Answers
Answer:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
Step-by-step explanation:
Given points:
(2±3√2, ±2)(5, 0)(-1, 0)Standard equation of a horizontal hyperbola (opening left and right):
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h±a, k)Points (5, 0) and (-1, 0) are the vertices of the hyperbola.
The center (h, k) is midway between the vertices. Therefore:
[tex]\implies h=\dfrac{5-1}{2}=2[/tex]
[tex]\implies k=0[/tex]
Substitute the found values of h and k into the formula:
[tex]\dfrac{(x-2)^2}{a^2}-\dfrac{y^2}{b^2}=1[/tex]
Substitute point (5, 0) and solve for a²:
[tex]\implies \dfrac{(5-2)^2}{a^2}-\dfrac{0^2}{b^2}=1[/tex]
[tex]\implies \dfrac{3^2}{a^2}=1[/tex]
[tex]\implies \dfrac{9}{a^2}=1[/tex]
[tex]\implies 9=a^2[/tex]
Substitute one of the (2±3√2, ±2) points and the found value of a² and solve for b²:
[tex]\implies \dfrac{(2+3\sqrt{2}-2)^2}{9}-\dfrac{2^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(3\sqrt{2})^2}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{18}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies 2-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{4}{b^2}=1[/tex]
[tex]\implies 4=b^2[/tex]
Substitute the found values of a² and b², together with the values of h and k, into the formula to create the equation of the hyperbola:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
Related Questions
An investor has $75,000 to invest in a CD and a mutual fund. The CD yields 6% and the mutual fund yields 7%.
The mutual fund requires a minimum investment of $10,000, and the investor requires that at least twice as much
should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the
mutual fund to maximize the return? What is the maximum return?
Answers
What is inequality?
Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Let x be the investment in CD
Let y be in mutual fund
Given;
Return = 6% x + 8% y
Return = 0.06 x + 0.08 y
The equation form;
we have a critical number as
(16000, 8000) :
return = 0.06 (16000 + 0.08 (8000) = $1600
(50000, 25000) :
return = 0.06 (50000) + 0.08 (25000) = $5000
(67000, 8000)
return = 0.06 (67000) + 0.08(8000) = $4660
As we can see the maximum benefit is $5000 so;
The investment in cd = x = $50000
The investment in mutual funds = $ 25000
The maximum return = $5000
Carol has 1\frac{5}{8} cups of yogurt to make smoothies. Each smoothie uses \frac{1}{3} cup of yogurt.
What is the maximum number of smoothies that Carol can make with yogurt?
Answers
Carol can make a maximum of 4 smoothies with the available yoghurt
Cups of yoghurt Carol has for making smoothies = 1 5/8 cups
Yoghurt Carol has in improper fractions = 13/8 cups
Cup of yoghurt used to make smoothie = 1/3 cups
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Number of smoothies Carol can make = Total available yoghurt with Carol/Yoghurt used to make a smoothie
= (13/8)/(1/3)
= 39/8
Converting the fraction into a mixed fraction we get: 4 7/8 smoothies
So, she can make 4 cups of smoothie
Learn more about fractions:
https://brainly.com/question/1301963
#SPJ1
S is less then or equal to 18 ; s is greater or equal to -9. What is the value of s
Answers
Answer: 18>=S>=-9
Explanation:
piggy bank contains 2.65$ in nickles and dimes. If the number of nickles is 7 less that three times the number of dimes, how many of each are there?
Answers
There are 29 nickels and 12 dimes in the piggy bank.
In this question, we have been given a piggy bank contains 2.65$ in nickels and dimes.
We need to find the number of nickels and dimes if the number of nickels is 7 less than three times the number of dimes.
Let x be the number of nickels and y be the number of dimes.
We know that, 1 dollar = 20 nickels
and 1 dollar = 10 dimes
So, we get an equation
0.05x + 0.1y = 2.65 ...........(1)
Also the number of nickels is 7 less than three times the number of dimes.
x = 3y - 7 .................(2)
Substitute above value of x in equation (1)
0.05(3y - 7) + (0.1)y = 2.65
0.15y - 0.35 + 0.1y = 2.65
0.25y = 2.65 + 0.35
0.25 y = 3
y = 12
Substitute above value of y in equation (2)
x = 3(12) - 7
x = 29
Therefore, there are 29 nickels and 12 dimes in the piggy bank.
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ1
Write 2400000 in standard form
Answers
Answer:
2.4x10^6
Step-by-step explanation:
someone help please!!!!!!!!!!!!!
Answers
Answer:
I believe it's 9 people
Step-by-step explanation:
When an integer is subtracted from 2 times the next consecutive odd integer, the difference is 9. Find the value of the greater integer.
Answers
The integer is 5 and the next consecutive odd integer will be 7.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
let the integer be x
then, next consecutive odd integer will be x + 2
Now, according to the question :
integer is subtracted from 2 times the next consecutive odd integeb the difference is 9 means :
2(x+2) - x = 9
2x+ 4-x = 9
x + 4 = 9
x = 5
Therefore, The integer is 5 and the next consecutive odd integer will be 7.
Read more about equations at :
https://brainly.com/question/12895249
#SPJ1
in 3-5, suppose z is a relation which includes the point (-3, 5). what other point must be included in the relation of z has the stated property?
3. z is odd
4. z is even
Answers
Z is Odd.
What are relations in Math?In mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets. In arithmetic, a relation is called a function if it connects each element of the domain to a single element of the codomain. A relation could be a function or it could not. Relations are all functions.Eg :- The Association between Height and Age
This is a relation since you would get various heights if you entered a specific age and checked all the persons of that age. Nevertheless, if you were to look at a person's height over time, it would depend on their age.
To learn more about : Relations and functions.
Ref : https://brainly.com/question/25638609
#SPJ13
A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles, answer the following questions. Round all answers to the nearest whole number.
Answers
TheThe number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48,135 miles.
Number of milesDistance from Station 1 to satellite:
tan8.7 = length of longest leg / length of longest leg
tan8.7 = 3963/length of shortest leg
Length of longest leg=3963/tan8.7°
Length of longest leg=3963/0.15302150298
Length of longest leg =25,898 miles
Distance from Station 2 to satellite:
sin 8.7 = length of longest leg / length of hypotenuse
sin 8.7 = 3963/length of hypotenuse
Length of hypotenuse =3963/ sin 8.7
Length of hypotenuse =3963/0.1526082024
Length of hypotenuse=26, 200 miles
Hence,
26, 200 miles - 3,963 =22,237 miles
Total distance:
Total distance = 25,898 miles + 22,237 miles
Total distance = 48,135 miles
Therefore the distance is 48,135 miles.
Learn more about distance here: https://brainly.com/question/24775607
#SPJ1
The complete question is:
A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.
How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?
i need help on these
Answers
Answer:
read below
Step-by-step explanation:
1. $4, five granola bars cost $20. $20/5 = $4
2. 40 miles per hour, travels 100 miles at a constant speed for 40 miles. 100/2.5 = 40 miles
3. 12.5 situps per minute, 50 situps in 4 minutes. 50/4 = 12.5
4. $1.43 per one ounce, 3 ounces cost $4.29. 4.29/3 = $1.43
Match the following. Match the items in the left column to the items in the right column.
1. total to fish
2. starfish to fish
3. starfish to total
4. fish to starfish
Answers
The items matched in the left column to the items in the right column are
total to fish = 8 : 3starfish to fish = 5 : 3starfish to total = 5 : 8fish to starfish = 3 : 5Matching the items in the left column to the items in the right columnRatio is the number representing a comparison between two named things or quantities.
Total = 8Fish = 3Starfish = 51. total to fish
= 8 : 3
2. starfish to fish
= 5 : 3
3. starfish to total
= 5 : 8
4. fish to starfish
3 : 5
In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5
Read more on ratio:
https://brainly.com/question/2328454
#SPJ1
A circular pond has a diameter of 15 feet which expression can be used to find the circumference in feet 
Answers
The expression used for finding the circumference of the circular pond is; C = 2π(d/2) feet.
What is defined as the circumference?The circumference of the circle, also known as the perimeter of the circle, is the measurement of the circle's boundary. The area of a circle, on the other hand, defines the region it occupies. If we expand a circle and draw a straight line through it, the length of the line is the circumference. It is typically measured in units such as centimeters or meters.For the given question;
Let 'd' be the diameter of the circular pond.
The diameter of the pond = 15 feet.
Let 'C' be the circumference of the circle;
The, the formula for finding the circumference of the circle is;
C = 2π(d/2) feet
For, d = 15 feet
C = 2π(15/2) feet
Take π = 3.14
C = 2×3.14×(15/2) feet
C = 47.1 feet
Thus, the circumference of the circular pond is found as 47.1 feet.
To know more about the circumference, here
https://brainly.com/question/18571680
#SPJ10
use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation.
Answers
im waiting in the lunch line. Im 18th in line when counting from the front, and 24th when counting from the back. How many poeple are in the line?
Answers
Under certain conditions the pressure of a gas varies directly with the temperature. When the - pressure is 800 psi, the temperature is 400°. What is the temperature when the pressure is 450
Answers
The temperature when the pressure is 450 is 225°.
What is Direct Variation?In the case of an increase or decrease in both quantities by the same factor, two quantities are said to follow a direct variation. As a result, when one quantity rises, the other follows suit, and vice versa when one quantity falls. In other words, if the ratio of the first quantity to the second quantity is a constant term, the quantities are said to be directly proportional to one another. The term "coefficient or constant of proportionality" refers to this constant number.Given:
The pressure of a gas varies directly with the temperature.
So, P ∝ T
P = kT , here k is the constant of proportionality
Pressure(P) = 800psi
Temperature(T) = 400°
Putting the values to get the value of k,
P = kT
800 = 400k
k = 2
We need to find the temperature when the pressure is 450.
P = kT
450 = 2T
T = 450/2
T = 225°
Therefore, the required temperature is 225°.
To learn more about direct variation visit:
https://brainly.com/question/11592410
#SPJ9
im struggling on this
Answers
The scale factor of figure A to figure B is 5/2
What is a scale factor?A scale factor can be defined as the ratio of the scale difference between a given original shape and a new shape.
It is seen as a number from which the size of a dimensional shape or figure can be transformed with respect to its original size or magnitude.
It is also described as the ratio between corresponding measurements of an object and a representation of that object.
The formula for scale factor is expressed as;
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
This is so for the downgrading of a shape
Now, we have;
Scale factor = Adjacent of the triangle A/adjacent of triangle B
Scale factor = 10/ 4
Reduce to simply forms
Scale factor = 5/ 2
Hence, the scale factor is 5/2
Learn more about scale factor here:
https://brainly.com/question/10253650
#SPJ1
-23x² + x² - 6x + 10 + 2x²
Answers
Answer:
-2(-10x^2 + 3x -5)
Step-by-step explanation:
Combine like terms
Then find the common factor
Answer:
[tex]-20x^{2} -6x+10[/tex]
Step-by-step explanation:
[tex]=-23x^{2} +x^{2} +2x^{2} -6x+10[/tex]
[tex]=-23x^{2} +3x^{2} -6x+10[/tex]
[tex]=-20x^{2} -6x+10[/tex]
Hope this helps
Which of the following exponential expressions are equivalent to 64? (Select ALL correct answers for full credit).
Answers
Answer:2 to the 5, 8 to the 2, and 4 to the third
Step-by-step explanation:
2x2x2x2x2=64
8x8=64
4x4x4=64
64^1
2^5
4^3
|PLSSSS SHELLPP URGENTTT
Answers
Triangle A is right angled triangle
Triangle B is right angled triangle
Triangle C is obtuse angled triangle
Triangle D is acute angled triangle
In right angled triangle one of the three angles in the triangle is 90 degrees
In acute angled triangle all the angels in the triangle is less than 90 degrees
In obtuse angled triangle one of the three angles in the triangle is greater than 90 degrees
In triangle A one of the angle is 90 degrees, then the triangles is right angled triangle
In triangle B one of the angle is 90 degrees, then the triangles is right angled triangle
In triangle C one of the angle is greater than 90 degrees, then the triangle is obtuse angled triangle
In triangle D all the angles are less than 90 degrees, then the triangle is acute angled triangle
Hence, Triangle A is right angled triangle
Triangle B is right angled triangle
Triangle C is obtuse angled triangle
Triangle D is acute angled triangle
Learn more about triangle here
brainly.com/question/27454289
#SPJ1
simplify 2(x - 4) + 9
Answers
Answer: 2x + 1
Step-by-step explanation:
We will simplify this expression down to it's lowest terms.
Given:
2(x - 4) + 9
Distribute:
2x - 8 + 9
Combine like terms:
2x + 1
2x+1
Vector v has initial point (-2, -1) and terminal point (8, -5). Write v as a linear combination of the standard unit vectors i and j.
Answers
Given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j
In this question, we have been given a vector whose initial point is (-2, -1) and the final point is (8, -5)
We need to write vector v as a linear combination of the standard unit vectors i and j.
Let (x1, y1) = (-2, -1) and (x2, y2) = (8, -5)
We know that for vector A having initial point (x1, y1) and terminal point (x2, y2), a linear combination of the standard unit vectors i and j is:
vec A = (x2 - x1)i + (y2 - y1)j
So, for given vector it would be,
vec v = (x2 - x1) i + (y2 - y1) j
vec v = (8 - (-2)) i + (-5 - (-1)) j
vec v = (8 + 2) i + (-5 + 1) j
vec v = 10 i -4 j
Therefore, given vector v as a linear combination of the standard unit vectors i and j would be, vec v = 10 i -4 j
Learn more about a vector here:
https://brainly.com/question/1563531
#SPJ1
Answer:
Step-by-step explanation:
how do I write this ?
Answers
Answer:
1: -⅔
2: -⅓
Step-by-step explanation:
You plug the number into the Equation.
1:
2 = 3x + 4
-2 = 3x
x = -⅔
2:
3 = 3x + 4
-1 = 3x
x = -⅓
Guadalupe quiere saber la longitud de un túnel construido a través de una montaña. Para ello, ella toma las medidas indicadas en la figura a continuación. Utilizar estas medidas para hallar la longitud del túnel.
Llevar a cabo los cálculos intermedios usando al menos cuatro posiciones decimales.
Redondear la respuesta a la décima de metro más cercana.
Answers
Puedes usar la Ley de los Cosenos.
Explicación:
recall that the perimeter of a square is 4 times as large as the length of one of the sides of the square. let x represent the length of one side of a square (in inches), and let y represent the perimeter of that square (in inches). y is a function of x , so we can define a function f to represent this relationship (e.g., f ( x )
Answers
The function which represents the relation between the perimeter and the length of the square is; y = 4x.
What is described as the function?A function is described as the connection between a collection of inputs that each have one output. A function is a relationship between inputs in which each input is connected to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), in which x is the input. A function's general representation is y = f. (x).For the given question;
Let x be the side of the square.
Let y be the perimeter of the square.
Perimeter is 4 times the side of the square.
Then,
Perimeter = 4×side
y = 4x.
Thus, the function which describes the relation between the perimeter and the side of square is y = 4x.
To know more about the function, here
https://brainly.com/question/11624077
#SPJ9
Please Help! :)
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{5}{2} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Slope (m) of a line can be calculated by using this formulae :
[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]
Considering two points [ (60 , 0) and (80 , 50) ]
[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{50 - 0}{80 - 60} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{50}{20} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{5}{2} [/tex]
So, slope of given line is 5/2
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
I have been struggling with this question for the past couple minutes I believe I have the formula correct, but it isn't working
Answers
Answer:
382.5 in^2
Explanation in attachment. Hope it helps! :)
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances
total $80. How much is each allowance?
You
Friend
Your allowance is $
and your friend's allowance is $
^
Answers
From the tape diagram, your allowance and your friends' allowance is $48 and $32 respectively.
What is tape diagram?
A tape diagram is a visual representation that looks like a piece of tape and is used to help with ratio calculations, addition, subtraction, and most frequently multiplication. A divided bar model, fraction strip, length model, or strip diagram are other names for it. It is employed in mathematics education to help elementary school-aged children solve word problems. Students can use a tape diagram as a pictorial model to represent a mathematical relationship or to better understand a mathematical concept. Although they are frequently used with word problems, tape diagrams are helpful for solving many different kinds of math problems.
Let the ratio is given by 3:2 and total is 5
hence, 5 parts represent $80, so each part represents= 80/5= 16
hence, your allowance is 3×16 =48 and your friend allowance is 2×16= 32
To know more about tape diagram, visit:
brainly.com/question/21764623
#SPJ9
Solve for x :
5x+8=7x-72
Answers
Answer:
x = 40
Step-by-step explanation:
We just have to manipulate the terms, putting each term that has the variable "x" on one side of the equation like this:
5x + 8 = 7x - 72
5x - 7x = - 72 - 8
-2x = -80
x = -80/--2
x = 40
Answer:
x = 40
Step-by-step explanation:
Given equation:
[tex]5x+8=7x-72[/tex]
Add 72 to both sides:
[tex]\implies 5x+8+72=7x-72+72[/tex]
[tex]\implies 5x+80=7x[/tex]
Subtract 5x from both sides:
[tex]\implies 5x+80-5x=7x-5x[/tex]
[tex]\implies 80=2x[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{80}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies 40=x[/tex]
Therefore, the solution to the given equation is x = 40.
When an integer is subtracted from 3 times the next consecutive integer, the difference is 23. Find the value of the lesser integer.
Answers
Answer:
10
Step-by-step explanation:
To find the value of the smaller integer, start by letting a variable be that integer. This helps us to refer to the integer with greater ease in our working.
Let the smaller integer be x.
Consecutive numbers refers to numbers coming after one another, such as 1, 2 and 3.
The next integer coming after the integer x would thus be (x +1). Three times the next consecutive integer would then be 3(x +1).
Subtract refers to a minus sign, thus the equation would be:
3(x +1) -x= 23
Expand:
3x +3 -x= 23
Simplify:
2x= 23 -3
2x= 20
Divide both sides by 2:
x= 20 ÷2
x= 10
Thus, the smaller integer is 10.
For a similar question on consecutive integers, check out: https://brainly.com/question/1753112
*Note that when b is subtracted from a, the expression would be a -b.
Hello users do you know how to solve. Please answer it properly and i need what is a correct answer.
Noted: This subject is science it is not a math
Answers
To convert Celsius to Fahrenheit, we take the given Celsius measurement, multiply it by 1.8, and add 32, and vice versa.
To convert Celsius to Kelvin, we add 273 into the given Celsius measurement, and vice versa.
1) 18oC to F and to K
18oC = 18 x 1.8 + 32 = 64.4oF = 18 + 273 = 291oK
2) 95oF to C to K
95oF = (95-32) : 9/5 = 35oC = 35 + 273 = 308oK