Answers
Answer:
When we have a rational function like:
[tex]r(x) = \frac{x + 1}{x^2 + 3}[/tex]
The domain will be the set of all real numbers, such that the denominator is different than zero.
So the first step is to find the values of x such that the denominator (x^2 + 3) is equal to zero.
Then we need to solve:
x^2 + 3 = 0
x^2 = -3
x = √(-3)
This is the square root of a negative number, then this is a complex number.
This means that there is no real number such that x^2 + 3 is equal to zero, then if x can only be a real number, we will never have the denominator equal to zero, so the domain will be the set of all real numbers.
D: x ∈ R.
b) we want to find two different numbers x such that:
r(x) = 1/4
Then we need to solve:
[tex]\frac{1}{4} = \frac{x + 1}{x^2 + 3}[/tex]
We can multiply both sides by (x^2 + 3)
[tex]\frac{1}{4}*(x^2 + 3) = \frac{x + 1}{x^2 + 3}*(x^2 + 3)[/tex]
[tex]\frac{x^2 + 3}{4} = x + 1[/tex]
Now we can multiply both sides by 4:
[tex]\frac{x^2 + 3}{4}*4 = (x + 1)*4[/tex]
[tex]x^2 + 3 = 4*x + 4[/tex]
Now we only need to solve the quadratic equation:
x^2 + 3 - 4*x - 4 = 0
x^2 - 4*x - 1 = 0
We can use the Bhaskara's formula to solve this, remember that for an equation like:
a*x^2 + b*x + c = 0
the solutions are:
[tex]x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
here we have:
a = 1
b = -4
c = -1
Then in this case the solutions are:
[tex]x = \frac{-(-4) +- \sqrt{(-4)^2 - 4*1*(-1)} }{2*(1)} = \frac{4 +- 4.47}{2}[/tex]
x = (4 + 4.47)/2 = 4.235
x = (4 - 4.47)/2 = -0.235
Related Questions
All you have to do is write the function!
A software CD can be manufactured for $0.10 each. The development cost to produce the CD is $500,000. The first 200 CDs were used by testers to test the functionality of the software and were not sold.
Write a function, f, for the average cost, in dollars, of a saleable software CD where x is the number of saleable software CDs.
Answers
Answer:
The function that represents the average cost in dollars of saleable software CD is given as follows;
f(x) = 500,020/x + 0.10
Step-by-step explanation:
The given parameters are;
The cost of manufacture of each software CD = $0.10
The development cost to produce the CD = $500,000
The number of CDs that are not sold = The first 200 CDs
The total cost of production. 'C', of the the CD is given as follows;
C = $500,000 + $0.10×200 = $500,020
The function, 'f' for the average cost in dollars of a saleable software CD where 'x' is the number of saleable software CDs is given as follows;
f(x) = (C + 0.10·x)/x = C/x + 0.10
∴ f(x) = 500,020/x + 0.10.
Make a VISUAL model and show your math evidence as you solve for x.
1)
2x - 5 = 9
Answers
Answer:
x=7
Step-by-step explanation:
2x-5=9
+5 +5
2x=14
/2 /2
x=7
I don't if this is what you mean by visual, but this is what I got.
2x = 9 + 5. Add them
2x = 14 divide
X=7
Polly's veterinarian told her a dog that weighs w kilograms needs 30w+70 calories each day to stay healthy. Polly's dog, Otis, weighs 22 kilograms. How many calories does Otis need each day to stay healthy?
Answers
Answer: 730 calories
Step-by-step explanation:
Since the function is given as: 30w+70 and Polly's dog, Otis, weighs 22 kilograms.
The amount of calories that Otis need each day to stay healthy will be:
= 30w + 70
= 30(22) + 70
= 660 + 70
= 730 calories
pleasssseeee!!!!!!!!!!!
Answers
Answer:
h= the number 7 duh-
Step-by-step explanation:
QUESTION 12
A person pays $2 to play a game using only the hearts from a deck of cards (2-10,J,Q,K, ace). If the person draws a number card (2-10).
they lose. If the player draws a face card ( Q,K), they win $3. If the player draws an ace, they win $io. Find the expected value. Is the
game fair?
Answers
Answer:
the value would be 6 and yes the game is fair
Anthony rode his skateboard for 4 miles in 20 minutes. What was his speed in miles per hour?
A. 5 miles per hour
B. 0.2 miles per hour
C. 12 miles per hour
D. 80 miles per hour
Answers
Answer:
Step-by-step explanation:
if he rode 4 miles in 20 minutes
1h=20*3=60 min
4*3=12 miles/hour
Answer:
A. 5 miles per hour.
Step-by-step explanation:
You divide 20 by 4 to get 5, which is per mile, so yea 5 miles per hour
What is the solution to the system shown?
x - y = 12
x + y = 20
A.
x = 3, y = -7
B.
x = 4, y = -7
C.
x = 15, y = 3
D.
x = 16, y = 4
Answers
Answer:d
Step-by-step explanation:
16-4=12 and 16+4=20
What is cos 0 + sin 90 ?
Answers
Answer:
[tex] \cos(0) + \sin(90) [/tex]
[tex]1 + 1 = 2[/tex]
Answer:
2
Step-by-step explanation:
[tex] \cos(0) = 1[/tex] and [tex] \sin(90) = 1[/tex]
So,
[tex] \cos(0) + \sin(90) = 1 + 1 = 2[/tex]
Need help ASAP
Which of the following x-values are approximate solutions to the equation f (x) = g(x) ? Select ALL that apply.
A) x = -3.3
B) x = -2
C) x = 2
D) x = 5.2
E) x = 6.5
Answers
Answer:
A and D
Step-by-step explanation:
I could be wrong but the solutions are the points of intersection between the two functions. By looking at it. I can see that its about -3.3 and 5.2
Hope this helps!
The x-values are approximate solutions to the equation f (x) = g(x) that is -3.3 thus the correct option is A.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.,Functions which repeats their values after a fixed interval, are called periodic function.
WE have been given the function x as
f (x) = g(x)
Therefore,
3(17x-6.5) = 108
Then Divide each side by 3;
3/3(17x-6.5) = -108/3
17x - 6.5 = -36
Add 6.5 to each side;
17x-6.5+6.5 = -36+6.5
17x = 42.5
Divide by 17;
17x/17 = -42.5/17
x = -3.3
The x-values are approximate solutions to the equation f (x) = g(x) that is -3.3 thus the correct option is A.
Learn more about function here:
https://brainly.com/question/2253924
#SPJ5
150% of what number is 49?
Answers
Answer:
32 2/6
Step-by-step explanation:
150% of what number is 49
Can be written as;
1.5x = 49
( To find the percent of a number, one has to move the decimal back two spaces on the percent ( because a percent is out of 100), and then multiply by the number)
Use inverse operations to solve;
1.5x = 49
/1.5 /1.5
x = 32 2/3
Of the 245 7th graders, 40% of them are in band. How many 7th graders are in band?
Answers
Explanation:
1. Turn 40% into a decimal by removing the “%” and placing “0.” In front of it. (0.4)
2. Multiply the decimal (0.4) by the number of students (245) to get the answer. (0.4x245=98)
2.
11 10 1 2 3
(-3, -2)
(3, 6)
Answers
find the equation in slope-intercept form of the line that passes through the points (-3,4) & (2, -1)
Answers
Answer:
y=-x+`1
Step-by-step explanation:
Just follow the slope-intercept form formula-
Formula: y=mx+b
Key:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept
Let me know if you have any questions, hope this helps! (:
An artist is using tiles and boards for a project. A tile has length 1/4 ft and width 1/4 ft. A board has length 1/4 yd and width 1/4 yd. What is the ratio of the length of the tile to the length of the board? What is the ratio of the area of the tile to the area of the board?
Answers
Answer:
Ratio of lengths is 1:3
Ratio of areas is 1:9
Step-by-step explanation:
Firstly, we need the units to be same
Mathematically, 1 yard = 3 feet
A length of 1/4 yards = 1/4 * 3 = 3/4 feet
A width of 1/4 yards = 1/4 * 3 = 3/4 feet
The ratio of the length of the tile to the length of the board
that would be;
1/4 : 3/4 = 1: 3
Let’s now work with area
Mathematically, area in both cases is length * width
For the board, we have that;
3/4 * 3/4 = 9/16 square feet
For the tile, we have that;
1/4 * 1/4 = 1/16 square feet
so the ratio of the tile area to the board area will be;
1/16 : 9/16 = 1: 9
Which of the following is a solution to this inequality?
y > 1/2x + 2
Answers
Answer:
We conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.
Step-by-step explanation:
Given the inequality
y > 1/2x + 2
FOR (1, 4)
y > 1/2x + 2
substituting x = 1, and y = 4
4 > 1/2(1) + 2
4 > 1/2+2
4 > 5/2
TRUE!
Reason: It is true because 4 is indeed greater than 5/2
Thus, (1, 4) satisfies the inequality.
Therefore, (1, 4) is a solution to this inequality.
FOR (-1, 1)
y > 1/2x + 2
substituting x = -1, and y = 1
1 > 1/2(-1) + 2
1 > -1/2+2
1 > 3/2
FALSE!
Reason: It is false because 1 can not be greater than 3/2
Thus, (-1, 1) DOES NOT satisfy the inequality.
FOR (2, 3)
y > 1/2x + 2
substituting x = 2, and y = 3
3 > 1/2(2) +2
3 > 1+2
3 > 3
FALSE!
Reason: It is false because 3 can not be greater than 3.
Thus, (2, 3) DOES NOT satisfy the inequality.
FOR (0, 2)
y > 1/2x + 2
substituting x = 0, and y = 2
2 > 1/2(0) +2
2 > 0+2
2 > 2
FALSE!
Reason: It is false because 2 can not be greater than 2.
Thus, (0, 2) DOES NOT satisfy the inequality.
Therefore, we conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.
Work out the area of this circle
Answers
Answer:
Want the environment here?
solve the following equations
15+ 10z=105
Answers
Step-by-step explanation:
15+10z=105
10z=105-15
10z=90
z=9
What's 2/3 written as a fraction with a denominator of 9?
A.2/9
B.3/9
C.6/9
D.9/9
Answers
How many 2s go into 6 and 9
Help me please I'm confused
Answers
Answer:
The point (x, y) = (3, -4) represents the solution of the given system of equations.
Please check the attached graph.
Step-by-step explanation:
Given the system of equations
[tex]y\:=\:-\frac{3}{2}x\:-\:3[/tex]
[tex]y\:=\:-x\:-\:1[/tex]
Please check the attached graph of the given system of equations
From the graph:
The red line represents the equation: [tex]y\:=\:-\frac{3}{2}x\:-\:3[/tex]The blue line represents the equation: [tex]y\:=\:-x\:-\:1[/tex]Point of Intersection:
We know that the point of intersection of two lines represents the solution of the system of equations.It is clear from the attached graph that the two lines intersect at the point (-4, 3).
i.e. at x = -4, y = 3
Therefore, the point (x, y) = (3, -4) represents the solution of the given system of equations.
Please check the attached graph.
A farmer has 890 acres of land. She grows crops on 60% of her land. How many acres DO NOT have crops?
Answers
Answer:
It should be 356 acres that don't have crops
is 5x - 7 + 3x and 3x = 7 + 5x equivalent
Answers
Answer:No
Step-by-step explanation:
What is the perimeter of triangle ABC?
5
A
B.
0 20 units
4
o 22 units
3
0 24 units
2
o 26 units
1
-5 4
-2 -1
4
2 3
5
-2
-4
с
-5
Answers
Answer: 24 Units
Step-by-step explanation:
Got it right on edge!
Directions: Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
82
Step-by-step explanation:
please help
solve log(3x+2)=3
Answers
Answer:
x=334
Step-by-step explanation:
Answer:
0.33 or 1/3
Step-by-step explanation:
1/3=0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333...
It goes on and on(infinite)
what was honesty from thank you ma'am
IF YOU READ IT BEFORE
Answers
Answer:
Honesty was respect in Thank you ma'am.
Step-by-step explanation:
Another math question that I am stuck on
Answers
Answer:
The 1st and 3rd are not functions, the 2nd one is a function.
Step-by-step explanation:
If we do the vertical line test, we can see if there are multiple points on that line. The points can not have a repeating x intercept.
Given a
27 and b
-16, what is – a - b?
Answers
Answer:
-11
Step-by-step explanation:
-27-(-16)=-11 or, -27+16=-11
hey guys if you can please write it on the paper because i don’t really understand when they type out the steps but if you can though, i need to solve and put the steps or else i’ll get it wrong , it’s due in 10 minutes and i don’t know what to do please help, giving brainlest:((
Answers
Answer: w=210
Step-by-step explanation:
Answer:
W = 210
[tex]\frac{210}{6}=35[/tex]
Step-by-step explanation:
just multiply the two numbers:
6 x 35 = 210
so , 210/6 = 35
so basically W = 210
There are 156 laptops and desktop computers in a lab. There are 8 more laptops than deskto
computers. What is the total number of desktops in the lab?
Answers
Answer:
It would be 70
Step-by-step explanation:
First step: Divide 156 by 2
156 / 2 = 78
Second Step: The half of 156 is 78. Now we have 78 laptops and desktops, and as we know the question says that "there are 8 more laptops than desktops", the next step to follow is to subtract 8 from 78 (Desktops) and add 8 to the 78 (Laptops).
78 - 8 = 70 Desktops
78 + 8 = 86 Laptops
Hope this helps :)
simplify (3x+5)(2x+3)
Answers
Answer:
5x • 8
Step-by-step explanation:
First you'd switch the numbers around so they can work together.
(3x+2x)(5+3)
Then you add them together.
5x • 8
This would be the equation simplified.