Answers
The highlighted part of circle shown below is known as segment.
What is the segment of a circle?A segment of a circle is a region of the circle that is bounded by a chord and the arc that it intersects. More specifically, a segment is the region between a chord and a minor or major arc of a circle.
The chord is the straight line that connects two points on the circumference of the circle, and the arc is the curved part of the circumference that lies between these two points. A segment is named according to its chord, for example, the segment determined by the chord AB is referred to as segment AB. The area of a segment of a circle can be calculated using the formula A = (1/2)r^2(θ-sinθ), where r is the radius of the circle, and θ is the central angle of the segment in radians.
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Related Questions
Every day Ms.Twinkle walks around a park near her house. The park is the shape of a rectangle 2 mi long and 1 3/10 mi wide. How far does she walk.
Answers
Ms. Twinkle walks a total of 6.6 miles around the park.
What is perimeter ?
Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
To find how far Ms. Twinkle walks, we need to find the perimeter of the rectangle-shaped park, which is the sum of the lengths of all its sides.
The length of the park is 2 miles and the width is 1 3/10 miles. We can write the width as a mixed number of 1 + 3/10 = 13/10 miles.
Therefore, the perimeter of the park is:
Perimeter = 2(length + width)
Perimeter = 2(2 + 13/10)
Perimeter = 2(20/10 + 13/10)
Perimeter = 2(33/10)
Perimeter = 66/10
Perimeter = 6.6 miles
Therefore, Ms. Twinkle walks a total of 6.6 miles around the park.
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At the movie theatre, child admission is $5.30 and adult admission is $8.70. On Saturday, 163 tickets were sold for a total sales of $1169.90. How many child tickets were sold that day?
Answers
The number of child tickets were sold that day are 73.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of child admission= $5.30
Cost of adult admission= $8.70
Now,
Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:
c + a = 163 (equation 1: the total number of tickets sold)
5.30c + 8.70a = 1169.90 (equation 2: the total sales)
We can use equation 1 to solve for "a" in terms of "c":
a = 163 - c
Substituting this expression for "a" into equation 2, we get:
5.30c + 8.70(163 - c) = 1169.90
Simplifying and solving for "c", we get:
5.30c + 1418.10 - 8.70c = 1169.90
-3.4c = -248.20
c = 73
Therefore, by algebra the answer will be 73.
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a library has fiction and nonfiction books. The ration of the number of fiction books to the total number of books is 5:8. What is the ratio of the fiction to the nonfiction books in the library?
Answers
The ratio of fiction books to nonfiction books in the library is 5:3.
What are Ratios?
A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.
Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).
Then, the number of nonfiction books in the library is 8x - 5x = 3x.
Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:
5x/3x = 5/3
So, the ratio of fiction books to nonfiction books in the library is 5:3.
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help................................................
Answers
Answer:
I think question #1 is C
Question #2 is C
and Question #3 is A
Mengxi has $10 000 to invest. She invests part in a term deposit paying 5% /year, and the remainder in Canada Savings Bonds paying 3. 5% /year. At the end of the year, she has earned simple interest of $413. How much did she invest at each rate? (Algebra)
Answers
Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.
Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.
At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).
Thus, we can write the following equation to represent the total interest earned:
0.05x + 0.035(10000 - x) = 413
Simplifying the equation, we get:
0.015x + 350 = 413
0.015x = 63
x = 4200
Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.
To check the answer, we can calculate the interest earned from each investment and add them up:
0.05(4200) + 0.035(5800) = 210 + 203 = 413
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A hat contains three slips of paper. One of the following names is written on each slip of paper. Analise, Benjamin, and Cora
Which list gives the sample space for pulling two slips of paper out of the hat with replacement?
Answers
The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. A sample space may contain a number of outcomes that depends on the experiment.
For example if a fair die is thrown, the probability of getting an even number. This means that the sample space of even number in a fair die is 3 i.e, 2,4 and 6
Similarly, There are three names with slip, Analise, Benjamin and cora, the sample space to bring 2 slips out with replacement has this results
The slips can be;
1. Benjamin, cora
2. Analise, cora
3. Benjamine, Analise
4. Analise , Benjamin
5. cora, Analise
6. cora, Benjamin
7. cora, cora
8. Benjamin, Benjamin
9. Analise, Analise
The list that shows these result or sample space is list 4
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Answer:
The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)
Step-by-step explanation:
Which situation could be described by the expression f + 1/2
Use the / as a fraction bar
A. Lela walked f miles yesterday, and mile today.
B. Lela walked f miles yesterday, and miles fewer today.
C. Lela walked mile yesterday, and f miles fewer today.
D. Lela walked mile yesterday, and f times as far today.
Answers
B. Lela walked f miles yesterday, and miles fewer today.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
The situation that could be described by the expression f + 1/2 is:
B. Lela walked f miles yesterday, and miles fewer today.
The expression f + 1/2 represents the total distance that Lela walked over two days, where "f" represents the distance she walked yesterday, and "1/2" represents the distance she walked today.
Option B describes the situation where Lela walked "f" miles yesterday and "1/2" times fewer miles today (or, equivalently, "1/2" times the distance she walked yesterday).
Therefore, the expression f + 1/2 is a valid way to describe this situation.
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please helppp!!!!!!!
Answers
Note that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
What is the definition of the Right Angle postulate?
The postulate indicates that if two lines intersect and make the two adjacent angles equal to each other, then each of the equal angle is a right angle. Also, the two lines that intersect this way is said to be perpendicular to each other.
Since the ∠MRS ≅ ∠MRO, we can state that the correct theorem or definition that justifies the given statement for the diagram is the definition of Right angle postulate.
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Answer:
nothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanksnothaanks
the circle has a central angle of 56° as shown in the diagram. what is the length of minor arc ab
Answers
In the diagram, the length of minor arc AB is approximately 3.9 inches
Calculating the length of an arcFrom the question, we are to calculate the length of the minor arc AB
To calculate the length of an arc, we can use the formula:
Arc Length = (Central Angle / 360) x (2πr)
Where:
Central Angle is the angle formed by the two radii at the center of the circle
r is the radius of the circle
From the given information,
Central angle = 56°
r = 4 in
Substituting the given values, we get:
Arc Length = (56° / 360) x (2π x 4 in)
Arc Length = 3.9095 in
Arc Length ≈ 3.9 in
Hence, the length of minor arc AB is approximately 3.9 inches
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Logan invested $3,800 in an account paying an interest rate of 5% compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
Answers
Answer:
Step-by-step explanation:
The formula to calculate the doubling time for continuously compounded interest is:
t = ln(2) / (r * ln(1 + (r/n)))
where t is the time in years, r is the annual interest rate as a decimal, and n is the number of times the interest is compounded per year (which is infinity for continuous compounding).
For Logan's investment, we have:
r = 0.05
n = infinity
t1 = ln(2) / (0.05 * ln(1 + (0.05/infinity)))
t1 ≈ 13.86 years
For Qasim's investment, we have:
r = 0.06
n = 1
t2 = ln(2) / (0.06 * ln(1 + (0.06/1)))
t2 ≈ 11.55 years
To find the difference in the time it takes for their investments to double, we can subtract t2 from t1:
t1 - t2 ≈ 13.86 - 11.55 ≈ 2.31
So it would take Logan's money approximately 2.31 years longer to double than Qasim's money, to the nearest hundredth of a year.
HELP ME IM GIVING 16 BRAINLIEST IF HELP
Answers
Answer:
277 milliliters
Step-by-step explanation:
945-668= 277
Abstract Algebra (6408 Math) Homework (3) Let \( R \) be a ring. Question 1 Show that \( 0_{R} x=0_{R} \) for all \( x \in R \). Question 2 If \( a, b \in R \), show that \( -(a b)=(-a) b \). Best wis
Answers
Abstract Algebra
By additive inverse property, \( 0_{R} x=0_{R} \) for all \( x \in R \) is hence proved. And by distributive property, \( -(a b)=(-a) b \) is proved.
Question 1: We know that the additive identity of a ring is 0. So, 0+0=0. Now, for any element x in R, we have 0x=(0+0)x=0x+0x. By the additive inverse property, we can subtract 0x from both sides to get 0=0x. So, 0x=0 for all x in R.
Question 2: We know that the additive inverse of an element a in a ring R is -a, such that a+(-a)=0. Now, for any elements a and b in R, we have ab+(-ab)=0. By the distributive property, we can rewrite this as ab+((-a)b)=0. So, -(ab)=(-a)b for all a and b in R.
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What are three equivalent ratios for 15/35
Answers
1) 3/7
2) 9/21
3) 150/350
Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through twelve!
Even Unlikely Impossible
Answers
The answer response are:
A duck with wings: Likely Duck number 7: Unlikely A duck with a number greater than 3: Certain Duck number 15: Impossible A duck with a number greater than 10: Unlikely A duck with a number: Certain Duck number 4: Likely A duck with sunglasses: Impossible A duck with a hat: Unlikely An even-numbered duck: LikelyHow do you explain the probability?A duck with wings: Likely
There is a high likelihood that all the ducks have wings since it is a natural characteristic of ducks.Duck number 7: Unlikely
There are 12 ducks in total, and only one of them is duck number 7, so the probability of choosing duck number 7 is 1/12, which is unlikely.A duck with a number greater than 3: Certain
There are 9 ducks with numbers greater than 3 (4, 5, 6, 7, 8, 9, 10, 11, 12), so it is certain that you will choose a duck with a number greater than 3.Duck number 15: Impossible
There are only 12 ducks, and none of them are numbered 15, so it is impossible to choose duck number 15.A duck with a number greater than 10: Unlikely
Only two ducks have numbers greater than 10 (11, 12), so the probability of choosing a duck with a number greater than 10 is 2/12 or 1/6, which is unlikely.A duck with a number: Certain
All ducks have numbers from 1 to 12, so it is certain that you will choose a duck with a number.Duck number 4: Unlikely
There is only one duck numbered 4, so the probability of choosing duck number 4 is 1/12, which is unlikely.A duck with sunglasses: Impossible
There is no information given that any of the ducks have sunglasses, so it is impossible to choose a duck with sunglasses.A duck with a hat: Unlikely
There is no information given that any of the ducks have hats, so the probability of choosing a duck with a hat is unlikely.Lastly, An even-numbered duck: Likely
There are six even-numbered ducks (2, 4, 6, 8, 10, 12), so the probability of choosing an even-numbered duck is 6/12 or 1/2, which is likely.Learn more about probability here:
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See transcribed text below
Date:
Period:
What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).
33
1. A duck with wings
2. duck number 7
3. a duck with a number greater than 3
4. duck number 15
5. a duck with a number greater than 10
6. a duck with a number
7. duck number 4
8. a duck with sunglasses
9. a duck with a hat
10. an even-numbered duck
The ducks are numbered From one through twelve!
Kibb
Certain
Likely
Even
Unlikely Impossible
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The sum of two numbers is 72. The difference of the two numbers is 50. Let x be the larger number and ybe the smaller number. Set up and evaluate a system of equations to determine the values of x and y.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."
First equation:
Write an equation that expresses the information in the sentence "The difference of the two numbers is 50."
Second equation:
Solve the system you have written above to find x and y.
x= . y= .
Answers
the bigger number x= 61 and the smaller number y = 11. The system of equations are x + y= 72 and x - y = 50
The sum of two numbers is 72 can be expressed as a linear equation: x + y = 72. The difference of the two numbers is 50 can be expressed as a linear equation: x - y = 50. We can set up a system of equations to determine the values of x and y:
First equation: x + y = 72
Second equation: x - y = 50
To solve the system of equations, we can use the elimination method. We can add the two equations together to eliminate the y variable:
x + y = 72
x - y = 50
--------------
2x = 122
Next, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 122/2
x = 61
Now that we know the value of x, we can plug it back into one of the equations to find the value of y:
61 + y = 72
y = 72 - 61
y = 11
So the solution to the system of equations is x = 61 and y = 11.
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find the measure of rhf
Answers
Answer:
<RHF = 68°
Step-by-step explanation:
<RHG and <FHY are vertical opposite angle which mean they equal to each other.
<RHG = <FHY
(6m+88) = (7m+84)
88 - 84 = 7m - 6m
4 = m
Plug m=4 into the <RHG to solve for the measurement.
<RHG = 6m+88
<RHG = 6*4+88
<RHG = 24+88
<RHG = 112°
<RHG and <RHF are supplementary angle which mean they both linear adding up to 180°
<RHF + <RHG = 180°
<RHF + 112° = 180°
<RHF = 68°
Chase starts an IRA (Individual Retirement Account) at the age of 26 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65 his retirement savings is $838,879.58, Determine the amount of money Chase deposited over the length of the investment and how much he made in interest upon retirement Formulas
Answers
The total number of months he made deposits and multiply that by the monthly deposit amount.
Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.
Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468
Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200
To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.
Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58
Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.
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A small kiddie pool starts with 110 gallons of water. The pool is being drained at a constant rate of 4 gallons per minute. How many minutes could have passed if the pool now has less than 74 gallons of water left? Write an inequality to represent the situation. Use x to represent the number of minutes.
Thank you sooo much if you answer this I have like five missing assignments and grades are due in two days and it takes that long for my teacher to grade it. She slow.
Answers
The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The amount of water remaining in the pool after x minutes is given by:
110 - 4x
We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.
110 - 4x < 74
To solve for x, we can first subtract 110 from both sides of the inequality:
-4x < 74 - 110
Simplifying, we get:
-4x < -36
Divide both sides of the inequality by -4,
x > 9
Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.
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5r^(2)-5r+2=0 How many real solutions does the equation have? no real one real two real solutions solution solutions
Answers
The equation 5r2 - 5r + 2 = 0 has two real solutions.
The two real solutions of the equation are:
x = (5 + 3i) / 10 and x = (5 - 3i) / 10
To solve this equation, you can use the Quadratic Formula:
x = (-b ± √(b2 - 4ac)) / (2a)
In this case, a = 5, b = -5, c = 2, so:
x = (-(-5) ± √((-5)2 - 4*5*2)) / (2*5)
x = (5 ± √(25 - 40)) / 10
x = (5 ± √(-15)) / 10
x = (5 ± 3i) / 10
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Just need answers thanks alot !! Problems in picture
Answers
The quadratic equation f(x) = 3 · x² + 36 · x + 33 shows the quickest choice to determine the y-intercept. The y-intercept is equal to (0, 33).
How to find the y-intercept of a quadratic equation
In this problem we must look up for the quickest way to determine the y-intercept of a quadratic equation, this can be done by evaluating at x = 0 when the expression is of the form, that is, standard form:
f(x) = a · x² + b · x + c
Where a, b, c are real coefficients.
The standard form f(x) = 3 · x² + 36 · x + 33 may help us to determine the y-intercept quickly. The y-intercept is equal to (0, 33).
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Sadie is making punch. How many more more quarts of lemon-lime juice will she use than orange juice
Answers
Volume is the quantum of space an object occupies. Saddie uses 8 pints of lemon- lime juice rather of orange juice.
This is simply because there are 4 cups of juice in 1 liter. volume is a measure of space possessed by matter.
It is frequently quantified using SI deduced units or colorful US Customary or Imperial units. The description of length refers to volume.
A liter is a measure of commodity liquid, like milk or makeup. A gallon is four liters.
Question:
Sadie is making punch. how numerous further quarts of bomb lime juice will she use than orange juice?
constituents for punch-
8qts Lemon Lime Juice. 4 scoops of vanilla ice cream and 8 mugs of orange juice
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PLEASE HURRY ITS DUE IN 24 MINUTES
A chicken breeder has chickens that are white, black or speckled. Speckled chickens have both black and white feathers. This is a co-dominant trait. The allele for white feathers is A and the allele FB for black feathers is F Determine the genotypes for the rooster and hen that the breeder should cross to produce the greatest percentage of speckled chickens. A. Place the alleles for the rooster and the hen that the breeder should cross in the blank boxes outside the Punnett square. B. Place the number that shows the percentage of speckled offspring that will result from this cross in the blank box. . You may use the allele labels more than once. • There may be more than one correct answer. • Place only one label in each blank box F F 25 50 75 100 2/5- Hen Rooster =% speckled
Answers
Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.
The Punnett square for this cross would be:
| F F
A | A F A F
A | A F A F
This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.
Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:
| F F
A | A F A F
A | A F A F
Hen Rooster
Letf(x)=x−21andg(x)=x3+2. Find the following functions. Simplify your answers.f(g(x))=g(f(x))=
Answers
The simplified functions of f(g(x)) and g(f(x)) are: f(g(x))=x3 and g(f(x))=x3−6x2+12x−6
To find the function f(g(x)), we need to substitute g(x) into f(x). This means we will replace the x in f(x) with the expression for g(x):
f(g(x))=f(x3+2)=(x3+2)−2
Simplifying this expression gives us:
f(g(x))=x3
Similarly, to find the function g(f(x)), we need to substitute f(x) into g(x):
g(f(x))=g(x−2)=(x−2)3+2
Simplifying this expression gives us:
g(f(x))=x3−6x2+12x−6
Therefore, the functions f(g(x)) and g(f(x)) are:
f(g(x))=x3
g(f(x))=x3−6x2+12x−6
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What is the % of the votes did MRS Naido receive write the answers to theearst whole%
Answers
With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to Gopalkrishna Gandhi, the opposition candidate, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.
According to the given information, M Venkaiah Naidu received 516 votes out of the valid votes cast in the vice-presidential election. The total number of valid votes cast was not explicitly mentioned in the statement, but we can calculate it by adding up the votes received by the two candidates. M Venkaiah Naidu received 516 votes, while his opponent Gopalkrishna Gandhi received 244 votes. Therefore, the total number of valid votes cast was 760 (516 + 244).
To calculate the percentage of valid votes that M Venkaiah Naidu received, we need to divide his number of votes by the total number of valid votes cast and then multiply by 100. Therefore, M Venkaiah Naidu received approximately 68% of the valid votes (516/760 x 100).
It's important to note that this calculation only considers the valid votes cast and not any abstentions or spoiled ballots. Additionally, this percentage reflects the support received by M Venkaiah Naidu among the MPs who voted and does not necessarily reflect the opinions of the broader public or electorate.
Complete question:
According to BJP sources, around two dozen MPs from opposing parties disobeyed their leaders and supported M Venkaiah Naidu for vice president of the NDA. Against the estimated 495 votes of pledged support, Mr. Naidu received 516 votes.
With nearly 68% of genuine votes going to Venkaiah Naidu and 32% going to the opposition's Gopalkrishna Gandhi, who earned 244 votes, the difference between the two candidates was bigger at 272 than Mr. Gandhi's total.
What is the % of the votes did MRS Naido receive to write the answers to the east wholw%
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Help me with this please
Answers
Answer:
we have to check the chemical property of the daisy perfume
Find the domain and range for the following functions:
(3 Marks)
a) y=1/√ x2-4
y=(2x^2)-2x+5
y=
1/(1-1/(x-1))
Answers
The domain and range for the given functions are: a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞) b) Domain: (-∞, ∞), Range: [9/2, ∞) c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
The domain of a function is the set of all possible values of x that can be input into the function. The range of a function is the set of all possible values of y that can be output from the function.
a) y = 1/√(x^2 - 4)
The domain of this function is all values of x that make the denominator nonzero and the square root positive. Therefore, x^2 - 4 > 0, which means (x - 2)(x + 2) > 0. The solution to this inequality is x < -2 or x > 2. So the domain is (-∞, -2) ∪ (2, ∞).
The range of this function is all positive values of y, since the square root in the denominator is always positive. So the range is (0, ∞).
b) y = (2x^2) - 2x + 5
The domain of this function is all real numbers, since there are no restrictions on the values of x. So the domain is (-∞, ∞).
The range of this function is all values of y greater than or equal to the vertex of the parabola. The vertex of this parabola is (-b/2a, f(-b/2a)), which is (1/2, 9/2). So the range is [9/2, ∞).
c) y = 1/(1 - 1/(x - 1))
The domain of this function is all values of x that make the denominator nonzero. Therefore, 1 - 1/(x - 1) ≠ 0, which means x ≠ 2. So the domain is (-∞, 2) ∪ (2, ∞).
The range of this function is all values of y except 0, since the denominator can never be zero. So the range is (-∞, 0) ∪ (0, ∞).
In conclusion, the domain and range for the given functions are:
a) Domain: (-∞, -2) ∪ (2, ∞), Range: (0, ∞)
b) Domain: (-∞, ∞), Range: [9/2, ∞)
c) Domain: (-∞, 2) ∪ (2, ∞), Range: (-∞, 0) ∪ (0, ∞)
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For each of the following, find the formula for an exponential
function that passes through the two points given.
a. (-2, 3/4) and (2,12)
f(x)=?
b. (-3,6) and (3,2)
g(x)=?
Answers
The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).
To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.
For part a:
3/4 = ab⁻²
12 = ab²
Dividing the second equation by the first equation gives us:
16 = b⁴
Taking the fourth root of both sides gives us:
b = 2
Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3
So the formula for the exponential function is:
f(x) = 3(2ˣ)
For part b:
6 = ab⁻³
2 = ab³
Dividing the second equation by the first equation gives us:
1/3 = b⁶
Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)
Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)
So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))
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A 30% increase followed by a 15% decrease, is it greater than original, smaller or same as
Answers
Answer:
1.3 × .85 = 1.105
10.5% greater than original
PLEASE HELP! 10 POINTS! ITS URGENT! NO EXPLANATION NEEDED!
Answers
Answer:its 80 i did the same problem
Step-by-step explanation:
(px + 4) (9x + 3) = 18x^2 + rx + 12 for all values of x, and p + q = 9. What are the two possible values of r? A) 3 and 6 B) 9 and 24 C) 12 and 18 D) 30 and 33
Answers
Expanding the left-hand side, we have:
(px + 4) (9x + 3) = 9px^2 + 3(4p + 9)x + 12
Comparing this to the right-hand side, we see that we must have:
9p = 18 (to get the x^2 term on the right)
4p + 9 = r (to get the x term on the right)
The first equation gives us p = 2, and substituting into the second equation gives us:
4(2) + 9 = r
r = 17
So one possible value of r is 17. To find the other, we use the fact that p + q = 9. Substituting p = 2, we have:
2 + q = 9
q = 7
Now we can use the same equation as before to find the other value of r:
4(2) + 9 = r
r = 17
So the two possible values of r are 17 and 17.
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