Find domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36
Answer:
[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]
Step-by-step explanation:
Domain of Functions
Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.
The question provides us with the following functions
[tex]\displaystyle f(x)=x^2-3x-18[/tex]
[tex]\displaystyle g(x)=x^2-36[/tex]
[tex]\displaystyle h(x)=\frac{x^2-3x-18}{x^2-36}[/tex]
We called h(x) to the newly created function f/g(x)
To investigate the possible points of nonexistence for h, we factor h(x)
[tex]\displaystyle h(x)=\frac{(x-6)(x+3)}{(x-6)(x+6)}[/tex]
We can clearly see the denominator has two zeros at
[tex]\displaystyle x=6,\ x=-6[/tex]
A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.
So, the domain of h is
[tex]\displaystyle (-\infty,\ -6 )\bigcup (-6,\ 6)\bigcup (6,+\infty )[/tex]
Or equivalently
[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]
The domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, is all real numbers except x = 6 and x = -6. This is because we can't have g(x) equals to zero in (f/g)(x). Hence the domain is (-∞, -6) U (-6, 6) U (6, ∞).
Explanation:In Mathematics, when dealing with the domain of the function (f/g)(x) it is important to understand that the domain is the set of all possible x values that we can input into the function. For the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, the denominator g(x) cannot be zero as this would mean dividing by zero, which is undefined in Mathematics. So we need to find the values of x for which g(x) ≠ 0. To do this, we set g(x) equal to zero and solve for x. So, x^2-36=0. Simplifying this, we get (x+6)(x-6) = 0. Hence the roots of the equation are x = 6, x = -6.
These are the values for which g(x) will become zero. Since we can't have g(x)=0 in (f/g)(x), the domain of the function (f/g)(x) is all real numbers except x = 6, x = -6. So, the domain of (f/g)(x) is (-∞, -6) U (-6, 6) U (6, ∞).
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Megan picks a card from a deck of cards numbered 1-10 and rolls a number cube. What is the probability she chooses a card with a 5 and rolls an even number?
Answer:
Step-by-step explanation:
a deck of cards labeled 1 thru 10......probability of picking a 5 are 1/10 because there is 1 five card out of a deck of 10 cards.
number cube is rolled, probability of rolling an even number is 3/6 or 1/2....because u have 3 even numbers and ur number cube has 6 total numbers.
probability of both events happening are : 1/10 * 1/2 = 1/20 or 1:20 <==
The probability Megan chooses a card with a 5 and rolls an even number is 1 out of 20.
Explanation:
The probability of choosing a card with a 5 is 1 out of 10, since there is only one card numbered 5 out of the 10 cards in the deck.
The probability of rolling an even number on a number cube is 3 out of 6, since there are 3 even numbers (2, 4, and 6) out of the 6 possible outcomes of rolling the cube.To find the probability of both events happening, we multiply the individual probabilities together.
So the probability of choosing a card with a 5 and rolling an even number is (1/10) * (3/6) = 1/20.Therefore, the probability Megan chooses a card with a 5 and rolls an even number is 1 out of 20.
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The owner of a baseball stadium found that he sells an average of 586 tickets to each game when he charges an average of $59 per ticket. In addition, he found that with every $6 increase in ticket price, the average number of tickets sold decreases by an average of 4.
Which of the following functions describes the baseball stadium's profit in terms of x, the number of $6 increases over $59?
A.
P(x) = $34,574 + $3,280x - $24x2
B.
P(x) = $34,574 + $3,516x
C.
P(x) = $59 + $3,280x
D.
P(x) = $59 - $3,752x - $24x2
Answer:
A: 34574+3280x-24x^2
Answer:
A
Step-by-step explanation:
took test
A concert sold out for 12 performances. Altogether 8,208 tickets were sold. How many tickets were sold for each performance?
Answer:
684 tickets were sold for each performance
Step-by-step explanation:
8,208 divided by 12 = 684
Answer:
684 tickets
Step-by-step explanation:
having been sold out means that all seats for 12 nights were sold with none left over.
given a total of 8,208 tickets were sold out for 12 nights,
number of tickets sold each night
= 8208 ÷ 12
= 684 tickets
I need help please and thanks
1st draw probability = 5/8
2nd draw probability = 4/7
probability of drawing two blue cards: 5/8 x 4/7 = 5/14
answer: 5/14
5n+-3n=-18 solve for n
Answer:
[tex] \: \: \: \: \: \: \: \: 5n + ( - 3n) = - 18 \\ = > 5n - 3n = - 18 \\ = > 2n = - 18 \\ = > n = \frac{ - 18}{2} \\ = > n = - 9[/tex]
Devonte is balancing his checking account. His account statement does not include a deposit of $107.00 that he made on
November 1st. What is Devonte's actual account balance?
10/5
Account Statement 10/1/13 through 10/31/13
Account Number: 98765624
Deposits
Deposit $520.00
Total Deposits
$520.00
Withdraw als
#057
10/3 $78.12
#058
10/16 $14.24
Total checks
$92.36
Total Other Withdrawals
$30.00
Total Withdrawals
$122.36
Balance as of 10/31
R $1223.26
Answer:
$1,330.26
Step-by-step explanation:
The solution is, Devonte’s actual account balance is $1,330.26.
What is a checking account do?A checking account gives smooth get admission to your money on your everyday transactional needs and facilitates keeping your coins cozy. clients can commonly use a debit card or exams to make purchases or pay payments. money owed may have special alternatives to help keep away from the month-to-month provider fee.
here, we have,
A transaction account, also called a bank account, chequing account, present-day account, call for a deposit account, or share draft account at credit score unions is a deposit account held at a financial institution or other monetary organization.
given that,
Devonte is balancing his checking account. His account statement does not include a deposit of $107.00 that he made on November 1st.
from the given data ,
so, we get,
Devonte’s actual account balance is $1,330.26.
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a=2/3b,b=15,c=?
please help dear lord
Answer:
10.
Divide b into thirds, and then add together 2 of those thirds.
15/3 = 5
5x2 is 10.
Sorry if that doesn't make sense but it's how I do it in my head lol.
Denzel is coming web sites for downloading music. One charges a 50 membershy lee plus
160.50 per song. Another Charges & 1.00 per song but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both web site
Question is not proper, Proper question is given below.
Denzel is comparing websites for downloading music. One charges a $5 membership fee plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both websites.
Answer:
Denzel would have to buy 10 songs to spend the same amount at both websites.
Step-by-step explanation:
Let the number of songs be 'x'.
Given:
One charges a $5 membership fee plus $0.50 per song.
So the total cost at one site will be membership cost plus charges per song multiplied by number of songs.
framing in equation form we get;
Total Cost at one site = [tex]5+0.5x[/tex]
Another website charges $1.00 per song, but has no membership fee.
So the total cost at Another site will be charges per song multiplied by number of songs.
framing in equation form we get;
Total Cost at Another site = [tex]1\times x=1x[/tex]
To find the number of songs that results in same cost we should equate the two expression and solve.
[tex]5+0.5x=x[/tex]
Combining like terms we get;
[tex]5 = x-0.5x\\\\5=0.5x[/tex]
Now Dividing both side by 0.5 we get;
[tex]\frac{0.5x}{0.5} = \frac{5}{0.5} \\\\x=10\ songs[/tex]
Hence Denzel would have to buy 10 songs to spend the same amount at both websites.
What is a reasonable distance between two cities? A. 200 km B. 200 m C. 200 cm D. 200 mm
Answer:
200 KM about 124 miles
Step-by-step explanation:
200 m is only 0.12 miles
200 cm is 78 inches
200 mm is 20 cm or 7.8 inches
if 10 custom engraved pens cost $100, how much will 8 of the same pens cost?
Answer:
They will cost $80.
Step-by-step explanation:
First, find the out how much 1 pen cost(unit rate).
To do that, divide 100 by 10.
100÷10= 10
So, each pen cost $10.
Now, multiply the cost of 1 pen times 8.
10×8= 80
This concludes that 8 of the same pens cost $80.
Determine the intercepts of the line.
-5x+9y=-18−5x+9y=−18
x-intercept: (__), (__)
y-intercept: (__), (__)
Answer:
x-intercept: (18/5,0)
y-intercept: (0,-2)
Step-by-step explanation:
btw .. you put the equation twice it's supposed to be " -5x+9y=-18 "
In the diagram m ∠ 3 = x + 30 and m ∠ 4 = 2x - 80. What is the measure of angle 3?
50
80
110
140
Answer:
140 degrees
Step-by-step explanation:
Due to ∠3 and ∠4 being vertical angles (they are across from one another) their measures are the same, therefore:
⇒ m∠3=m∠4
and since their measures are given in terms of x to find x just substitute:
⇒ x+30=2x-80 ⇒ x=110
We substitute x in m∠3=x+30 and find that m∠3=140 degrees
Answer:
The answer is 140 i just did the lesson
Step-by-step explanation:
Pre cal help please
We have the following function
[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]
We want to know what is the value of f(x) when x is 19
[tex]f(19)=\frac{3}{19+2}-\sqrt{19-3}=1/7-4=\boxed{-27/7}[/tex]
If you have additional questions feel free to ask.
Hope this helps.
If you know a root of a function is -2 + the square root of 3i then _____. 2 + the square root of 3i is a possible root. 2 + the square root of 3i is a known root. -2 - the square root of 3i is a possible root. -2 - the square root of 3i is a known root. Just finished the assignment got it wrong but the correct answer is -2 - the square root of 3i is a known root
Answer:
-2 - the square root of 3i is a known root
Step-by-step explanation:
we know that
The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial
we have that
The root of a function is [tex]-2+\sqrt{3}i[/tex]
so
Applying the conjugate root theorem
[tex]-2-\sqrt{3}i[/tex] ---> is also a root of the function
therefore
-2 - the square root of 3i is a known root
Answer:
-2 - Squared 3i is a known root
Step-by-step explanation:
The angels of elevation of a ladder against a wall is 60 degree and the foot of the ladder is 4.6 m away from the wall.The length of the ladder is
Answer:
The length of the ladder is 9.2 meters
Step-by-step explanation:
Given as :
The angels of elevation of a ladder against a wall = 60°
The Distance of the foot of the ladder fro the wall = d = 4.6 meters
Let The length of the ladder = h meters
Now, According to question
cos angle = [tex]\dfrac{\textrm base}{\textrm hypotenuse}[/tex]
Or, cos 60° = [tex]\dfrac{\textrm d}{\textrm h}[/tex]
Or, 0.5 = [tex]\dfrac{\textrm 4.6}{\textrm h}[/tex]
∴ h = [tex]\dfrac{\textrm 4.6}{\textrm 0.5}[/tex]
i.e h = 9.2
So,The length of the ladder = h = 9.2 meters
Hence The length of the ladder is 9.2 meters Answer
Marley went to the candy store to buy her family some peppermints. All 4 members of her family each want 1 ¼ pound of peppermints. How many total pounds of peppermints must Marley buy?
All you must do is multiply 4 by 1 and 1/4, so 5 total pounds.
Hope this helps, if not, comment below please!!!!
Which is an exponential decay function?
f(x)=3/4(7/4)^x
f(x)=2/3(4/5)^-x
f(x)=3/2(8/7)^-x
f(x)=1/3(-9/2)^x
Answer: c
Step-by-step explanation:
Answer:
f(x)=3/2(8/7)^-x
Step-by-step explanation:
If you turn the fractions into decimals ([tex]\frac{3}{2}(\frac{8}{7} )[/tex]^-x = 1.5(1.14)^-x), put that number into y= in your graphing calculator and press graph you will be able to see, verses the other functions, that the line decreases.
90 PTS HELP
Maria has already written 2/5 of her 1,000 word essay. If she continues writing at the same pace of 6 words per minute, which expression shows the amount of time it will take her to write the rest of the essay?
Answer:
[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]
Step-by-step explanation:
First, let's find out how many words Maria has left to write. If she has already finished 2/5 of her essay, she has 3/5ths left to write. We can do 3/5 times 1000 to find out how many words are left.
[tex]\frac{3 }{5} * \frac{1000}{1}[/tex]
[tex]\frac{3000}{5}[/tex]
[tex]600[/tex]
Thus, there are 600 words left to write.
Now to find the amount of time, we can find how take to write 600 words at a pace of 6 words per minute by dividing 600 by 6.
[tex]\frac{600}{6}[/tex]
[tex]100[/tex]
It will take 100 minutes for Maria to write the rest of her essay. Now let's think about an expression that tells us this information. It sounds like your questions is supposed to have options, but I doesn't seem like you've posted them, no worries however.
So first, the amount she has left to write.
[tex](\frac{3}{5} * 1000)[/tex]
We know this is 600, but we don't have to simplify it for the expression.
Now thinking back to how we found the time, we can divide this '600' by 6.
[tex]\frac{(\frac{3}{5}*1000) }{6}[/tex]
This is the expression that shows the amount of time it will take to write the rest of the essay.
[tex]\frac{((1-(\frac{2}{5})*1000) }{6}[/tex] is also a valid solution.
Final answer:
Maria has 600 words left to write in her essay, and at 6 words per minute, it will take her 100 minutes to finish writing the remaining part.
Explanation:
Maria has written 2/5 of her essay, which means she has written 400 words (2/5 of 1,000 words). To find out how long it will take her to write the remaining 3/5 of her essay, we need to calculate 3/5 of 1,000 words, which is 600 words. If she writes at a pace of 6 words per minute, we can find the time by dividing the remaining number of words by her writing pace.
The expression that shows the amount of time it will take her to finish the essay is:
(Total remaining words) / (Words per minute)
= (3/5 of 1,000) / 6
= 600 / 6
= 100 minutes
HELP FAST PLS
What is the difference between the Pythagorean Theorem and its converse?
A. The Pythagorean Theorem states that the sum of the squares of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that the sum of the squares of the two shortest sides of a triangle that is not a right triangle does not equal the square of the longest side.
B. The Pythagorean Theorem states that the sum of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that the sum of the two shortest sides of a triangle that is not a right triangle does not equal the square of the longest side.
C. The Pythagorean Theorem states that the sum of the squares of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that if the sum of the squares of the two shortest sides of a triangle equals the square of the longest side, then the triangle is a right triangle.
D. The Pythagorean Theorem states that the sum of the two shortest sides of a right triangle equals the square of the longest side. The converse of the Pythagorean Theorem states that if the sum of the two shortest sides of a triangle equals the square of the longest side, then the triangle is a right triangle.
Answer:
The converse of the Pythagorean theorem states that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Answer:
its C basically
Step-by-step explanation:
Why is 3 x 1/10 less than 3 x 10
3 x 1/10 is 0.3 because it represents one tenth of 3, while 3 x 10 is 30 as it increases the value of 3 tenfold. Powers of ten and negative exponents demonstrate that each step in exponent changes the scale of the number by a factor of ten.
The reason why 3 x 1/10 is less than 3 x 10 is due to the values being multiplied by 3. When multiplying 3 by 1/10, you are essentially taking one tenth of 3, which gives you 0.3. However, when multiplying 3 by 10, you are increasing 3 tenfold, which results in 30.
To understand the scale, considering that each positive power of 10 is ten times bigger than the previous one, for instance from 3.2 to 3.2 x 10, and each negative power is ten times smaller, like from 3.2 to 3.2 x 1/10 . Powers of ten and their associated exponents allow us to easily compare and calculate with vastly different magnitudes, and this concept underlies the multiplication comparisons posed in the initial question.
What are like terms for 28?
Answer:
all the constants
Step-by-step explanation:
help asap will give BRAINLIEST
a. < 2 and < 8
b. < 3 and < 7
c. < 2 and < 4
d. < 1 and < 8
The answer: d. < 1 and < 8
A sequence of transformations which moves ΔRST onto ΔXYZ shows that ΔRST ≅ ΔXYZ. Which part of the triangles are congruent by CPCTC?
Answer:
Here's what I get
Step-by-step explanation:
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
If ΔRST ≅ ΔXYZ then
∠R = ∠X
∠S = ∠Y
∠T = ∠Z
RS = XY
ST = YZ
RT = XZ
To prove ΔRST ≅ ΔXYZ, perform a sequence of transformations and apply CPCTC to identify congruent parts.
Explanation:To prove that ΔRST ≅ ΔXYZ, we need to perform a sequence of transformations that move ΔRST onto ΔXYZ. Once the triangles are superimposed, we can use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to identify congruent parts.
CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent. In this case, the parts of ΔRST that are congruent to the corresponding parts of ΔXYZ are:
Side RS is congruent to side XYSide ST is congruent to side XZAngle R is congruent to angle XLearn more about Congruent Triangles here:https://brainly.com/question/31700817
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(PLEASE HELPPPP 20 POINTS)
Marc left his house to drive to work. He slowly pulls out of his driveway at a constant speed, and then his speed increases steadily until he reaches the speed limit. He uses cruise control to drive the speed limit until he comes upon some traffic. He then slows down to a new constant speed. When he gets near his office, his speed steadily decreases until he comes to a stop right in front of his office building.
Which graph represents Marc’s drive to work?
Answer:
The 3rd picture.
Hope this helps :)
Answer:
yeah its the third picture hope this helped you
If 3 inches represents 90 miles on a scale drawing, how long would a line segment be that represents 240 miles?
Answer:
8 inches
Step-by-step explanation:
90 miles -------------> represented by 3 inches
1 mile -------------> represented by 3/90 inches
240 miles ----------> represented by 3/90 x 240 = 8 inches
To determine the length of a line segment that represents 240 miles on a scale drawing, set up a proportion using the information given. The line segment would be 8 inches long.
Explanation:To determine the length of a line segment that represents 240 miles on a scale drawing, we can set up a proportion using the information given. The scale in the drawing states that 3 inches represent 90 miles. We can cross-multiply and solve for the unknown length as follows:
3 inches / 90 miles = x inches / 240 miles
To solve for x, we can multiply both sides of the equation by 240 and then divide by 90:
x inches = (3 inches / 90 miles) * 240 miles
x inches = 8 inches
Therefore, a line segment that represents 240 miles on the scale drawing would be 8 inches long.
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Graph the solution of the inequality on a number line 2(x-3)-5x
Answer:
Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.
Step-by-step explanation:
The inequality is given as follows:
[tex]2\left(x-3\right)-5x<x-2[/tex]
Let's solve your inequality step-by-step
[tex]2\left(x-3\right)-5x<x-2[/tex]
[tex]2x-6\right)-5x<x-2[/tex]
[tex]-3x-6<x-2[/tex]
[tex]-6+2<x+3x[/tex]
[tex]-4<4x[/tex]
Divide both sides by -4.
[tex]x>-1[/tex]
Graph the solution of the inequality on a number line is attached in figure a that satisfies the graph of the solution set x > -1.
Keywords: inequality, graph solution
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the label on a 1 and 1/2 pound bag of wildflower seeds states thatbit will cover an area of 375 Square feet.Bags are sold by the pound and cost $2.50 per bag.If silas wants to cover 1,000 square feet ,how much does he need to spend on tthe wildflower seeds?
Answer:
I think its like $6.67
Step-by-step explanation:
divide 1000 by 375 then multiply the answer to that by 2.50 u should get 6.666666666666667 round it to 6.67
write an equation of a line parallel to y = 5x + 4 that passes through (-1, 2)
Answer:
[tex]y=5x+7[/tex]
Step-by-step explanation:
step 1
Find the slope of the line parallel to the given line
we know that
If two lines are parallel, then their slopes are equal
The equation of the given line is [tex]y=5x+4[/tex]
The slope of the given line is [tex]m=5[/tex]
so
The slope of the line parallel to the given line is also [tex]m=5[/tex]
step 2
Find the equation of the line parallel to the given line
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=5[/tex]
[tex]point\ (-1,2)[/tex]
substitute
[tex]y-2=5(x+1)[/tex]
step 3
Convert to slope intercept form
Isolate the variable y
[tex]y-2=5x+5[/tex]
[tex]y=5x+5+2[/tex]
[tex]y=5x+7[/tex]
Solve this problem -9z=-207
Answer:
Step-by-step explanation:
-9z=-207
Dividing each term by -9
z = -207/-9
z = 23
Answer:
23
Step-by-step explanation:
-9z=-207
divide by 9 on both sides
z=23
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