The foci and the vertices of the hyperbola are labeled.
Which equation represents the hyperbola shown in the graph?
Answer is B
Answers
The answer is B and pls mark me brainiest
The equation of the hyperbola is:
(x - 3)² / 9 - (y - 2)² / 16 = 1.
To find the equation of the hyperbola with the given foci and vertices, we need to determine the center, semi-major axis (a), and semi-minor axis (b) of the hyperbola.
The center of the hyperbola is the midpoint between the two vertices:
Center = ((3 + 3) / 2, (5 + (-1)) / 2) = (3, 2).
The distance between the center and one of the vertices gives us the semi-major axis (a):
a = distance between center and vertex = 5 - 2 = 3.
The distance between the center and one of the foci gives us the distance c (the distance from the center to the focus):
c = distance between center and focus = 7 - 2 = 5.
Now, we can find the value of b (the semi-minor axis) using the relationship between a, b, and c in a hyperbola:
c² = a² + b²
5² = 3² + b²
25 = 9 + b²
b² = 25 - 9
b² = 16
b = 4.
Now that we have the center (h, k) = (3, 2), the semi-major axis (a) = 3, and the semi-minor axis (b) = 4, we can write the equation of the hyperbola in standard form:
For a hyperbola (center at (h, k)), the equation is:
(x - h)² / a² - (y - k)² / b² = 1.
Plugging in the values:
(x - 3)² / 3² - (y - 2)² / 4² = 1.
The equation of the hyperbola is:
(x - 3)² / 9 - (y - 2)² / 16 = 1.
Learn more about hyperbola here
https://brainly.com/question/16457232
#SPJ2
Related Questions
What are the values of h and x in the right triangle?
Answers
h = 60, x = 25 (option B)
Explanation:x/leg 1 =leg 1/ (x + 144)
leg 1 = 65
144/leg 2 = leg 2/(x + 144)
leg 2 = 156
To avoid a quadratic equation, we will go with the equation having leg 2
\(\begin{gathered} \frac{144}{156}=\frac{156}{x+144} \\ \text{cross multiply:} \\ 144(x\text{ + 144) = 1}56(156) \end{gathered}\)\(\begin{gathered} 144x\text{ + 20736 = 24336} \\ 144x\text{ = 3600} \\ x\text{ = 3600/144} \\ x\text{ = 25} \end{gathered}\)To get height (h), apply geometric mean:
\(\begin{gathered} \frac{h}{x}=\frac{144}{h} \\ h^2\text{ = 144(x)} \\ h^2=144(25) \\ h^2\text{ = 3600} \\ h\text{ = }\sqrt[]{3600} \\ h\text{ = 60} \end{gathered}\)h = 60, x = 25 (option B)
HELPP!!!! I'm stuck on this question
Answers
Answer:
15/17
Step-by-step explanation:
SOH-CAH-TOA
Sine is the ratio of the length of the side opposite to the angle to the hypotenuse of the right triangle.
: determine the entropy of the sum that is obtained when a pair of fair dice are rolled. (use the definition of the entropy of a random variable provided on page 683 of ross 10th edition)
Answers
The entropy of the sum obtained when a pair of fair dice are rolled is 7.6.
This can be calculated by first working out the probability of each possible sum of two dice. There are 36 possible outcomes when two fair dice are rolled (6 x 6 = 36).
Each of the possible sums, from 2 to 12, will occur with a probability of 1/36.
The entropy of a probability distribution is calculated using the formula: Entropy = -(sum of (Probability of each outcome x log2 of probability of that outcome)).
Therefore, the entropy of the sum of two fair dice is:
- (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36))
= - (1/36 x 5.17) - (1/36 x 4.32) - (1/36 x 3.58) - (1/36 x 2.93) - (1/36 x 2.37) - (1/36 x 1.90) - (1/36 x 1.51) - (1/36 x 1.19) - (1/36 x 0.93) - (1/36 x 0.72) - (1/36 x 0.56) - (1/36 x 0.43)
= 7.6
As a result, the sum that results from the roll of two fair dice has an entropy of 7.6.
Complete Question:
Determine the entropy of the sum that is obtained when a pair of fair dice is rolled.
To learn more about probability visit:
https://brainly.com/question/24756209
#SPJ4
if a cup has a diameter of 8 centimeters and a height of 12 centimeters , how much juice will the cup hold.
Answers
The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³
How do i know the amount of juice the cup can hold?To know the amount of juice the cup can hold, we shall obtain the volume of the cup.
We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:
Diameter of cup = 8 cmRadius of cup (r) = diameter / 2 = 8 / 2 = 4 cmHeight of cup (h) = 12 cmVolume of cup (V) =?Volume = πr²h
Volume = 3.14 × 4² × 12
Volume = 3.14 × 16 × 12
Volume = 602.88 cm³
Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³
Learn more about volume of cylinder:
https://brainly.com/question/28512386
#SPJ1
11. m<2-34°. Find m<4 and explain how you know. (2 points)
Answers
Answer:
21
Step-by-step explanation:
If you had to write the fractions 1/3 and 3/4 as fractions with common denominators what would be the answer 2/6 and 6/8,2/6 and 5/6, 1/12 and 3/12,4/12 and 9/12
Answers
Answer:
3/12, 4/12
Step-by-step explanation:
You would first find a common denominator, which is 12. We can multiply the denominator and numerator by 3 for 3/4 and get 9/12. We can also multiply 1/3 by 4 for the denominator and numerator, we get 4/12. Our answer would be 3/12, 4/12
Happy to help you :)
Zachary buys a one pint bottle of juice for $3.20. What is the unit rate of the cost of the juice per fluid ounce?
How many fluid ounces of juice did Zachary buy?
Answers
Answer:
Zachary bought 16 ounces of juice
Step-by-step explanation:
First you figure out how many ounces are in a pint ( Which in case your wondering it's 16)
Then you take that number and divide $3.20 by 16 which gives you .20 cents.
You can double check my answer by multiplying .20 by 16 which gives you $3.20.
Hope this helps. ^w^
1- Random response The question on the right appears on a survey. Why are people told to roll a dice? It makes the survey more fun to do If they have lied about being sick they will be more likely to answer truthfully It will bring them good luck if their boss finds out they've been lying % When 420 people are surveyed, 115 tick the yes box. Estimate the proportion of people who have lied to their boss about being sick. Round your answer to 1 d. p. [1] [5] OFFICIAL SURVEY Roll a dice. If the dice shows 6 tick the box marked yes. If the dice shows a different number, answer the question. Have you ever lied to your boss about being sick in order to get a day off work?
Answers
A company sells artwork using a website. Information about the number of people that visited the website and the number of pieces of artwork purchased on a single day is listed below.
117 people did not purchase any artwork
24 people purchased one piece of artwork
9 people purchased more than one piece of artwork
Based on the data from that day, what is the probability that the next person who visits the website will purchase more than one piece of artwork
Answers
Answer: 3/50
Step-by-step explanation: add up 117 + 24 + 9 = 150
Then do 9 (the number of people who purchased more than one art work) (written as a fraction) over 150
Then simplify 9/150 to 3/50
a patient needs of a low-dose pain reliever. the pharmacy sends pills marked . how many should be administered? round to the nearest tenth of a pill.
Answers
The pharmacy should send two pills marked for the patient to take.
To answer this question, we can use the formula below;
Dosage = (Amount of Drug x Patient's Weight) / Time
Since we don't have any information about the patient's weight or the time, we can't calculate the dosage.
However, we can calculate the number of pills required.
So, let's proceed with the calculation.
Each pill contains 2.5 mg of the pain reliever.
We need to administer a low dose, so let's assume the dose required is 5 mg.
To administer this dose, we need to give two pills, i.e., 2 x 2.5 = 5mg.
However, the question asks us to round the answer to the nearest tenth of a pill.
Since we can't divide a pill into parts, we need to round the answer up or down to the nearest whole pill.
In this case, since we need two pills, the answer is 2 pills.
For similar question on administer.
https://brainly.com/question/13152057
#SPJ11
a physician orders to give 3 grams of an antibiotic intravenously to a patient over 1 hour. The vial of antibiotic comes in 4 grams and must be diluted with 20 mililiters of sterile water. How many mililiters of antibiotic must be drawn out of the vial for a 3 gram dose?
Answers
15 milliliters of antibiotic must be drawn out of the vial for a 3-gram dose.
To determine how many milliliters of the antibiotic must be drawn out of the vial for a 3-gram dose, follow these steps:
1. Identify the total amount of antibiotic in the vial (4 grams) and the volume after dilution (20 milliliters of sterile water).
2. Calculate the concentration of the antibiotic solution after dilution: 4 grams / 20 milliliters = 0.2 grams/mL.
3. Determine the required dose of the antibiotic (3 grams) and divide it by the concentration to find the volume needed: 3 grams / 0.2 grams/mL = 15 milliliters.
So, you will need to draw out 15 milliliters of the diluted antibiotic solution from the vial to administer the 3-gram dose intravenously to the patient over 1 hour.
Learn more about concentration here:
https://brainly.com/question/31587441
#SPJ11
A trader old a writ watch for h.3150 after giving a 10% dicount.Find the marked price of the watch
Answers
The marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
Let the marked price be x.
So,
According to the question;
x - x * 10% = 3150
x - x * 10/100 = 3150
100x - 10x / 100 = 3150
90x = 3150 * 100
x = 3150 * 100 / 90
x = 3500
So, the marked price is $3500.
Thus, the marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.
To learn more about percentage visit:
brainly.com/question/14307889
#SPJ1
how many groups of 1/8 are in 11/12
Answers
Answer:
2
Step-by-step explanation:
I need to make it 20 character long.
Whether the function is even or odd
Answers
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
An example of a rule is a function, which produces one output for a single input.
If the graph of a function is symmetric with respect to the y-axis, then it is said to be an even function. Otherwise, it is odd function.
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
To Learn more about function from the link:
https://brainly.com/question/10439235
#SPJ1
At Downtown Dogs, 10 of the last 15 customers wanted mustard on their hot dogs. What is the experimental probability that the next customer will want mustard? Write your answer as a fraction or whole number.
Answers
Answer:
yes
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
its on ixl
a man 6 feet tall is walking at a rate of 3 ft/s toward a street light 18 ft high. at what rate is the tip of the shadow moving? at what rate is the shadow length changing?
Answers
Answer:
Step-by-step When he is 10 feet from the base of the light, the rate at which the tip of his shadow moves is 10ft/s (b) When he is 10 feet from the base of the light, the rate at which the length of his shadow changes is 4ft/s
please tell me y what 6(2y−9)=-42
Answers
Answer:
y =1
Step-by-step explanation:
6(2y−9)=-42
Divide each side by 6
6/6(2y−9)=-42/6
2y -9 = -7
Add 9 to each side
2y -9+9 = -7+9
2y =2
Divide by 2
2y/2 = 2/2
y =1
Please help fast! Calculate the mean and explain the mean that would signify the entire population of fish by using this sample
Answers
The answer is 2
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 4 feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle. Use b for the base length of the triangular logo.
Answers
Examine the statement.
Rules for naming compounds are beneficial to the scientific community.
Do you agree or disagree with the statement? Be sure to explain the reasons for your viewpoint when you answer.
Furthering the Discussion
If you need more material to continue the conversation, use these questions as a guide.
What types of real-life situations or scenarios do you think benefit from having rules?
What types of real-life situations do you think are hindered by having rules?
Answers
Answer/Explanation:
I agree with the statement because primary function of chemical nomenclature is to ensure that a spoken or written chemical name leaves no ambiguity concerning which chemical compound the name refers to: each chemical name should refer to a single substance. The first separation of importance is to distinguish between inorganic and organic compounds.
How much would a 5% tip be on a bill that cost $75.00?
Answers
Answer:
Step-by-step explanation:
it would be a 20% tip
Answer:
3.75
Step-by-step explanation:
5% of 75 is 3.75
write at least 5 arithmetic sequence and determine the common difference
Answers
An arithmetic sequence is a sequence where we use addition or subtraction to get to the next term.
Examples:
1, 3, 5, 7, 9...
Common Difference: Add 2
2, 6, 10, 14, 18, 22..
Common Difference: Add 4
100, 90, 80, 70, 60, 50..
Common Difference: Subtract 10.
25, 30, 35, 40, 45..
Common Difference: Add 5
1, 10, 19, 28, 37..
Common Difference: Add 9
Hope it helps!
\(ANSWERED:\\GraceRosalia\)
find the slope of the following points
(-1,2), (-3,4)
(5,-2), (5,10)
(-3,0), (-3,6)
(8,9), (11,16)
Answers
Answer:
24) -1
25) indefinite/infinite
26) indefinite/infinite
27) 7/3
Step-by-step explanation:
24)
\(\frac{4-2}{-3+1}\\= 2/-2\\= -1\\\)
25)
\(\frac{10+2}{5-5}\\\\= \frac{12}{0}\)
= indefinite/infinite
26)
indefinite/infinite
27)
\(\frac{16-9}{11-8}\\\\= \frac{7}{3}\\\)
Feel free to mark this as brainliest! :D
Aspherical model of planet Earth has a radius of 3 ft. What is the approximate volume of the model of planet earth? Use 3.14 to approximate pi. Round to the nearest hundredth if necessary.
Answers
Answer:
113.1
Step-by-step explanation:
Like and give 5 star rating
Anyone know the answer ????
Answers
Answer:
4
Step-by-step explanation:
4 is the next number in this number line
Answer:
4 is the missing number! ☆ ☆ ☆ ☆
Step-by-step explanation: ⭐︎ ⭐︎ ⭐︎
It's a number line with integers! :)
PLEASE mark Brainliest!
Three siblings are comparing the ages. Jenna is the youngest. Her brother Carl is 6 years older than her. Her sister Eva is twice her age. The sum of the ages is 42. Let J represent Jenna’s age. Calculate the ages of the three siblings.
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to get the ages of the three siblings.
Step 1: Let us represent the ages of the siblings
Let J represent Jenna's age
Let C represent Carl's age
Let E represent Eva's age
Step 2: Write the statements in a mathematical form
\(\begin{gathered} \text{Jenna is the youngest and Carl is 6 years older than her} \\ C=J+6---\text{equation 1} \\ \text{Eva is twice the age of Jenna} \\ E=2J---\text{equation }2 \\ \text{The sum of the ages is 42} \\ C+E+J=42---\text{equation }3 \end{gathered}\)Step 3: We solve for the ages by using the substitution method
\(\begin{gathered} \text{Substitute (J+6) for C and 2J for E in equation 3} \\ C+E+J=42\Rightarrow J+6+2J+J=42 \\ \text{Collect like terms} \\ J+2J+J=42-6 \\ 4J=36 \\ J=\frac{36}{4} \\ J=9 \\ \text{Jenna is 9 years old.} \end{gathered}\)Step 4: Get the age of Carl and Eva using both equat
Solve ab +c= d for b
Answers
ab +c= d
To solve for b;
First subtract c from both-side of the equation
ab + c - c = d-c
ab = d-c
Then divide both-side of the equation by a
\(b\text{ =}\frac{d-c}{a}\)A survey of 61 randomly selected homeowners finds that they spend a mean of $62 per month on home maintenance. construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. assume that the population standard deviation is $13 per month. round to the nearest cent.
Answers
The 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is $58.06 to $65.94.
To construct a confidence interval for the mean amount of money spent per month on home maintenance by all homeowners, we can use the formula:
CI = \(\bar{X}\) ± Zα/2 * (σ/√n)
where \(\bar{X}\) is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
In this case, we have:
\(\bar{X}\) = $62 (the sample mean)
α = 0.02 (since we want a 98% confidence interval, which means α/2 = 0.01)
Zα/2 = 2.33 (from the standard normal distribution table)
σ = $13 (the population standard deviation)
n = 61 (the sample size)
Substituting these values into the formula, we get:
CI = $62 ± 2.33 * ($13/√61)
Simplifying this expression, we get:
CI = $62 ± $3.94
Therefore, the 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is $58.06 to $65.94.
This means that we can be 98% confident that the true population mean falls within this range. In other words, if we were to repeat the survey many times and construct confidence intervals in the same way, about 98% of the intervals would contain the true population mean.
It's important to note that this assumes that the sample is representative of the population, and that the population standard deviation is known. If these assumptions are not met, then the confidence interval may not be accurate.
To know more about confidence interval, refer to the link below:
https://brainly.com/question/30637686#
#SPJ11
in how many ways can first, second, and third prizes be awarded in a contest with 170 contestants? your answer is
Answers
There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.
To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.
Learn more about permutation
brainly.com/question/30649574
#SPJ11
Selena has been hired as a sales associate at Better Rooms furniture store. She has two salary options. She can choose to receive either a fixed salary of $850 per week or a salary of $400 per week plus a 6% commission of her weekly sales. Which solution set below represents the dollar amount of sales that she must generate each week in order for the option with commission to be the better choice? Let s represent the sales for the week.
{s|s>$2,400}
{s|s>$5,100}
{s|s>$6,200}
{s|s>$7,500}
Answers
Answer:
D.
Step-by-step explanation:
7500 * 6% = 450 which would just barely be enough to get paid the same amount as the fixed salary.
hopefully this helps