what is the domain of the function f(x)=x-9/x+8? Write your answer in interval notation.
Answers
Answer: [tex](-\infty, -8) \cup (-8, \infty)[/tex]
Step-by-step explanation:
I'm assuming you meant [tex]f(x)=\frac{x-9}{x+8}[/tex]
For this function, we need to make sure the denominator is not equal to 0, because if it was, then the fraction would be undefined.
Thus, [tex]x+8 \neq 0 \longrightarrow x \neq -8[/tex]
In interval notation, this is [tex](-\infty, -8) \cup (-8, \infty)[/tex]
Related Questions
If f(x) = 3x − 1 and g(x) = x + 2, find (ƒ– g)(x)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]
[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]
Simple procedure :
[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]
[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]
[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
Answers
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
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what is the variable equal to y8=40
Answers
You can divide 40 by 8 and you get 5. y=5
Answer:
5
Step-by-step explanation:
We need to isolate the variable, aka make y on one side. So, if we divide 8 on both sides, it will be
y8=40
y8/8=40/8
y=5
Tickets for a soccer game cost $5 for students and $8 for adults. the number of students was 7 less than 11 times the numbers of adults. the amount of the money from tickets was 3682 how many of each tickets were sold?tichets
Answers
The number of students will be 642 and the number of the adults will be 59.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Tickets for a soccer game cost $5 for students and $8 for adults.
The number of students was 7 less than 11 times the numbers of adults.
The amount of the money from tickets was 3682.
Let x be the number of students and y be the number of the adults.
Then the equation will be
x = 11y – 7 …1
5x + 8y = 3682 …2
From equation 1 and 2, we have
5(11y – 7) + 8y = 3682
55y + 8y – 35 = 3682
63y = 3717
y = 59
Then the value of x will be
x = 11 × 59 – 7
x = 642
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Question 2(Multiple Choice Worth 4 points)
If (89)P=818, what is the value of p?
02
09
10
18
Answers
Answer:
p = 2
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](8^{9}) ^{2}[/tex] = [tex]8^{9(2)}[/tex] = [tex]8^{18}[/tex]
so value of p = 2
Which statements are true from the graph ? Check all that apply:
the line is horizontal the line is vertical
Answers
The statements that are true from the graph are:
The line is horizontalThe line goes through (4, 4 )The y- values are all 4Calculations and ParametersGiven the graph, we can note some things:
There is a line with a slope of zero.This is a horizontal line parallel to the x-axis.The equation of the line is y = cc is the value of the y- coordinates the line passes through.
The line passes through (0, 4 ) with a y- coordinate of 4
Therefore, the equation of the line of y= 4
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The stock of Company A lost 2% today to $73.50. What was the opening price of the stock in the beginning of the day?
Answers
The opening price of the stock in the beginning of the day will be $75.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
The stock of Company A lost 2% today to $73.50.
Let x be the opening price of the stock in the beginning of the day.
Then the opening price of the stock in the beginning of the day will be
0.98 · x = 73.5
x = 73.5 / 0.98
x = $75
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What is the median of this data set?
22, 37, 49, 15, 72
Answers
Steps:
Order the numbers from least to greatest.
15, 22, 37, 49, 72
The median value is the middle number.
37
forty percent of participants in a math contest were boys. fifty percent of the boys revived medals. the number of boys who received the medals was equal to the number of girls who received the medals. what percent of the participants were girls who received medal?
Answers
20% of the participants are girls and got a medal, and 33% of the girls got a medal.
What percent of the participants were girls who received medal?
First, we know that 40% of the participants were boys, so the other 60% were girls.
We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:
P = (0.4)*(0.5) = 0.2
So, 20% of the participants are boys and got a medal.
We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.
Then if the percentage of girls that got a medal is x (in decimal form), we must have that:
Q = (0.6)*(x) = 0.2
x = 0.2/0.6 = 0.33
x = 0.33
This means that 33% of the girls got a medal.
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An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
Answers
Reason
You can use the formula y=mx+b for this
We know y is the total bill of $99
We know b is the $40 fee (y intercept or starting point)
We know x is 2 hours
We are looking for m or rate
Substitute numbers for letters in formula
99= m(2) +40
Subtract 40 from both sides to isolate m
59=2m
Divide both sides by 2 to solve for m
M=$29.50
We can prove our answer by inserting our answer for “m” in the formula
99=29.50x2+40
99=99
Answer is correct
Help me with this question please!! :)
Answers
Answer: 20/63
Step-by-step explanation:
The probability that the first marble is red is 16/28.The probability that the second marble is red is 15/27.Multiplying these probabilities, we get (16/28)(15/27) = 20/63
Please help, been stuck on this for ages!
Answers
Answer:
[tex]\boxed {192 cm^{2}}[/tex]
Step-by-step explanation:
Find the volume of separate cuboids :
Volume (top cuboid) :
⇒ V = 2 x 6 x (10 - 2)
⇒ V = 12 x 8
⇒ V = 96 cm²
Volume (lower cuboid) :
⇒ V = 8 x 6 x 2
⇒ V = 48 x 2
⇒ V = 96 cm²
Volume (prism) :
⇒ 96 + 96
⇒ 192 cm²
6x -8=16 solve equation
Answers
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 16 (add 8 to both sides)
6x = 24 (divide by 6 on both sides)
x = 4
Brainliest, please :)
Step-by-step explanation:
6x=16+8
6x=24
6x/6=24/6
x=4
so the answer is 4
Factor out the GCF from the polynomial.
r(2²-24) + (2²-24)
Answers
Answer: -20
Step-by-step explanation: i hope its right
Find X and QT. The shape is a Rhombus
Answers
Answer:
See below ~
Step-by-step explanation:
Sides of a rhombus are equal.
⇒ QT = TS
⇒ x² - 4x - 10 = 6x + 14
⇒ x² - 10x - 24 = 0
⇒ x² + 2x - 12x - 24 = 0
⇒ x (x + 2) - 12 (x + 2) = 0
⇒ (x + 2)(x - 12) = 0
⇒ x = -2 or x = 12
Substitute both values and see which gives a positive value for QT :
When x = -2 :
QT = (-2)² - 4(-2) - 10QT = 4 + 8 - 10QT = 2When x = 12 :
QT = (12)² - 4(12) - 10QT = 144 - 48 - 10QT = 86The 2 possible answers are :
x = -2, QT = 2x = 12, QT = 86Find the value of x.
Answers
Answer:
Step-by-step explanation:
plug in x try numbers
x = 14.2
What is the surface area of the cylinder below?
Answers
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
Based on the vertical bar chart below, in which of the following months were just over 10% of professional European soccer players
born?
March
B) January
April
May
Professional European soccer player birth months
Relative frequency (%)
20%
15%
10%
5%
Jan Feb Mar Apr May Jun
ایل
Month
....
Aug Sep Oct Nov Dec
Answers
By critically observing the vertical bar chart, only the month of May had a birth of just over 10%.
What is a bar chart?A bar chart refers to a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
Based on the vertical bar chart (see attachment), the relative frequency (&) with the birth of over 10% are:
Jan Feb Mar Apr MayHowever, only the month of May had a birth of just over 10%.
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3a =2b + -6 (solve for a)
Answers
Answer:
shown below
Step-by-step explanation:
3a = 2b - 6
a = (2b - 6) / 3 or 2b / 3 - 2
Answer:
a = (2b-6)/3
Step-by-step explanation:
3a = 2b + -6
lets make a the subject of the formula
divide both sides of the equation by 3
3a/3 = a = (2b-6)/3
a = (2b-6)/3
A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?
Answers
The worker's expected weekly bonus is $30.0
How to determine the worker's expected weekly bonus?The amounts and the probabilities are given as:
x $10 $50
P(x) 0.75 0.25
The worker's expected weekly bonus is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = $10 * 0.75 + $50 * 0.25
Evaluate the product
E(x) = $17.5 + $12.5
Evaluate the sum
E(x) = $30.0
Hence, the worker's expected weekly bonus is $30.0
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Calculate the gross earning for an apple picker based on the following differential pay scale: 1- 1000:$0.03 each 1001-1600:$0.06 each over 1600:$0.07 each. Calculate the Gross earning
Answers
If he picks 1965, then the Gross earning will be $85.55.
The missing part of the question is given below.
If he picks 1965, then Calculate the Gross earning.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Calculate the gross earning for an apple picker based on the following differential pay scale:
1 – 1000: $0.03 each
1001 – 1600: $0.06 each
over 1600: $0.07 each
Total apples picked by Lindbergh = 1965
So, for 1000 apples, he will get =1000 × 0.03 = $30
Now, remaining apples = 1965 – 1000 = 965
Now for next 600 apples (from 1001-1600), he will get = 600 × 0.05 =$30
Now, remaining apples = 965 – 600 = 365
So, for remaining 365 (above 1600) apples, he will get = 365 × 0.07 = $25.55
So, total gross earning = $30 + $30 + $25.55
⇒ $85.55 is total gross earning
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Which results only in a horizontal compression of Y=1/x
by a factor of 6?
Answers
Step-by-step explanation:
[tex] y = \frac{1}{x} [/tex]
In order to compress by a factor of 6, we multiply the variable x by 6. It would compress the hyperbola
[tex]y = \frac{1}{6x} [/tex]
What is the value of the expression 24 + 3²? What is the value of the expression 24 + 3² ?
Answers
Answer:
33
Step-by-step explanation:
3² = 3.3 = 9 => 24 + 9 = 33
Find the measure of PR.
Answers
The length of PR = 18 .
What is a Chord ?A chord is a line segment whose both points lie on the circle.
When a chord is extended it is called secant .
When two chords meet outside the circle , the product of length of the secant and its external segment is equal to the product of length of other secant and its external segment.
According to the given data
FR and FP are the secants of the circle
To determine the measure of PR
From the secant theorem
(7+9) * 9 = (5x+8) * 8
16 * 9 = (5x+8) *8
2 *9 = 5x+8
18 = 5x+8
5x = 10
x = 2
Therefore the length of PR = 5x+8 = 10+8 = 18
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list 4 factors of 24. list 4 multiples of 24.
Answers
Answer:
Factors of 24: 1, 2, 3, 4, 6 etc.
Multiples of 24: 48, 72, 96, 120
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Factors of 24:24 can be written as:
= 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.
Multiples of 24 are:1 × 24 = 24
2 × 24 = 48
3 × 24 = 72
4 × 24 = 96
and so on...
So, the first 4 multiples of 24 are 24, 48, 72 and 96.
[tex]\rule[225]{225}{2}[/tex]
what is the answer to the question?
Answers
Using logic concepts, the correct statement is given by:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
What are the events in this problem?The events are:
Event P: Henry is wearing a red shirt.Event Q: Henry is wearing khaki shirts.The statement is:
Henri is wearing a red or blue shirt today with jeans.
A red or blue shirt can be represent by p or not p, that is:
[tex](p \vee \neg p)[/tex]
Jeans is not khaki, hence the second part is:
[tex]\neg q[/tex]
Combining the statements, we have that the expression is:
[tex](p \vee \neg p) \wedge \neg q[/tex]
Since p and q are true, [tex]\neg q[/tex] is false, and the entire statement is false. Hence the correct option is:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
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When completing the square on the equation c^2 + 11c = 12, the resulting solution is
Answers
Answer:
Attached file is the solutions
Step-by-step explanation:
The sequence an = 1(3)n − 1 is graphed below: coordinate plane showing the points 1, 1; 2, 3; and 3, 9 Find the average rate of change between n = 1 and n = 3. (6 points)
Answers
Answer:
4
Step-by-step explanation:
[tex] \frac{9 - 1}{3 - 1} = 4[/tex]
The average rate of change on the interval [3, 9] will be 4.
How to find the average rate of change?The average rate of change between two points is given by the slope formula:
m = average rate of change = (y2 -y1)/(x2 -x1)
The sequence an = 1(3)n − 1 is graphed below:
m = (9 -1)/(3 -1) = 8/2
m = 4
The average rate of change on the interval [3, 9] will be 4.
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Please help!!! I will give 20 points to the correct answer !! Thanks so much
Answers
Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.
Answers
When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
Prices = 1,650,000
Exchange rates = ¥197/£
Change in exchange rate = ¥190/£
So, here Original price of the Toyota tundra is
= 1,650,000 ÷ 197
= 8375.63
New import price is = 1,650,000 ÷ 190
= 8,684.21
Percentage change in the price of the imported trucks should be
= ( New price - Old price) / old price *100 = (8,684.21 - 8375.63) ÷ 8375.63 = 3.68%
Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).
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