asymptote is 2.
Hence,we have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
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Related Questions
1. The perimeter of the square is f(x) = 4x, where x is the side of the square. Find the domain of the function.
A. Set of rational numbers
B. Set of whole numbers
C. Set of integers
D. All of the choices
2. Find the domain of the function y = 3x + 8(3 - x).
A. Set of real numbers
B. Set of integers
C. Set of whole numbers
D. Set of natural numbers
Answers
Question 1
B. Set of whole numbers
Eliminate A and C because negative integers are in those sets.Question 2
A. Set of real numbers
The equation represents a line, which has a domain of all real numbers.If the perimeter of the square is 4x then the domain of the function will be set of rational numbers and the domain of the function y=3x+8(3-x) is set of real numbers.
Given The perimeter of the square is f(x)=4x and the function is y=3x+8(3-x)
We will first solve the first part in which we have been given that the perimeter of the square is 4x and we have to find the domain of the function.
First option is set of rational numbers which is right for the function.
Second option is set of whole numbers which is not right as whole number involves 0 also and the side of the square is not equal to 0.
Third option is set of integers which is not right as integers involve negative number also and side of square cannot be negative.
Hence the domain is set of rational numbers.
Now we will solve the second part of the question
f(x)=3x+8(3-x)
we have not told about the range of the function so we can put any value in the function and most appropriate option will be set of real numbers as real number involve positive , negative and decimal values also.
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Christmas bulbs made of different colours are set to light after 8seconds,10 seconds and 14 seconds. How many times will they light simultaneously in one hour if they start together
Answers
Answer:
36 seconds will be the answer... by looking down here↓:
Step-by-step explanation:
6 secs x 6 cycles = 36 seconds
9 secs x 4 cycles = 36 secs
12 ses x 3 cycles = 36 secs
Please answer these questions!!!!
Answers
Answer:
BEC = C. 50
BCD = A. 120
Step-by-step explanation:
BEC
65 + 65 = 130
180 - 130 = 50
BCD = 180 - 60 = 120
BEC is 50
Explanation: The angle ACD shows 180°. We are given 60°. 180°-60°=120°, Hope this helped! :D
Please help me answer this mathematics question
Answers
Answer:
[tex]x = 172.75[/tex]
Hope this help!!!
Have a good day♡
A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?
Answers
The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.
To solve the problem, we must:
Know how many 30-minutes have passed during the time period.
1 day = 24 hours
1 hour = 60 minutes = 2 × (30 minutes)
1 day = 24 hours × 2 × (30 minutes)
1 day = 48 × (30 minutes)
Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.
Friday = 48 × [tex]\frac{1}{2}[/tex] = 24
Saturday = 48
Sunday = 48
Monday = 48 × [tex]\frac{3}{4}[/tex] = 36
TOTAL = 24 + 48 + 48 + 36 = 156
Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.
Divide the number of total seconds late by the number of 30-minutes passed.
That is, the number of total seconds late= 468 seconds ÷ 156
= 3 seconds
Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
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Write the equation using function notation f(x). then find f(0)
2x^2 - 3y = 6
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = -2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{2} - 3y = 6[/tex]
[tex]\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: 3y = 2 {x}^{2} - 6[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {x}^{2} - 6 }{3} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[ here, y can be replaced with f(x) because y is a function of x ]
[tex]\qquad \tt \rightarrow \: f(x) = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[tex] \large\textsf{Find f(0):} [/tex]
[tex]\qquad \tt \rightarrow \: f(0) = \cfrac{2 {}^{} }{3} {(0)}^{2} - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = 0 - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = - 2[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
f(x) = -3 +3
Which graph represents the inverse of function ?
-3
N
-1
4
3-
2-
1-
-2+
-3-
-4+
-5+
W.
Y
54
-1-
4-
3-
2
-4
-2
N
-3
-5+
X.
Y
4-
3-
2-
-1-
3
X
e
Answers
Answer: Y
Step-by-step explanation:
Since f(x) passes through (0,3), its inverse should pass through (3,0).
This eliminates X and Z.Also, since f(x) has a negative slope, so its inverse should also have a negative slope.
This eliminates W.The graph of the inverse of function is shown in figure.
We have to given that,
Function is defined as,
f (x) = - 3x + 3
Hence, The inverse of function f (x) is,
f (x) = - 3x + 3
y = - 3x + 3
Solve for x,
3x = y + 3
Divide by 3;
x = (y + 3) / 3
Hence,
f⁻¹ (x) = (x + 3) / 3
f⁻¹ (x) = x/3 + 1
Therefore, The graph of the inverse of function is shown in figure.
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find the missing values in this sequence; -6;...;3...;15.
Answers
That’s the answer
Explenatkon.
Answer:
Maybe 9 and 12 ?
Step-by-step explanation:
-6 + 9 = 3
then 3 + 9 = 12
then 12 + 3 = 15
each term is the sum of the two that are before it
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation.
Answers
Answer:
Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Evaluate:
10
Σ¹0 4(1)n-1 = [?]
Round to the nearest hundredth.
Enter
Answers
Answer:
Step-by-step explanation:
we are essentially calculating:
4(1/4)^0 + 4(1/4)^1 + 4(1/4)^2 + ... + 4(1/4)^9
Formula: [tex]\frac{a(1-r^n)}{1-r}[/tex]
4(1-(1/4)^10)/ (1-1/4) approximates to 5.33
convert 0.390 as a fraction
Answers
Answer:
390/1000
This is the answer and hope it helps
21% of hospital patients stay for less than 1 day. If 1,134 patients in January stay less than 1 day what total of number of patients did the hospital treat in January?
Answers
Somebody help me solve;
(1)A fair die is being rolled.
a) Find the probability that at least 5 rolls are needed to obtain the first
one.
b) Find the probability that it will take fewer than seven rolls to obtain the
second one if the first one occurs on the third roll.
Answers
Fewer than 7 rolls to get second 1 after first takes 3 rolls means second occurs on 4th, 5th or 6th roll
The probability of each of these is 1/6, 5/6 x 1/6 and 5/6 x 5/6 x 1/6 respectively.
P(second 1 on 4th, 5th or 6th roll) = 1/6 + 5/36 + 25/216 = 91/216 = 0.4213 (4sf)
If it is now 1:15, what time will it be in 1 1/2 hours' time?
Answers
Answer:
2:45
Step-by-step explanation:
1 1/2 hour is 1 hour and 30 minutes.
If we add 30 minutes to 1:15, we get 1:45
if we add 1 hour to 1:45, we get 2:45, which is our answer.
what are the intercepts of x^2 +8x+16
Answers
Answers:
x intercept = -4
y intercept = 16
The graph is shown below.
=======================================================
Explanation:
To determine the x intercept(s), we set the expression equal to zero and solve for x. In other words, we plug in y = 0 and solve for x.
y = x^2 +8x+16
0 = x^2 +8x+16
x^2 +8x+16 = 0
(x+4)^2 = 0
x+4 = 0
x = -4
There's only one x intercept. It's located at the vertex of the parabola.
The location of the x intercept is the point (-4,0)
------------
To find the y intercept, we plug in x = 0 and compute like so:
y = x^2 +8x+16
y = (0)^2 +8(0)+16
y = 16
The y intercept is 16 which is located at (0,16)
Check out the graph below. It was made using the free app Desmos.
what is the length of the squares side?
Answers
Answer:
side ≈ 4.24= [tex]\frac{6}{\sqrt{2} }[/tex]
Step-by-step explanation:
sides a = b
[tex]6^{2} =a^{2} +a^{2}[/tex]
[tex]6^{2} =2a^{2}[/tex]
[tex]a^{2}= \frac{6^{2} }{2} =\frac{36}{2} =18[/tex]
[tex]a=\sqrt{18} =4.24=\sqrt{(9)(2)} =\frac{6}{\sqrt{2} }[/tex]
Hope this helps
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common? Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
Answers
The statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). What is the domain and range for the function of y = f(x)?The domain of a function is the set of values of input for which the function is valid.
The range is the dependent variable of a set of values for which the function is defined.
Given that:
f(x) = 4 - x
The slope (m) of the function = -1x-intercept = (4,0)y-intercept = (0,4)Domain = [4,∞)For function g(x) = -1 ×[tex]\mathbf{\sqrt{x-4}}[/tex]
The domain = x ≥ 4 and the solution set is [4,∞)The range g(x) = ≤ 0 and the solution set is [-∞, 0)The function g(x) does not have a y-intercept.Therefore, from the given options, the statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).Learn more about the domain of a function here:
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Answer:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
I got it right on the test.
Placement Assessment
A certain drug is made from only two ingredients: compound A and compound B. There are 7 milliliters of compound A used for every 4 milliliters of compound
B. If a chemist wants to make 946 milliliters of the drug, how many milliliters of compound A are needed?
milliliters of compound A
X
Time Remaining: 22:11:23 I Question 17
?
Libbi
Est
Answers
Answer:
[tex]7 469.8.56[/tex]
nossa nem sei como é bom saber se fala com a mãe e o pai do mundo e vc não tem mais nada pra comer e não tem como fazer a gente vai ficar muito tempo sem fazer a mãe dela não e vc como tá o trabalho rede de nada em casa e é só pra mim né não é fácil de fazer a mãe dela e a mãe dele tá bem né não é fácil de fazer o que vc quer que Deus quiser vai dar pra mim né e não tem como fazer d id da x não vou poder é o que eu te abençoe e ilumine e ilumine todos os dias entre?01029)
(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball (x) and the number of minutes he plays volleyball (y) every day. (5 points)
Part B: How much time does Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball for 25 minutes longer than he plays volleyball? Explain your reasoning. (2 points)
Answers
Eric spend 60 minutes for basketball and 35 minutes for volleyball.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, let Eric plays basketball for x minutes.
and volleyball for y minutes.
Total time spend on playing basketball and volleyball everyday = 95 minutes.
Duration of Basketball 25 minutes more than volleyball
Now, according to question,
x + y = 95 ..........(i)
x - 25 = y ...........(ii)
On solving equation (i) and (ii), we get
x + x - 25 = 95
2x = 95 + 25
2x = 120
x = 120 / 2
x = 60
put value of x in equation (ii), we get
60 - 25 = y
y = 35
Yes, it is possible and clearly described in above calculation.
Thus, Eric spend 60 minutes for basketball and 35 minutes for volleyball.
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A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number greater than 2
Answers
Follow the steps to find the area of the shaded region.
First use the formula below to find the area of the whole sector.
Sector Area= ( angle of sector/360). R2
Sector Area = ? Cm^2
Round to four decimal places.
14 cm
46°
14 cm
Answers
The area of the sector, to 4 decimal places, is 78.6794 cm².
We have given that,
Sector Area= ( angle of sector/360). R2
We have to determine the Sector Area
What is the Area of a Sector of a Circle?
Area of sector = ∅/360 × πr².
We have given the following:
∅ = 46°
Radius (r) = 14 cm
Area of sector = 46/360 × π(14²)
Area of sector ≈ 78.6794 cm²
The area of the sector is approximately 78.6794 cm².
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what is it asap please
Answers
That’s one way to do it.
Another way to solve this is as follows:
Since 22 pupils use the swimming pool and 34 use the gym, that means 56 pupils use both total. 56/80 reduces to 7/10, which as a decimal is 70% or 0.7.
Your final answer: Probability = 70%
If you need more help, let me know and I will gladly assist you!
WHAT DOES THIS MEAN???
"If you take Nia out for mexican food, have an air freshener on standby."
Answers
Answer: Beans cause Nia to Fart!
Step-by-step explanation:
Mexican food usually contains beans, which beans are a known catalyst of flatulence. Beans induce farts and Nia does so! Farts usually stink, so an air freshener is needed.
A company had the following purchases and sales during its first year of operations:
Purchases Sales
January: 10 units at $120 6 units
February: 20 units at $125 5 units
May: 15 units at $130 9 units
September: 12 units at $135 8 units
November: 10 units at $140 13 units
Answers
The final answer of the Inventory is $3540.
What is Inventory?The term inventory refers to the raw materials used in production as well as the goods produced that are available for sale.
FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold
Ending inventory comprises of goods bought in May, September and November
cost of the ending inventory :
(4 x $130) + (12 x $135) + (10 x$140) = $3540
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urgent help wanted/ needed
Answers
The equation in slope-intercept form is: y = -x + 5
The equation in point-slope form is: y - 3 = -1(x - 2)
How to Find the Equation of a Line in Point-Slope Form and Slope-intercept Form?Where (a, b) is a point on the line and m is the slope of the line, the equation in point-slope form for such line would be: y - b = m(x - a).Where b = y-intercept and m = slope, the slope-intercept form for the equation of the line is expressed as: y = mx + b.Slope (m) = rise/run = -(2/2) = -1
Y-intercept (b) = 5 (where the line intercepts the y-axis)
Using a point, (2, 3) = (a, b) and m = -1, the equation in point-slope form is:
y - 3 = -1(x - 2)
Rewrite in slope-intercept form:
y - 3 = -x + 2
y = -x + 2 + 3
y = -x + 5
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what is (x^2y^3)^1/3 / 3 sqrt x^2
Answers
Answer: y/(3x^1/3)
Step-by-step explanation:
Tan + Cos / 1 + Sin = Sec
Answers
[tex]\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x[/tex]
Help please and thank you!! :)
Answers
Answer:
33 elements
Step-by-step explanation:
Set A has 59 elements. Set A and Set B share 26 elements.
This means that 26 out of the 59 elements in Set A are also in set B.
Therefore, to find the number of elements not in Set B, you need to subtract the common elements from the total amount of elements in Set A.
59 (total in Set A) - 26 (common in Set A) = 33 (unshared elements).
Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select one that applies.
Answers
Answer:
Graph 1: No, a linear model would be more appropriate.Graph 2: YesGraph 3: No, a quadratic model would be more appropriate.what is the answer please??
Answers
Answer:
See below
Step-by-step explanation:
Area of a circle = pi * r^2
for this circle : Area = 3.142 * 10 * 10 = 314.2 cm^2
The formula for area of a circle is [tex]\pi r^{2}[/tex]
So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.
Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.
If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.
Brainliest if helpful.
