Answers
9514 1404 393
Answer:
a) f: all real numbers except 1 and 2; g: all real numbers except 2
b) f(x) = 5/(x -2) . . . . x = 2 is a vertical asymptote
c) f(x) = -5/4, -5/3, -5/2, undefined, undefined, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undefined, 5, 5/2
d) f(x) is also undefined at x=1
Step-by-step explanation:
a) Any question about the domain of a function concerns the values of the variable for which the function is defined, or not. A rational function, such as these, will be undefined when its denominator is zero. So the question of domain becomes a question of the values of x that make the denominator zero.
The zeros of the denominator of f(x) can be found by factoring it.
x^2 -3x +2 = (x -1)(x -2)
These factors are zero when x=1 and when x=2. Hence, these values are excluded from the domain of f(x).
domain of f(x): all real numbers except x=1 and x=2
Then, by inspection, the domain of g is similar, but a little different:
domain of g(x): all real numbers except x=2
__
b) Based on our work for part (a), we find that f(x) can be factored and simplified like this.
[tex]f(x)=\dfrac{5x-5}{x^2-3x+2}=\dfrac{5(x-1)}{(x-1)(x-2)}\\\\\boxed{f(x)=\dfrac{5}{x-2}\quad x\ne1}[/tex]
There will be a vertical asymptote at x=2. The attachment shows a graph of f(x) with its vertical asymptote.*
__
c) The difference between the two functions is that f(x) is undefined at x=1.
x = -2, -1, 0, 1, 2, 3, 4
f(x) = -5/4, -5/3, -5/2, undef, undef, 5, 5/2
g(x) = -5/4, -5/3, -5/2, -5, undef, 5, 5/2
__
d) The functions differ in that f(x) is undefined at x=1, whereas g(x) is not.
_____
* The fact that f(x) is undefined at x=1, but there is no vertical asymptote at that point, means the function has a "hole" in its graph there. This is illustrated on the graph by an open circle, meaning the function is not defined at that point.
Related Questions
The figures below are similar. Find the length of the missing side.
7
91
91
11
7
х
4
52
X=
Answers
Answer:
63 is this right?
Step-by-step explanation:
10 x 9 = 90
so 7 x 9 = 63
Given the following system, the x-value of the solution is -1. Solve for y.
Answers
Y= 3
Y=3
Explanation
If you need to show work I can put it in the comments:)
Answer:
1. y=3
2. y=3
Step-by-step explanation:
Let's start with the first one, 2x-2y=-8...
Substitute x with -1 -----> 2(-1)-2y=-82 times -1 makes -2 so new equation is ---> -2-2y=-8Now add 2 on each side to get rid of 2 and get this ----> -2y=-6Now divide -6 by -2 to get this ----> y=3Let's start with the second one, 2x+2y=4
Substitute x with -1 -----> 2(-1)+2y=42 times -1 makes -2 so new equation is ---> -2+2y=4Now add 2 on each side to get rid of 2 and get this ----> 2y=6Now divide 6 by 2 to get this ----> y=3I hope my explanation and answer helps:)
Anthony earned $131 in tips last night while working at the restaurant. If his tips
consisted of $1 bills and $5 bills only and he counted 47 bills in total, then how
many $5 bills did Anthony receive?
Answers
Given:
Total income form tips = $131
His tips consisted of $1 bills and $5 bills only.
Total number of bills = 47
To find:
The number of $5 bills.
Solution:
Let x be the number of $1 bills and y be the number of $5 bills.
Total bills : [tex]x+y=47[/tex] ...(i)
Total income : [tex]x+5y=131[/tex] ...(ii)
Subtract (ii) from (i), we get
[tex]x+5y-(x+y)=131-47[/tex]
[tex]x+5y-x-y=84[/tex]
[tex]4y=84[/tex]
[tex]y=21[/tex]
Therefore, the number of $5 bills is 21.
Shelley just finished a new book about a time-traveling magician. She read the same amount every day and completed the book in just 10 days! The book had 85 pages. How many pages did Shelley read each day?
Answers
The reads 8.5 pages each day
Answer:
8 1/2
Step-by-step explanation:
For a party, Samantha bought eight half gallon bottles of soda. About how many cups of soda did Samantha buy?
A) 64
B) 128
C) 8
D) 4
Answers
Answer:
Step-by-step explanation:
a
Answer:
your answer is A 64
Step-by-step explanation:
there is 16 cups in a gallon so half a gallon is 8 cups 8x8 is 64
For Part A, use a piece of paper. For parts B-D, use the text box below.
A. Plot the data on a piece of paper. (make sure you label your axes and put a title). Draw a line of best fit.
B. Write an equation for the line of best fit.
C. What income would a person have if he attended school for 2 years? Explain how you got the answer.
D. How many years would you need to attend college in order to have an income of at least $50,000?
Answers
Answer:
wait you want me to answer this
Calcula a través de sustitución, igualación, reducción y gráficas:
3x + 2y = 7 5x + 3y = 11
4x - 3y = -2 3x + y = 5
*Este problema se puede resolver de una sola forma o método (sustitución, igualación, reducción o en gráficas).
PROBLEMA:
En el cajero de un banco entrega a un cliente 40 monedas de 50 centavos y de un peso si lo que entrego importa $32 pesos, ¿cuántas monedas hay de cada denominación?
**SI NO TE SABES LA RESPUESTA POR FAVOR EVITAME EL QUE TE REPORTE Y NO RESPONDAS OTRRA COSA INADECUADA GRACIAS**
Answers
Answer:
2 different problems?
what is 1,296 divided by 22
Answers
Answer:
58.9090 rounded to nearest whole it's 59
Step-by-step explanation:
Hope this helps ya!
If you need work tell me.
how do you calculate the area and perimeter of a slope triangle?
Answers
Answer:
How you find the area of a triangle is by, multiplying two of the sides together then multiplying that by 1/2 or .5 . To find the perimeter of the triangle add all the three sides together!
Step-by-step explanation:
Please help! 30 points!
Use the numbers:
6 3 5 4 2 1
in that order to make 100. Use brackets and the four operations.
Answers
Answer:
((6 x 3 + 4/2) x 5 ) / 1
A gym all machine contains 23 green gum balls, 52 red gum balls, 34 blue gum balls, 61 yellow gum balls, and 30 pink gum balls.
What percent of the gum balls are red
Answers
Answer:
26%
Step-by-step explanation:
total gum balls 200
52/200 = x/100
52×100=5200
5200÷200=26
please help this is due tomorrow!! (SQUARE ROOTS)
Ill give brainliest!! find the value
√b^6
3√-x^6
3√-y^9
Answers
Example: √12 is simpler as 2√3
Get your calculator and check if you want: they are both the same value!
Here is the rule: when a and b are not negative
√(ab) = √a × √b
And here is how to use it:
Example: simplify √12
12 is 4 times 3:
√12 = √(4 × 3)
Use the rule:
√(4 × 3) = √4 × √3
And the square root of 4 is 2:
√4 × √3 = 2√3
So √12 is simpler as 2√3
Another example:
Example: simplify √8
√8 = √(4×2) = √4 × √2 = 2√2
(Because the square root of 4 is 2)
And another:
Example: simplify √18
√18 = √(9 × 2) = √9 × √2 = 3√2
It often helps to factor the numbers (into prime numbers is best):
Example: simplify √6 × √15
First we can combine the two numbers:
√6 × √15 = √(6 × 15)
Then we factor them:
√(6 × 15) = √(2 × 3 × 3 × 5)
Then we see two 3s, and decide to "pull them out":
√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10
Fractions
There is a similar rule for fractions:
root a / root b = root (a / b)
Example: simplify √30 / √10
First we can combine the two numbers:
√30 / √10 = √(30 / 10)
Then simplify:
√(30 / 10) = √3
Some Harder Examples
Example: simplify √20 × √5√2
See if you can follow the steps:
√20 × √5√2
√(2 × 2 × 5) × √5√2
√2 × √2 × √5 × √5√2
√2 × √5 × √5
√2 × 5
5√2
Example: simplify 2√12 + 9√3
First simplify 2√12:
2√12 = 2 × 2√3 = 4√3
Now both terms have √3, we can add them:
4√3 + 9√3 = (4+9)√3 = 13√3.
I need help with #18 & 20 ASAP!!!!!!!
Please explain so I can understand
Answers
So, you would just subtract the 3 from the 5 and then your answer would be -3X+4Y=2
Please help its7to10 it’s easy but I’m lazy
Answers
Answer:
sure
Step-by-step explanation:
Infer Jamal is in a car going north. He looks out his window and thinks that the northbound traffic is moving very slowly. Ellen is in a car going
south. She thinks the northbound traffic is moving quickly. Explain why Jamal and Ellen have different ideas about the motion of the traffic.
Answers
Answer:
relax jamal dont pull up the 9
Step-by-step explanation:
PLEASE HELP ME ON THIS QUESTION IVE BEEN STUCK ON IT FOR 10 MINUTES!!!!!
Alice, Maggie, Luna, and Zeinab were making necklaces for the school fair. Alice made 52 necklaces that are each 8.2 inches long. Maggie made 46 necklaces that are each 7.8 inches long. Luna made 21 necklaces that were each 7.7 inches long. And Zeinab made 31 necklaces that were each 8.7 inches long. They all used beads that were each 2 centimeters long. how much beads would the girls use to fit all of the necklaces they made?
Alice:_______
Maggie:_______
Luna:_______
Zeinab_______
40 POINTS!!!
Answers
Answer:
Step-by-step explanation:
PLEASE MARK BRAINLIEST
A punch bowl contained 2 liters of soda, 1 liter of orange juice,
and 1 liter of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 2 to 4.
The ratio of the orange juice to the raspberry juice is 1 to 1.
The ratio of the entire punch bowl to soda is 4 to 2.
The ratio of soda to the entire punch bowl is 1 to 4.
The ratio of orange juice to soda is 2 to 1.
Answers
Answer:
The ratio of the orange juice to the raspberry juice is 1 to 1.
The ratio of the entire punch bowl to soda is 4 to 2.
An arts academy requires there to be teachers for every students and for every . How many students does the academy have per teacher? Per tutor? How many
Answers
This question is incomplete
Complete Question
An arts academy requires there to be 6 teachers for every 132 students and 4 tutors for every 44 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 132 students?
Answer:
a)How many students does the academy have per teacher?
22 students per teacher
b) Per tutor?
11 students per tutor
c) How many tutors does the academy need if it has 132 students?
12 tutors
Step-by-step explanation:
a)How many students does the academy have per teacher?
6 teachers = 132 students
1 teacher = x
6 × x = 132 × 1
x = 132 × 1/6
x = 22 students
Hence, we have 22 students per tutor
b) Per tutor?
4 tutors = 44 students
1 tutor = x students
Cross Multiply
4 × x = 1 × 44
x = 44/4
x = 11 students
Hence, we have 11 students per tutor
c) How many tutors does the academy need if it has 132 students?
44 students = 4 tutors
132 students = x tutors
Cross Multiply
44 × x = 132 × 4
44x = 132 × 4
x = 132 × 4/44
x = 12 tutors
The academy needs 12 tutors if they have 132 students.
What in 5 plus 5 divided by 2 plus 100
Answers
1.02 looooooool
Answer:
107.5
Step-by-step explanation:
Make sure you use PEMDAS! (parentheeses, exponets, multiplication, divison, addition, and subtraction!)
So, 5/2 is 2.5 plus 100 is 102.5 plus another 5 is 107.5! Hope this helped :)
Twice as many students go to the park than to the theater. Five more students go to the theater than to the museum. If 16 students go to the park, how many students go to the museum?
Answers
Answer:
3 students
Step-by-step explanation:
Twice as many students go to the park than to the theater :
Let number who go the theater = t
Number who goes to park = 2t
5 more students go to the theater than to the museum
Number who goes to museum = t - 5
If number of students who goes to park = 16
How many students goes to the museum :
2t = 16
t = 16/2
t = 8
Number who goes to museum = t - 5
t - 5 = 8 - 5 = 3
Hence, number of students who goes to the museum = 3
A. What is the slope of the trend line?
B. What is the meaning of the slope in context of the problem?
C. What is the y-intercept?
D. What is the equation?
E. Predict how many words per minute Jaime would type after 11 weeks. Explain how you made your prediction.
Answers
Answer:
Slope is 4/9 The y intercept is where the line crosses on the Y line of the graph i think its 15 or something along those lines. I dont have enough time to answer the rest but i really hope somebody else does!!
Step-by-step explanation:
_________ 5) What is the average rate of change of the function g(x) = -2x +1 over the interval [5, 6]?
Answers
Answer:
-2
Step-by-step explanation:
They are asking for the slope. y2-y1/x2-x1
Make a table of results for the equation
x y
5 -2(5)+1=-10+1=-9 Y1
6 -2(6)+1=-12+1=-11 Y2
-11--9=-11+9=-2
6-5=1
Average rate pf change os -2/1=-2
What is the nature of the solution set to the following system of equations?
5x - y = 2
2x -0.5y = 3
O One solution at (-4,-4)
O Infinitely many solutions
O One solution at (-4,-22)
ONo solutions
Answers
Answer:
One solution at (-4, -22)
Step-by-step explanation:
5x - y = 2
y = 5x - 2 --(1)
2x - 0.5y = 3 --(2)
sub (1) into (2):
2x - 0.5(5x - 2) = 3
2x - 2.5x + 1 = 3
-0.5x = 2
x = -4
when x = -4, y = 5(-4) - 2 = -22
The nature of the solution set to the system of equations are,
⇒ One solution at (-4,-22).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
5x - y = 2 .. (i)
2x - 0.5y = 3 .. (ii)
Now, We can simplify as;
From (i);
5x - y = 2
y = 5x - 2
Put above value in (ii);
2x - 0.5 (5x -2) = 3
2x - 2.5x + 1 = 3
- 0.5x = 2
x = - 4
From (i);
y = 5 × - 4 - 2
y = - 20 - 2
y = - 22
Thus, The nature of the solution set to the system of equations are,
⇒ One solution at (-4,-22).
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
can u peoples help me
Answers
f(x) = 2x + 1
h(x) = one-halfx – one-half
h(x) = one-halfx + one-half
h(x) = one-halfx – 2
h(x) = one-halfx + 2
Answers
write a equation that passes through the points 5,2 and 2,8
Answers
Answer:
y = -6/3x + 8
Step-by-step explanation:
what’s 5 x 1/8? please explain how to do this problem too :)
Answers
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]\frac{5}{1}[/tex] × [tex]\frac{1}{8} = \frac{5}{8}[/tex]I hope this helps!
Answer:
5/8 or 0.625
Step-by-step explanation:
multiply the numerator so that equals 5
multiply the denominator so that equals 8
the fraction answer is 5/8
the decimal answer is 0.625; this is because when you divide 5 and 8, you get 0.625
if you need more explanation, 5/1 times 1/8
just multiply across the top and bottom to get your answer
(8+t)^3-6
t=2
(3 is an exponent)
The value is:
Answers
Answer:
994
Step-by-step explanation:
PEMDAS
Parentheses: 8+2 = 10
Exponents: 10^3 = 1000
Subtraction = 1000-6
= 994
What is 12.18 x 103 =
Answers
Answer:
1,254.54
Step-by-step explanation:
Answer:
1,254.54
Step-by-step explanation:
Solve the following formula for
x
y=2mx+3b
Answers
Answer:
X=2m+3b/y. I th ink that the answer.