Which statements about the hyperbola are true? Check all that apply. There is a vertex at (–5, 2). The center of the hyperbola is at (–2, 2). There is a vertex at (–2, 7). The transverse axis is vertical. The directrices are vertical lines.
Answers
First , second and last option are relevant to hyperbola . So , they are correct.
Review each statement to determine if it is true for a hyperbola
It is confirm that the first statement is true because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is It is confirm that the second statement is true because the center of a hyperbola is the midpoint of the vertices
It is confirm that the third statement is false because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is confirm that the fourth statement is false because the transverse axis of a hyperbola is the line segment that contains the vertices and the foci
It is confirm that the fifth statement is true because the directrices of a hyperbola are two lines parallel to the conjugate axis and located a distance from the center equal to the distance from the center to the foci.
Therefore, the first, second, and last options are correct.
Question :
Equation of the axes: The equation of the axes of a hyperbola is x = h, where h is the x-coordinate of the center of the hyperbola.
Equation of the asymptotes: The equation of the asymptotes of a hyperbola is y = ±(b/a)x, where a and b are the distances from the center to the vertices along the transverse and conjugate axes.
Equation of the conjugate hyperbola: The equation of the conjugate hyperbola can be found by interchanging a and b in the equation of the original hyperbola.
Review each statement to determine if it is true for a hyperbola
1. "A point on a hyperbola that sits on the transverse axis is called a vertex." - True. That's because the vertices of a hyperbola are indeed points on the hyperbola that line up with the transverse axis.
2. "The center of a hyperbola is right in the middle of its vertices." - True. Think of it like finding the midpoint between two ends. That's where the center of the hyperbola sits.
3. "A hyperbola's vertex is exactly where it meets the transverse axis." - false.
4. "The transverse axis of a hyperbola is the line connecting its vertices and foci." - False. The transverse axis actually links the vertices directly, not the vertices and the foci.
5. "The directrices of a hyperbola are two lines that run parallel to its conjugate axis, and they're positioned at a distance from the center to match the distance from the center to the foci." - True. It's like setting up boundaries at a certain distance from the center to guide the shape of the hyperbola.
So, yes, you're right about the first, second, and last statements being true.
incomplete question
Related Questions
26 Points!!! Select True or False for each equation.
Answers
Answer:
The first one is true, meanwhile the second is false!
Step-by-step explanation:
The first one both simplify to -3.
The second one, -6/-2 ( fraction ) simplifies to positive 3 because dividing or multiplying by 2 negative numbers cancels out the negative sign.
Hope it helps!
Answer:
1) True
2) False
Step-by-step explanation:
- 6/2 = -3
please help with this question its in the picture :)
Answers
If you horizontally stretch the quadratic parent function, f(x) = x², by a factor
of 3, what is the equation of the new function?
O A. g(x) = x2
O B. g(x) = (3852
O C. g(x) = (3x)2
o D. g(x) = 3x²
Answers
Answer:
d
Explanation:
You multiply the X by 3
Which is a Linear Equation?
A. Y=3-2x
B. Y= -7x^2
C. Y=2-3x^2
D. Y=-7×^3
Answers
Answer:
(A)
Step-by-step explanation:
A linear equation can be written in slope intercept form, [tex]y=mx+b[/tex].
X must be in it's first power in a linear equation. X being in any other power will result in a curved line.
This eliminates B, C and D already. X is not in it's first power in the given three options.
The best option is A.
A relative frequency table is made from data in a frequency table.
Relative Frequency Table: A 4-column table with 3 rows. The first column has no label with entries likes S, T, total. The second column is labeled U with entries 26%, 21%, 47%. The third column is labeled V with entries 42%, k, 53%. The fourth column is labeled total with entries 68%, 32%, 100%.
What is the value of k in the relative frequency table? Round the answer to the nearest percent.
2%
11%
20%
33%
Answers
Answer:
k = 11 let me know if you don't understand how I got this.
Step-by-step explanation:
I'm gonna write it out
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
So, you want to look at the column and row labeled total, this is the key. for the row total, it sums up everything in the column above it. so for the u column, the total value is 47 while the two values above it are 26 and 21. These two values sum to 47. This is the same for all other columns, and you can use the same reasoning with the total column as well summing rows.
This gives you two ways to solve for k. either 21 + k = 32 or 42 + k = 53. Either way gets you the answer k = 11
The value of k in the relative frequency table is 11%.
What is relative frequency?The ratio of the frequency of a particular event in a statistical experiment to the total frequency.
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
As, when we add the column data 26+ 21 = 47 which shows that the total consist of sum of column data.
So,
21 + k = 32
k = 11
Learn more about relative frequency here:
https://brainly.com/question/16832475
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Liz flips a coin 50 times. The coin lands heads up 20 times and tails up 30 times. Complete each statement. The theoretical probability of the coin landing heads up is ______. Based on Liz’s results, the experimental probability of the coin landing heads up is_____. The theoretical probability is than the experimental probability in this experiment________.
Answers
Answer:
50% or 50/100 or 25/50 40% or 40/100 or 20/40MoreStep-by-step explanation:
The theoretical probability is more than the experimental probability in this experiment
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the number of times the coin is flipped be n = 50
And , the number of times the heads is shown = 20 times
The number of times the tails is shown = 30 times
The theoretical probability of a coin being head or tail P ( A ) = 50 %
So , the experimental probability of being a head is P ( B ) = 20/50
P ( B ) = 40/100 = 40 %
Therefore , P ( A ) > P ( B )
Hence , theoretical probability is more
To learn more about probability click :
https://brainly.com/question/17089724
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PLEASE HELP NEED ASAP
Answers
Answer:
Side WZ=9
Step-by-step explanation:
Since he two are similar you need to make a ratio of the two parallelograms
The first tells you side FE is 2 and side EH is 3 so write it like this 2/3.
Next you need to do the same thing with the second parallelogram, so you know side XW is 6 but you don't know side WZ so you'd write this one 6/x.
You can do this since FE is similar to XW, because it is the same shape just bigger.
Next you take the two fractions adn set them equal to each other.
2 6
_ = _
3 x
Now cross multiply (2 timesx and 6 times 3)
It should look like this now
2x=18
Now all you have to do is divide by 2.
A bag contains 5 red, 4 green, and 3 blue marbles. What is the probability of randomly picking a green marble, replacing it, and then randomly picking a blue marble?
Answers
Final answer:
The probability of first picking a green marble, replacing it, and then picking a blue marble from a bag containing 5 red, 4 green, and 3 blue marbles is 1/12.
Explanation:
The question is about calculating the probability of selecting a green marble and then a blue marble from a bag with a replacement in between the picks. The process involves two independent events since the green marble is replaced before picking the blue marble.
To calculate the probability of picking a green marble first, we consider the total number of marbles and the number of green marbles. Given there are 5 red, 4 green, and 3 blue marbles, the total number of marbles is 5+4+3=12. The probability of picking a green marble is thus 4/12 or 1/3. Because we replace the green marble, the bag's contents remain the same for the second pick.
The probability of picking a blue marble after replacing the green marble is therefore based on the same total of 12 marbles. The probability is 3/12 or 1/4. Now, since these are independent events, we multiply the two probabilities together to get the overall probability of both events happening in sequence: (1/3) * (1/4) = 1/12.
In summary, the probability of first picking a green marble, replacing it, and then picking a blue marble is 1/12.
Final answer:
The probability of randomly picking a green marble, replacing it, and then randomly picking a blue marble is 1/12.
Explanation:
To find the probability of randomly picking a green marble, replacing it, and then randomly picking a blue marble, we need to first calculate the individual probabilities.
The bag initially contains 5 red, 4 green, and 3 blue marbles. The probability of picking a green marble is 4/12, since there are 4 green marbles out of a total of 12 marbles.
Since the first marble is replaced, the bag still contains the same number of green marbles, so the probability of picking a blue marble on the second draw is also 3/12, since there are 3 blue marbles left out of 12 marbles.
To find the probability of both events happening, we multiply the individual probabilities: (4/12) * (3/12) = 1/12.
A math teacher who likes baseball conducts a survey of 100 students. He asked the students about their favorite sport and about their favorite subjects in order to determine the number of students who like math or baseball. The two way table below shows part of the results of the survey. Enter the percentage of students in the survey who’s favorite subject is math or who’s favorite sport is baseball.
[this is written response, so there are no answer choices]
Answers
Answer:
46%
Step-by-step explanation:
see image attached!
The sum of the present ages of a father and his son is 80 years. When the
father's age was equal to the present age of the son, the sum of their ages
would be 40 years. Find their present ages.
Answers
Answer:
Father=60
Son=20
Step-by-step explanation:
Let the father's age be x
Let the son age be y
Present age of them
X+y=80...(1)
Since the father's age equals to the present age of the son
Y+y=40
2y=40....(2)
Make y the subject of formula by dividing both sides by 2
Y=20
Substitute the value for x into (1)
20+x=80
Substrate 20 from both sides
X=60
Therefore the father's age is 60 and the son's age is 20
Let f(x) = 8x + 5 and g(x) = -2x - 4 Find the value of f(2) + g(5) *
Answers
Answer: lock down
Step-by-step explanation: f(x)= 8x2 + 5=21--> f(x)=21
g(x)= -2x5 - 4=-14--> g(x)=-14
f(2)+g(5) = 7
Step-by-step explanation:
Given,
f(x) = 8x+5
g(x) = -2x-4
To find f(2)+g(5)
Now,
f(2) means putting the value of x = 2 in f(x)
g(5) means putting the value of x = 5 in g(x)
f(2) = 8(2)+5 = 21
g(5) = -2(5)-4 = -14
Hence,
f(2)+g(5) = 21-14 = 7
Please help it’s for my brother!!
Answers
Answer:
the answers B
Step-by-step explanation:
i got B
I have a few questions!
a) x−1.27=4.09
b) 2.3−y=2.301
c) t+3.04=14.3
d) 1.1+k=5.67
Answers
Answer:
a.) x = 5.36
b.) y = - 0.001
c.) t = 11.26
d.) k = 4.57
Step-by-step explanation:
a) x−1.27=4.09
b) 2.3−y=2.301
c) t+3.04=14.3
d) 1.1+k=5.67
Solving. right?
a.) x = 4.09 + 1.27 = 5.36
b.) y = 2.3 - 2.301 = - 0.001
c.) t = 14.3 - 3.04 = 11.26
d.) k = 5.67 - 1.1 = 4.57
HELP! WILL MARK BRAINLIEST!!!!! QUESTION IN THE PHOTO
Answers
Answer:
Step-by-step explanatio
Simplify.
-6+[4-(x-2)]
Answers
-6+6-x
-x
Answer : -x
Answer:
-x
Step-by-step explanation:
-6+[4-(x-2)]
Distribute the minus sign
-6+[4-x+2]
Combine like terms
-6+4 +2 -x
-x +0
-x
In 3 years, a gyms membership went up from 6,400 to 8,400. Which expression shows how to find the percent of increase (A) 2,000/8,400 (B) 2,000:6,400 (C) 6,400/2,000
Answers
Answer:
B. 2000/6400
Step-by-step explanation:
Percent increase is told by the attached formula.
Plugging it in, you get 2000/6400.
Just Checking
2. A consumer watchdog organization received customer complaints about
the performance of one brand of batteries. To investigate, the researchers
purchased 24 of these batteries and ran them until they died. This sample
lasted a mean of 47 hours with a standard deviation of 3 hours.
a) What assumption must we make about battery life in order to use a t
model?
b) Find a 95% confidence interval for the mean lifespan of this brand of
batteries.
c) Write a conclusion based on your confidence interval.
Answers
6. In the year of 2017, the highest number of ambulance calls in a month was 8,312. The
lowest number of ambulance calls in a month was 791 times. The difference between the
highest and lowest use in a month is about ______ calls.
a. 7,300 b. 7,500 c. 7,800
Answers
Answer: The answer would be (b), or 7,500
Step-by-step explanation:
Stack the numbers and have 8,312 on top of 791Subtract You get the answer 7,521Round to the nearest hundred by looking at the tens place, anything below 5 will round it down to 500 and anything 5 or more will round it up to 600You end up with 7,500 as your rounded answer (about is a clue word to let you know you need to round)The radius of a circle is 2 miles. What is the diameter?
2 mi
Give the exact answer in simplest form.
Answers
Answer:
S
Step-by-step explanation:
Answer:
4 Miles
Step-by-step explanation:
D=r2
If $500 yields $51.76 in simple interest over 7yrs, what is the annual rate? Answer need to be rounded to the nearest thousandth
Answers
The annual rate of interest is 1.479%.
Step-by-step explanation:
Given,
Principle (P) = $500
Interest (I) = $51.76
Time (T) = 7 years
To find out the rate of interest (R).
Formula
Simple interest (I) = [tex]\frac{PTR}{100}[/tex]
According to the problem,
[tex]\frac{PTR}{100}[/tex] = 51.76
or, R = [tex]\frac{51.76X100}{PT}[/tex]
or, R = [tex]\frac{51.76X100}{500X7}[/tex]
= 1.4788 = 1.479% (approx)
Answer:
1.5%
Step-by-step explanation:
Principal, P = $500
Simple interest S.I. = $51.76
Period, T = 7 years
Simple interest = P*R*T / 100
Let's make rate, R the subject of formula
R = 100 * S.I. / P * T
Slot in the respective values
R = 100 * 51.76 / 500 * 7
R = 1.5%
Put these in order from least to greatest 1/2, 1/3, 2/5, 0.6 , o.3
Answers
Answer:
0.3, 1/3, 2/5, 1/2, 0.6
Step-by-step explanation:
Answer:
ok first lets make them all decimals
1/2=0.5
1/3= 0.3333333
2/5= 0.4
ok now we got 0.5, 0.33333, 0.4, 0.6, 0.3,
now lets also add zeros to the back to make it a more clear picture
0.50, 0.33, 0.40, 0.60, 0.30 ok now put the in order
0.30 , 0.33, 0.40, 0.50, 0.60
Step-by-step explanation:
Which set of ordered pairs does NOT represent y as a function of x?
Question 5 options:
{(1, 1), (2, 1), (3, 1)}
{(1, 1), (2, 2), (2, 3)}
{(1, 2), (2, 3), (3, 3)}
{(1, 2), (1, 3), (1, 1)}
Answers
Answer:
the 3rd choice
Step-by-step explanation:
Answer:
The last one {(1, 2), (1, 3), (1, 1)}
Step-by-step explanation:
This is because the domain x is repeated. For a set of ordered pairs to be a function the domain can not repeat.
Hi i need help with this math problem(IN the picture)
Answers
Answer:
138
Step-by-step explanation:
Because they are same-side interior angles, their sum is 180. You set up an equation and get:
180 = 42 + x
Which simplifies to
138 = x
Solve for h
35=1/2h (5+2)
Answers
Answer:
10
Step-by-step explanation:
35= 1/2h(7)
1/2 of 7 is 3.5
3.5(10)=35
h=10
Answer:
Solve for h
35=1/2h (5+2)
Multiply (5+2) by 1 divided by 2, then we have
7/2h= 35
cross multiply
35 x 2h= 7
70h= 7
divide both sides by 70
h= 7/70
h= 1/10
Step-by-step explanation:
4x + 3y = 6
-4x + 2y = 14
Answers
Answer:
x= −3/2 y=4
Step-by-step explanation:
What is the length of the third side of the window frame below
15
27
25
32
Answers
Answer:
25
Step-by-step explanation:
What is the mean absolute deviation of the data: 10, 20, 15, 17, and 13?
Answers
Answer:
2.8
Step-by-step explanation:
1) find the mean of the data set. = 15
2) find the abs value of the diff between each data value and the mean: |data value – mean|.
|10-15|=5, |20-15|=5, |15-15|=0, |17-15|=2, |13-15|=2
3) find the sum of the abs values of the diff = 14
4) divide the sum of the abs value by the number of data values = 14/5 = 2.8
Which of the given points would be in a table generated by the equation below?
pm + gy = 5
А. (0, 9)
B. (0, й)
C. , о)
D. (2 , 0)
Answers
2.75 cups of water mixed with 3.5 cups of pancake mix will make 19 pancakes. How much water is needed if there is only 1.5 cups of pancake mix left?
Answers
Answer:
You would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left
Step-by-step explanation:
So the ratio of water to pancake mix is 2.75 : 3.5 (which makes 19 pancakes)
To get from 3.5 cups of pancake mix to 1.5 cups of pancake mix you would subtract 2 cups. Since this is a ratio, you would not only subtract 2 cups from the pancake mix, but also from the water. 2.75 - 2 = .75 Therefore, you would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left. Hope this helps!
Answer:
1 5/28 cups of water
Step-by-step explanation:
Water : pancake mix
2.75 : 3.5
X : 1.5
2.75/X = 3.5/1.5
X = 2.75 × 1.5/3.5
X = 33/28 or 1 5/28 cups
Exterior angles of a triangle...help?
Answers
Answer:
Angle 4 is the exterior angle
Step-by-step explanation:
Exterior mean "outside"
Angle 4 is the only angle outside of the triangle