Mathematics College

How do I write the equation of hyperbola in standard form with center (0,0),endpoints of the transverse axis (±6,0) and length of latus rectum is 16?

Answers

Answer 1

Answer:

Length of latusrectum =9=

⇒b

..... (i)

and e=

∵1+

∴1+

[from Eq. (i)]

⇒

⇒a=8

On putting the value of a in Eq. (i), we get

9×8

=36⇒b=6

∴ Equation of hyperbola is

−

=1⇒

−

Related Questions

What is the solution of 7x + 14 − 3x = 30?

Answers

X=4, hope this helps :)

First, we would want to combine like terms. So, we should combine 7x and 3x by subtracting them.
7x + 14 - 3x = 30
4x + 14 = 30
Subtract 14 from both sides; whatever you do to the left you must do to the right
4x = 16
Divide by 4
x = 4

You have budgeted 2/5 of your monthly income for rent and utilities. Your monthly income is $2100.
a) What amount have you budgeted for rent and utilities?
b) What amount is left over for expenditures during the month?

Answers

Answer:

a. $840

b. $1,260

Step-by-step explanation:

a. 2/5 x 2100 = 840

b. 2100 - 840 = 1,260

A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $27. For 9 pounds of jelly beans and
7 pounds of almonds, the total cost is $51. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans:
Cost for each pound of almonds:

Answers

Answer:

Cost for each pound of jelly beans: $2.75

Cost for each pound of almonds: $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

$\implies 3J + 5A = 27$

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

$\implies 9J + 7A = 51$

Therefore, the system of equations is:

$\begin{cases}3J+5A=27\\9J+7A=51\end{cases}$

To solve the system of equations, multiply the first equation by 3 to create a third equation:

$3J \cdot 3+5A \cdot 3=27 \cdot 3$

$9J+15A=81$

Subtract the second equation from the third equation to eliminate the J term.

$\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}$

Solve the equation for A by dividing both sides by 8:

$\dfrac{8A}{8}=\dfrac{30}{8}$

$A=3.75$

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

$3J+5(3.75)=27$

$3J+18.75=27$

$3J+18.75-18/75=27-18.75$

$3J=8.25$

$\dfrac{3J}{3}=\dfrac{8.25}{3}$

$J=2.75$

Therefore, the cost of one pound of jelly beans is $2.75.

Alejandro bought $3.50 worth of pencils and erasers at the school store. Pencils cost $0.50 apiece, and erasers cost
$0.75 apiece. Which equation written in standard form represents the number of pencils, p, and the number of erasers,
e, that Alejandro bought?
O 0.75e = 3.50 -0.50p
O 0.50p + 0.75e = 3.50
O 3e = 14 -2p
O 2p + 3e = 14

Answers

The only thing I know is 4.75 all added up

What is least to greatest 7/8.5/11,2/3

Answers

The arrangement of the fraction from least to greatest is 5/11, 2/3 and 7/8.

What is a fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers

The fraction can be changed to percentage to make it easier.

7/8 = 7/8 × 100 = 87.5%

5/11 = 5/11 × 100 = 45.5%

2/3 = 2/3 × 100 = 66.7%

The arrangement is 5/11, 2/3 and 7/8.

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6. Use the following matrices to answer the questions. (2 points each)
5 -8
2 -6
-8
-2 3
A
외
B =
[4
18] c- [5 5] -
C=
9 1
03
9
1
a. Is the operation E + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
b. Is the operation B + C possible? Circle YES or NO
If yes, state the dimensions of the answer:
c. Is the operation E. D possible? Circle YES or NO
If yes, state the dimensions of the answer:
d. Is the operation D E possible? Circle YES or NO
If yes, state the dimensions of the answer:
e. Is the operation A D possible? Circle YES or NO
If yes, state the dimensions of the answer:
1
-1 10
E
11
7 -1 0

Answers

Answer:

its a such a hard questions i think you should ask to you're teacher ?

Can you solve this please.

Answers

1) simplify the expression using the rule of exponent

y^12 * y^5

y^17

Answer

y^17

Answer: y^17 have a good day

All students in the 6th grade either purchased their
lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the 6th grade?

i need a really detailed answer

Answers

The number of students in the 9th grade is 250.

How to calculate the value?

Based on the information, the percentage of those who brought their good from home will be:

= 100 - 24%

= 76%

Therefore, 76% of x = 190

0.76x = 190

x = 190/0.76

x = 250

Therefore, the number of students in the 9th grade is 250.

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Please graph y=log3(x+2) and then find the asymptote domain and range

Answers

Answer:

Step-by-step explanation:

y = a * log_b (x - h) + k

(h,k) = (x,y)

h = shift right/left

k = shift up/down

Original Points of y = log_3

y = log_3 (x + 2)

h = -2 thus shift left.

Asymptote: x = -2
Domain: [-2 , +inf)

Range: (-inf , +inf)

classafy the numbers some numbers are more than 1 box numbers are 54,72,84,90,96 sections are divisible by 5 and 9 divisible by 6 and 9 divisable by 2 and 6

Answers

Here's the classification:

Divisible by 5 and 9: 90
Divisible by 6 and 9: None
Divisible by 2 and 6: 72, 84, 96

So the numbers 54, 72, 84, 90, and 96 can be placed into the following boxes:

More than 1 box: 72, 84, 96
Divisible by 5 and 9: 90
Divisible by 6 and 9: None
Divisible by 2 and 6: 72, 84, 96

and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern

Answers

Answer:

quadratic

Step-by-step explanation:

This graph has a parabola form wich is a propertie for qaudratic functions

Answer:

Step-by-step explanation:

At a local pizza parlor, patrons have 3 choices of cheese and 5 choices of meat. In how many different ways can a patron choose 1 type of cheese and 1 type of meat? 10 30 o 15 0 8 o Termsat a local pizza parlor that runs has three choices of cheese and five choices of meat in how many different ways can a pageant use one type of cheese and what type of meat

Answers

Answer:15

Step-by-step explanation:

The length of a rectangle is three times linger that the width. The perimeter of the rectangle is 40 inch. What is the length of the rectangle in inches

Answers

Answer:

Step-by-step explanation:

L=3W

P=2L+2W

40= 2 (3W)+2W

40=6W+2W

8W=40

W=40/8

W=5 in

L=15 in (3W= 3*5=15)

Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have the same zeros. b. f(x) has a higher maximum than g(x). c. f(x) and g(x) have the same y intercept. d. f(x) and g(x) are odd functions.

Answers

None of the Options are true both the given functions are parabolic functions.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function are, f(x)=-15x²+32 and g(x)= -17x²+5x+32,
Zeros for the functions are,
x = ± 1.461 and x = -1.233 and 1.527,
Where g(x) has a higher maximum than f(x), the Intercept of f(x) is greater than g(x). As shown in the graph.

Thus, none of the options are true because both of the supplied functions are parabolic.

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Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have

can someone please help

Answers

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

$13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2$

Now,

$CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46$

Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 3 > 3

Answers

The correct graph of the inequality ( |x| + 3 > 3) is attached accordingly.

Here is how the above was solved

Recall that the absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.

A number's absolute value can be conceived of as its distance from zero along the real number line.

So, given |x| + 3 > 3

Add minus three to both sides

|x| + 3 + (-3) > 3 + (-3)

|x| > 0

Thus, the absolute value of x is

x > 0 or x < -0

put in the form of inequality, we have

x > 0 or x < 0

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A school has 300 students and 30 teachers. What is the ratio between the number of teachers and the number of students of the school?

Answers

30 : 300
Simplify
10:100
1:10

A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses. If there are N packages (N ≥ 2) and the total value of them is $2021 and if each of X, Y, and N are positive integers, what is X+Y+N?

Answers

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

What are system of inequalities?

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition

Answers

Answer:

The equation 1+0=1

Step-by-step explanation:

Other options are not eligible because

1 option -Natural numbers cannot be closed under subtraction

2 option-The equation is not having proper rational numbers, they are decimals

3 option-Whole numbers cannot be closed under subtraction

Thank you!

what is 13.6 - x = -64.2

Answers

Answer:

13.6 - x = -64.2

Step-by-step explanation:

x = 77.8

13.6 - 77.8 = -64.2 True!

Answer:

x=77.8

Step-by-step explanation:

13.6-x=-64.2

-13.6. -13.6

---------------------

since there is already -x it wouldn't be -77.8 bc that would cancel it out

if you take away 25 from a number you will be left with two and halftimes 30. what is the number?

Answers

The answer would be 100.
If you take away 25 from (100) you get 75.
70 also equals 2.5*30

plsss help me i neeed it

Answers

Answer:

A:24 7/20

B:12 19/21

C:11 1/2

D:284 13/80

E:10

Step-by-step explanation:

hope it helps to you

10 minutes past noon in analog time

Answers

Answer:

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through: ... Angle traced by hour hand in 12 hrs = 360°.Jul 1, 2010

Explain your answer to the question in the picture with steps please, thank you.

Answers

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Need Help please, here is screenshot

Answers

The axis of symmetry is x = -6.

Vertex is (-6, 26).

f(x) has a maximum value.

f(x) is concave down.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

f(x) = -x² - 12x - 10

This is in the form of ax² + bx + c.

a = -1, b = -12, c = -10

The axis of symmetry is x = -b/2a

x = 12/(-2)

x = -6

Now,

f(x) = -x² - 12x - 10

f(x) = -(x² + 12x + 10)

f(x) = - { (x² + 12x + 36) - 36 + 10}

f(x) = -(x + 6)² + 26

This is in the form of f(x) = a (x - h)² + k

a = -1, h = -6, k = 26

Vertex = (h, k) = (-6, 26)

Now,

f(x) = -x² - 12x - 10

f'(x) = -2x - 12

f''(x) = -2

It is a negative value.

This means f(x) has a maximum value.

Now,

From the graph, we see that f(x) is concave down.

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A pond has been created in a remembrance garden. It has an approximate diameter of 10 metres. A person walks around the
pond four times a day. How far have they travelled per day to the nearest metre?
(Circumference of a circle is 2T or C=Td, where te=3.14)

Answers

Answer:

126 meters

Step-by-step explanation:

First, let's find the circumference of the pond. We know that C = πd, π = 3.14 and d = 10 so the circumference is 3.14 * 10 = 31.4 meters. However, the person walks around the pond 4 times so the answer is 31.4 * 4 = 125.6 meters which rounds to about 126 meters.

what is the maths formula for area

Answers

Answer:

Quick internet search:

The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?

Answers

Answer:20

Step-by-step explanation:this is wrong

Answer:

Step-by-step explanation:

subtract median of dogs and median of cats

1.652 when 5 is underlined round to the place of the underlomed digit

Answers

Answer:

1.650

Step-by-step explanation:

4 below hit the floor

5 above goes through the roof

literally a goat if someone gives me an answer for this please

Answers

Answer: D, 100

Step-by-step explanation:

Answer: 100 (D)

Step-by-step explanation:

cuz

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