Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Answers
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
Related Questions
The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
Answers
Use the ratios to determine the number that you should multiply by.
See details:
Consider the data set displayed on the following box plot. -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 © 2018 StrongMind. Created using GeoGebra. Which of the following statements about the data set are true? Select all that apply. There are no outliers. There is one outlier The interquartile range is 8. O The data is skewed. The data is symmetric. The interquartile range is 10. There are two outliers.
Answers
The first one is TRUE since there are not outliers
The second one is FALSE
The interquartile range is 10, so the third one is FALSE
The data is skewed since the median is not in the middle,so the fourth is TRUE and the fifth is FALSE
The sixth one is TRUE
The last one is FALSE.
Summirizing, we have
True
False
False
True
False
True
False
Select all the equations that have the same solution as 2x-5=15
Answers
Answer:
B, D, E
Step-by-step explanation:
2x - 5 = 15
2x = 20
x = 10
B) 2x = 20
x = 10
D) 2x - 20 = 0
2x = 20
x = 10
E)4x - 10 = 30
4x = 40
x = 10
can i gett some help pls
Answers
Answer:
26.425
Step-by-step explanation:
0.9(x+1.4)−2.3+0.1x=1.6
please help, I'm really not sure how to do this.
Answers
Answer:
x = 2.64
Step-by-step explanation:
Do the distributive property first.
0.9(x + 1.4)
0.9(x) + 0.9(1.4)
0.9x + 1.26 - 2.3 + 0.1x = 1.6
Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.
0.9x + 0.1x + 1.26 - 2.3 = 1.6
1x - 1.04 = 1.6
1x is the same as x, so I am going to remove the 1. Solve for x.
x - 1.04 + 1.04 = 1.6 +1.04
x = 2.64
a company has its employees choose a password which consists of 9 characters: 3 letters, followed by 2 symbols, followed by 4 digits. there are a total of 11 symbols that the employees can choose from. letters, symbols and digits can be repeated. how many possible passwords are there?
Answers
The total possible choices of password that are available is 21,266,960,000.
The length of the password has to be of 9 characters.
Three of them should be letters, 2 should be symbols from the 11 choices of the symbols and 4 have to be digits.
Any of the following can be repeated in the password,
So, making the combination of 9 characters.
As we know, letters are 26, so, there are 26 choices each for three places.
Also, if 11 symbols are available, then there are 11 choices each are available for the two places and the total number of 10 which are 0 to 9, so, there are 9 choices each for the last four places,
Hence the final combination would be,
= 26 x 26 x 26 x 11 x 11 x 10 x 10 x 10
= 21,266,960,000
Hence the total password available are 21,266,960,000.
To know more about combinations, visit,
https://brainly.com/question/28065038
#SPJ4
-6+ (-3) how to find answer?
Answers
Answer:
-9
Step-by-step explanation:
−6 − 3
= −6 + −3
= -9
Answer:
-9!
Step-by-step explanation:
When you add negatives, it becomes more negative. Think of -6 getting 3 smaller.
a raised rectangular garden is two feet more than three times as long as it is wide. the depth of the pool is half the width. if the length is 11 feet, what is the volume?
Answers
Answer:
49.5ft³
Step-by-step explanation:
If it is 2 ft more than 3 times as long as it is wide then:
l = 3w + 2
which means:
w = (l-2)/3
and:
d = 1/2((l-2)/3)
Now just substitute in 11 for l
w = (11 - 2)/3
w = 9/3
w = 3
d = 1/2((11-2)/3)
d = 1/2(9/3)
d = 1/2(3)
d = 1.5
So the total volume is:
11 * 3 * 1.5
49.5
The midpoint of UV is (5,−11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V.
Answers
Using the mid point, the coordinates of the end point V is (7, -27)
How to find the coordinate using the mid point?A midpoint is a point lying between two points and is in the middle of the line joining the two points.
In other words, the midpoint of a line segment is a point that lies halfway between 2 points.
Therefore, the coordinates of the endpoint V can be found as follows:
using the mid point,
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
(5, -11) = (3 + x₂ / 2, 5 + y₂ / 2)
Hence,
5 = 3 + x₂ / 2
cross multiply
10 = 3 + x₂
10 - 3 = x₂
x₂ = 7
Hence,
- 11 = 5 + y₂ / 2
-22 = 5 + y₂
-22 - 5 = y₂
y₂ = - 27
Therefore, the coordinates of V is (7, -27)
learn more on mid point here: https://brainly.com/question/24467835
#SPJ1
4x+4≤9x+8
please help
Answers
Answer:
x ≥ - [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
4x + 4 ≤ 9x + 8 ( subtract 5x from both sides )
4 ≤ 5x + 8 ( subtract 8 from both sides )
- 4 ≤ 5x ( divide both sides by 5 )
- [tex]\frac{4}{5}[/tex] ≤ x , then
x ≥ - [tex]\frac{4}{5}[/tex]
Answer:
4x + 4 ≤ 9x + 8 Subtract 4x from both sides
4 ≤ 5x + 8 Subtract 8 from both sides
-4 ≤ 5x Divide both sides by 5
≤ x
x ≥
Step-by-step explanation:
Jake has a 8 pounds of lunch meat to serve for a picnic lunch. He plans to serve each adult 2/3 of a pound. Part B: The price of lunch meat is $7.36 per pound. Which equation can be used to determine the total cost, c, for lunch meat that weighs a total p pounds? Then find the cost of the lunch meat. •p/7.36=c •p=7.36c, the cost is $1.09 •c=7.36p, the cost is $58.88 •p+7.36-c, the cost is $15.36
Answers
Part B
The most appropriate choice for linear equation will be given by -
Third option is correct
c = 7.36p is the required equation for total cost of p pounds of meat
The cost is $58.88
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Price of one pound of meat = $7.36
Cost of p pounds of meat = $7.36p
By the problem,
c = 7.36p
This is the required equation for total cost of p pounds of meat
Putting p = 8
c = [tex]7.36 \times 8\\[/tex]
c = $58.88
Third option is correct
To learn more about linear equation, refer to the link:
https://brainly.com/question/2030026
#SPJ9
2The shape shown is made up of three similar right-angled triangles.22The smallest triangle has two sides of side-length 2, as shown.What is the area of the shape?1412 + 12V22824 + 20V56Erase
Answers
The triangles are similar. The smaller is isosceles, so the 3 of them are as well.
Let's Start by finding the hypotenuse of the smaller one:
a² = 2
Cuanto es 25 dividido en 386,4
Answers
Bethany is building a storage trunk. 5ft long, 4ft height and 2ft wide. how much wood is needed to make the trunk
Answers
Answer:
76 square feet of wood.
Explanation:
Bethany is building a storage trunk with the following dimensions:
• Length = 5 ft.
,• Height = 4 ft.
,• Width = 2 ft.
We are to determine how much wood is needed to make the trunk.
The amount of wood that will be needed to make the truck is the surface area of the trunk. The storage trunk is in the shape of a rectangular prism.
The surface area of a rectangular prism is found using the formula below:
[tex]\text{Surface Area=2(LW+LH+WH)}[/tex]Substitute the given dimensions:
[tex]\begin{gathered} \text{Surface Area}=2(5\times2+5\times4+2\times4) \\ =2(10+20+8) \\ =2\times38 \\ =76\; ft^2 \end{gathered}[/tex]Bethany needs 76 square feet of wood to make the trunk.
What is the answer to this question
Answers
i hope this helps!! <3
a recipe uses 1 aubergine for every 3 people. how many aubergines should you buy for 10 people
Answers
Answer:
3 1/3 I am assuming that you cannot by 1/3 of an aubergines, so you would need to buy 4. if you can buy a partial one then it would be 3 1/3
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] = [tex]\frac{a}{10}[/tex] Set up a proportion and then cross multiply and solve for a
3a = 10 Divide both sides by 3
a = [tex]\frac{10}{3}[/tex] = 3 1/3
A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 11
packages of coffee and 50 packages of tea, for which customers paid a total of $288. The day
before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of
$248. How much does each package cost?
Answers
The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y = [tex]\frac{248}{2}[/tex]
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
[tex]y = \frac{364}{91}[/tex]
y = 4
Putting the value of y in (2),
6x + 19[tex]\times[/tex]4 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
[tex]x = \frac{48}{6}\\x = 8[/tex]
8 packages of coffee and 4 packages of tea are sold.
To learn more about simultaneous linear equation, refer to the link:
https://brainly.com/question/26310043
#SPJ9
The most appropriate choice for Simultaneous linear equation will be given by -
8 packages of coffee and 4 packages of tea are sold.
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here,
A coffee shop sold 11 packages of coffee and 50 packages of tea, for which customers paid a total of $288
So,
11x + 50y = 288 ...............(1)
The day before, 12 packages of coffee and 38 packages of tea was sold, which brought in a total of $248
So,
12x + 38y = 248
2(6x + 19y) = 248
6x + 19y =
6x + 19y = 124 ....................(2)
Multiplying (1) by 6 and (2) by 11,
66x + 300y = 1728
66x + 209 y = 1364
Subtracting above two equations,
91 y = 364
y = 4
Putting the value of y in (2),
6x + 194 = 124
6x + 76 = 124
6x = 124 - 76
6x = 48
8 packages of coffee and 4 packages of tea are sold.
To learn more about simultaneous linear equation, refer to the link:
brainly.com/question/26310043
#SPJ9
railroad accidents a researcher wishes to study railroad accidents. he wishes to select 4 railroads from 15 class i railroads, 2 railroads from 8 class ii railroads, and 1 railroad from 7 class iii railroads. how many different possibilities are there for his study?
Answers
Different possibilities for the given case are, 267540
4 railroads chosen from 15 class I railroads
2 railroads chosen from 8 class II railroads
1 railroad chosen from 7 class III railroads
So total combinations = ¹⁵C₄ ˣ ⁸C₂ ˣ ⁷C₁
= (15!)/(4!*11!) x (8!)/(2!6!) x (7!)/(1!6!)
= 15 x 7 x 13 x 4 x 7 x 7 = 267540
To learn more about Combinations click here:
https://brainly.com/question/20211959
#SPJ4
In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
Thus, Military Might: The Mycenaeans had a strong military force and were expert warriors. They used sophisticated bronze weapons and chariot warfare as a tactic.
They were able to increase their influence and take control of neighbouring territories thanks to their military might.
Control over Trade Routes: The Mycenaeans had complete control over key trade routes in the Mediterranean, particularly those that extended from the Aegean to the eastern Mediterranean and beyond.
Thus, In the Mediterranean, the Mycenaeans rose to prominence by a mix of military prowess, economic connections, and cultural sway.
Learn more about Economy, refer to the link:
https://brainly.com/question/33857387
#SPJ6
a group of 90 students is to be split at random into 3 classes of equal size. all partitions are equally likely. joe and jane are members of the 90-student group. find the probability that joe and jane end up in the same class.
Answers
The probability that joe and jane end up in the same class is 0.3258 .
In the question ,
it is given that
90 students is to be split into 3 equal size classes , so ,
the three classes will have 30 students each .
let these classes be Class A , Class B and Class C .
Let Joe and Jane be in Class A .
the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .
Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students in C(88,28) ways ,
So , the probability that Joe and Jane end up in the same class is
= C(88,28)/C(90,30) .
Since there are three classes ,
the required probability is 3*C(88,28)/C(90,30) .
= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]
= 29/89
= 0.3258
Therefore , the probability that joe and jane end up in the same class is 0.3258 .
Learn more about Probability here
https://brainly.com/question/8885214
#SPJ1
D
E
F
The measure of angle D is 50°, the measure of angle E is 80°, and the
measure of angle F is 10 x. What is the value of x?
Answers
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Since angle D is 50, E is 80, we can add those two for now, 50+80=130, to make it 180, we can do 180-130 which gives us 50. So the value of x is 5. Sorry that its pretty confusing
An empty 16 gallon tank is being filled with gasoline at a rate of 2 gallons per minute. State the Domain and Range using interval notation or set notation
Answers
The volume of gasoline in the tank as a function of time can be determined as,
[tex]V=2t[/tex]The time taken to fill the tank can be determined as,
[tex]\begin{gathered} 16=2t \\ t=8 \end{gathered}[/tex]Thus, the requried domain is,
[tex]t\in\lbrack0,8\rbrack[/tex]The range of the function can be determined as,
[tex]V\in\lbrack0,16\rbrack[/tex]Thus, the above expressions gives the required domain and range of the function.
A tree initially measured 18 feet tall. Over the next 3½ years, it grew to a final height of 35½ feet. During those 3½ years, what was the average yearly growth rate of the height of the tree?
Answers
Answer:
The average yearly growth o
Explanation:
Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.
The growth within these years is:
35 1/2 - 18
= 35.5 - 18
= 17.5
Now, this averages:
17.5/3.5 (3.5 is the number of years)
= 5
The average is 5 ft per year
The total cost (c) in dollars of renting a car and driving it m
miles is given by the equation: c=15+2m. If the total cost
was $225, how far was the car driven?
Answers
The car was driven 105 miles.
What is rent?
An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.
In the given example the cost function is, c = 15 + 2m
Where, c is the total cost and m is the number of miles car driven.
The total cost was $225.
So, plug c = $225 in the above equation.
225 = 15 + 2m
210 = 2m
m = 105
Therefore, the car was driven 105 miles.
To know more about the renting, click on the link
https://brainly.com/question/13351715
#SPJ13
Please help, i really need help please
Answers
Answer:
m∠1 = 151°
m∠2 = 29°
m∠3 = 151°
Step-by-step explanation:
We can use knowledge of vertical angles and supplementary angles.
➜ Vertical angles are congruent
➜ Supplementary angles are equal to 180° when added together
Answer:
m∠1 = 151, m∠2 = 29, m∠3 = 151.
Step-by-step explanation:
We know m∠4 is equal to 29. We know m∠4 and m∠2 are equal because they are vertical angles. That means m∠2 is 29. Now, m∠4 and m∠3 equal 180, and m∠2 and m∠1 also equal 180. Since we know m∠4 is 29, you can do 29 + m∠3 = 180. You get m∠3 = 151. Now, m∠1 and m∠3 are also equal because they are vertical angles. That means m∠1 is equal to 151 as well. So your final answers are m∠1 = 151, m∠2 = 29, and m∠3 = 151.
2x-3=4+2x solve for x
Answers
Answer:
no solution
Step-by-step explanation:
After you level up solving equations, sometimes there is NO solution (and sometimes there is infinite solutions) instead of always getting a number answer.
How do you know when?
Solve as usual:
2x - 3 = 4 + 2x
Subtract 2x from both sides.
-3 = 4
When all your variables "fall out" of the equation and you end up with a false statement, then you have NO Solution.
what is the probability that when a coin is flipped six times in a row, it lands heads up every time? (enter the value of probability in decimals. round the answer to three decimal places.)
Answers
The probability that the coin lands heads up six times in a row is 0.016
Probability is the term used in mathematics to understand how likely an event is to happen or can also be described as how likely it is that a proposition is true.
It can be determined by dividing the favorable outcomes or events by the total number of outcomes.
As the coin has two sides, the probability that when the coin lands, it lands heads up is determined as follows;
Probability = 1 / 2
Now the probability that the coin lands heads up six times in a row can be calculated as follows;
Probability = (1^6) / (2^6)
Probability = 1 / 64
Probability = 0.015625
Rounding it to three decimal places as follows;
Probability = 0.015625 = 0.016
Therefore, the probability that the coin lands heads up six times in a row is calculated to be 0.016
To learn more about probability; click here:
https://brainly.com/question/25870256
#SPJ4
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
The answer is 75 degrees
Step-by-step explanation:
Remember that the sum of the three angles of any triangle is 180 degrees.
So, 180=58+47+x
180=105+x
75=x
Stephanie has 5 pizzas. She shares 4-
of the pizzas with her friends. Estimate how much pizza Stephanie has left.
8
16
02/20
pizzas
O2 pizzas
O
01/P
pizzas
01 pizza
Answers
After subtraction we can see Stephanie has only 1 pizzas left.
What is subtraction?
The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.
We are given that,
Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends
Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza
Therefore the correct option is option D)
To learn more about subtraction please refer
https://brainly.com/question/13378503
#SPJ13
Eric has 23 cookies, but she ate 19 cookies,
How many does eat cookies left.
(100 POINTS)
Answers
Answer: 23 - 19 = 4
Step-by-step explanation:
Answer:
how many does eat cookies left??? what
Step-by-step explanation:
anyway, it should be 4 cookies i guess?
23 - 19 = 4
...unless this is like a trick question with bad grammar
WHATS THE ANSWER PLSZ HELP
Answers
Answer:
a. 0.8 = 0.5 + 0.3
b. 30.9 = 2.7 + 28.2
c. 15.4 = 3.1 + 2.4 + 9.9
d. 17.4 = 15.2 + 1.4 + 0.8
e. 42.5 = 39.2 + 2.5 + 0.8
f. 8 = 4 + 4
g. 35 = 23 + 8 + 4
h. 84 = 53 + 3 + 28
i. 121 = 11 + 17 + 93
j. 35 = 24 + 8 + 3