Answers
The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.
How to determine the domain of a rational function
In this problem we have a rational function, the domain of rational functions is the set of all real numbers except the values such that the denominator becomes zero. First, we need to simplify the division of two rational functions:
[tex]h(x) = \frac{\frac{3\cdot x^{2} + 17\cdot x + 20}{3\cdot x^{2} + 10\cdot x - 8} }{\frac{3 \cdot x^{2} + 8\cdot x + 5}{x^{2}-3\cdot x - 4} }[/tex]
[tex]h(x) = \frac{(3\cdot x^{2}+17\cdot x + 20)\cdot (x^{2}-3\cdot x - 4)}{(3\cdot x^{2}+10\cdot x - 8)\cdot (3\cdot x^{2}+8\cdot x + 5)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x^{2}+\frac{17}{3}\cdot x + \frac{20}{3} \right)\cdot (x^{2}-3\cdot x - 4)}{\left(x^{2}+\frac{10}{3}\cdot x -\frac{8}{3}\right)\cdot \left(x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} \right)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x + \frac{5}{3} \right)\cdot (x+4)\cdot (x - 4)\cdot (x+ 1)}{\left(x-\frac{2}{3} \right)\cdot (x + 4)\cdot (x + 1)\cdot \left(x + \frac{5}{3} \right)}[/tex]
[tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex]
The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.
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Related Questions
#5:20 < 6+(-7x)
HINT! What is an equivalent way to write 6+ (-7x)?
What letter from the chart above matches the
solution to this inequality? Type your answer as a
CAPITAL letter.
Answers
Answer:
the answer i got was x<-2
Step-by-step explanation:
The difference of 8 and 2 times m
Answers
The capacity of a container is 2,060 mil liters convert this to liters
Answers
Answer:
2,060 ml ÷ 1,000 = 2.06 liters
Step-by-step explanation:
4. It takes 2 minutes to boil a single
egg. How many minutes will it take
to boil 5 eggs?
a. 10
b. 4
c. 2
d. 5
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{\#4). It takes 2 MINUTES to boil a SINGLE egg. How MANY minutes}\\\large\text{ to boil 5 eggs?}[/tex]
[tex]\large\text{\bf{Keyterm(s)}}\downarrow\\\large\text{\bf{2 minutes to boil ONE egg}}\\\large\text{\bf{Number of minutes it will take to boil FIVE eggs}}[/tex]
[tex]\textsf{Well, if one egg takes approximately two minutes, then we have we have to}\\\textsf{MULTIPLY 2 from 5, to find out your answer!}[/tex]
[tex]\large\text{\bf{2(5)}}\\\large\text{\bf{2 minutes * 5 eggs = 10 minutes to boil FIVE eggs}}\\\boxed{\boxed{\large\text{\bf{Answer: A. 10}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Darryl is buying apples and bananas. He bought a pounds of apples that cost $2 per pound and b pounds of bananas that cost $1 per pound. The total amount of his purchase is given by the expression 2a + b. Select the terms of the expression. Mark all that apply. A 2a B 2 C A. D. B. E. 1b
Answers
Answer:
Step-by-step explanation:
I’m late lol
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
y = -x
Step-by-step explanation:
Let the equation representing the table attached is,
y = mx + b
Here, m = Slope of the line
b = y-intercept
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table attached,
Slope of the line passing through (23, -23) and (33, -33),
m = [tex]\frac{-33+23}{33-23}[/tex]
m = -1
Equation of the line will be,
y = -x + b
Since, this line passes through another point (43, -43),
-43 = -43 + b
b = 0
Therefore, equation of the line representing the table will be,
y = -x
For a certain strain of bacteria, k is 0.683 when t is measured in days. Using the formula y = aek, how long will it take 12 bacteria to increase to 732 bacteria?.
Answers
Answer:
5.9 miliseconds
Step-by-step explanation:
it is it because there is a second to millisecond on a watch
Can removing two outliers not have an effect on the mean? Justify your responses.
Answers
At a football stadium, 4% of the fans in attendance were teenagers. If there were 260 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
solution
4%=260
100%=?
=(100x260)/4
=6500
Percentage of fans in the stadium who were teenagers = 4%
Number of teenagers in the match = 260
Let the total number of people at the stadium be x.
Which means :
[tex] =\tt 4\% \: \: of \: \: x = 260[/tex]
[tex] =\tt \frac{4}{100} \times x = 260[/tex]
[tex] =\tt \frac{4 \times x}{100} = 260 [/tex]
[tex] = \tt \frac{4x}{100} = 260[/tex]
[tex] = \tt4x = 260 \times 100 \\ \tt \: \: \: = 26000[/tex]
[tex] =\tt x = \frac{26000}{4} [/tex]
[tex]\color{plum} =\tt x = 6500[/tex]
▪︎Therefore, number of people at the stadium = 6500
3x^2 + 4x -8 = 0 How many solutions will there be?
Answers
Answer:
Step-by-step explanation:
graph the ordered pairs on the coordinate plane
Answers
Answer:
where is the graph and the ordered pair
This data gives the average number of hours different students spend on the computer each day.
Average time (hours): 1.6, 2.0, 2.0, 2.0, 1.8, 1.8, 1.5, 2.0, 1.9, 1.6, 1.9, 1.7, 1.6, 1.6, 2.0, 1.8, 1.5, 2.0
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Answers
Answer:
2 on 15, 4 on 16, 1 on 17, 3 on 18, 1 on 19 5 on 20
Step-by-step explanation:
I took the test <>_<>
40% of x is 35.
Write an equation that shows the relationship of 40%, x, and 35.
Use your equation to find x. Show your reasoning.
i really need help
Answers
So, 35/.4 is 87.5.
X= 87.5
And to change a percentage into decimals, move the . two places to the right. So, 40.0 is .4
H E L P ! !
The cover of a memo book must have an area of 115 cm^2. Approximately, to the nearest tenth of a centimeter, how long should each side be to make a square cover?
Answers
Answer:
10.7cm
Step-by-step explanation:
x^2= 115
x = √115
x = 10.7
If 4 out of 21 people prefer diet soda to regular soda, about how many regular sodas should be bought to serve 864 people, if each person
receives one soda?
Answers
~700 regular sodas to server 864 people
(the actual answer is 699.4285)
The number of regular sodas that should be bought will be 700 regular sodas.
If out of 21 people prefer diet soda to regular soda, then it means that 17 people prefer regular soda.
Since the number of people are 864 people, then the number of regular sodas that'll be bought will be:
= 17/21 × 864
= 699.42
= 700 Approximately
Therefore, the number of regular sodas that should be bought will be 700 regular sodas.
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https://brainly.com/question/21058142
HELP PLEASE! giving brainliest What would be the slope of a line parallel to the line below
Answers
-3\2 I think
Plz help with the problem in the picture. Thanks
Answers
They call me human calf
Answer: x(0,0)y(0,0) tell me more I don't really understand it
x=3.4
Step-by-step explanation:
PLsssss I have this due in 10 minutes!!!!
Stress and strain causes rock layers to fold. The process of folding is illustrated in the diagrams below.
Which of the following correctly uses the Law of Superposition to compare the rock layers in diagram C?
Diagram C shows that layer P is above layer R and is the youngest layer.
Diagram C shows that layer P is below layer Q and remains the oldest layer.
Diagram C shows that layers P through T are in the same order as in diagram A.
Diagram C shows that layers Q through T are on the surface and are all the same age.
Answers
Answer: D
Step-by-step explanation:
Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178 more cans than Shane.
write an inequality to determine the number of cans that Shane could have collected
Answers
Answer:
x+178x=2000 cans
Step-by-step explanation:
Hope this Helped
a probability experiment consists of fair eight sided die find the probability of rolling number greater than 4
Answers
Answer:
Probability[Number greater than 4] = 1/2
Step-by-step explanation:
Given:
Total side of die = 8
Find:
Probability[Number greater than 4]
Computation:
Number greater than 4;
[5,6,7,8]
Total number greater than 4 = 4
Probability[Number greater than 4] = Total number greater than 4 / Total side of die
Probability[Number greater than 4] = 4 / 8
Probability[Number greater than 4] = 1/2
ANSWER ASAP I WILL GIVE BRAINLIST
Answers
Answer:
its upside down
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
Geometry plz someone help me out
Answers
Answer:
x = 7 times the square root of 3
y = 14
Step-by-step explanation:
Sally is flying a kite at an angle of 41 degrees. If the kite is 10 feet up in the air, how
long is the kite string?
Answers
Answer:
15.24feet
Step-by-step explanation:
Using the method of SOH CAH TOA;
Length of the kite is the hypotenuse = x
If the kite is 10 feet up in the air, then the height = 10feet (opposite)
Angle of elevation = 41 degrees
Sin theta = Opposite/hypotenuse
Sin 41 = 10/x
x = 10/sin41
x = 10/0.6561
x = 15.24 feet
Hence the kite is 15.24feet long
The function f(x) = 3/4(10)–x is reflected across the x-axis to create the function g(x). Which ordered pair is on g(x)?
Answers
Answer:
u already have the answer
Answer:
For people that can't see the picture it's
C (2,-3/400) third option
Step-by-step explanation:
I need help with graphing
Answers
Ok I can help you with graphing
2. The ratio of white marbles to blue marbles is equal to 2:3. There are more than 20
marbles in the bag. What is a possible number of white marbles and blue marbles in the
bag? (Eg. white marbles, blue marbles)
Answers
Answer:
24 white marbles, 36 black marbles
Step-by-step explanation:
System of Inequalities:
x + y > 20
2/5y + 3/5x > 20
solve first inequality for 'y':
y > 20 - x
Use substitution to solve for 'x':
2/5(20 - x) + 3/5x > 20
8 - 2/5x + 3/5x > 20
1/5x > 12
x > 60
2/5 of 60 = 24
3/5 of 60 = 36
A newborn turtle has a shell with a 1-inch diameter. The shell keeps a similar shape as the turtle grows. After a year, the shell is 3 inches in diameter. Note: you do not need to know the shape of the shell to complete this question.
1. How many times greater is the volume of the turtle's shell after a year than it was when it was born?
2. How many times greater is the surface area of the turtle's shell after a year than it was when it was born?
Answers
Answer:
I think the volume would be 9 times greater, and the surface area would be 3 times greater
Step-by-step explanation:
Answer:
the volume would be 9 times greater
the surface area would be 3 times greater
Step-by-step explanation:
Because if the shell grows from 1 inch diameter to 3 inch diameter, the surface area will increase 3x more. And the volume I assume is 3x greater because of the height is presumably 3 inches as well.
Find the average rate of change please
Answers
Answer:
The Average rate of change of function f(x)
A(x) = 3
Step-by-step explanation:
Step(i):-
Given function f(x) = x²-2
Given values x = a = -1 and x = b =4
The Average rate of change of function f(x)
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given function f(x) = x²-2
f(a) =f(-1) = (-1)²-2 = 1-2 = -1
f(b) = f(4) = (4)²-2 = 16-2 = 14
Step(ii):-
The Average rate of change of function f(x)
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]
[tex]A(x) = \frac{14-(-1)}{4-(-1)} = \frac{14+1}{4+1} = \frac{15}{5} =3[/tex]
Final answer:-
The Average rate of change of function f(x)
A(x) = 3
What is the place value of 6
Answers
Answer:
6 is in ten place and its place value is 60,
Which of the following gives the correct negation of the statement "P: x is an even number"?
Question 2 options:
A)
P: ∼x is not an even number.
B)
∼P: x is an even number.
C)
P: ∼x is an even number.
D)
∼P: x is not an even number.
Answers
Answer:
The answer is D
Step-by-step explanation:
The negation of a statement has the opposite meaning of the original statement. The negation of a statement is formed by adding the word “not”.
Consider statement P again:
P: x is greater than 9.
The negation of P is:
∼P: x is not greater than 9.
Note that the symbol ∼ is used before a statement to show that it's a negation.
The negation of the statement is x is an odd number or x is not an even number.
What is Conditional Statement?A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences. P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement. The implication of "If P then Q" is that whenever P is true, Q must also be true.
We have,
P: x is an even number.
As, Negation indicates that the conditional statement's statement is false.
Conditional: P: x is an even number.
Negation: ~P: x is an odd number or x is not an even number.
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