which one is greater 0.503 or 0.53

Given:

Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).

To find:

The equation of hyperbola.

Solution:

We have, directrices at y = ±2 so this hyparabola is along the y-axis.

The standard form of hyperbola is

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]      ...(i)

where, (h,k) is center, foci are [tex](h,k\pm c)[/tex] and directrix are [tex]y=k\pm \dfrac{a^2}{c}[/tex].

On comparing foci, we get

[tex](h,k\pm c)=(0,\pm 6)[/tex]

[tex]h=0,k=0,c=6[/tex]

On comparing directrix we get

[tex]k\pm \dfrac{a^2}{c}=\pm 2[/tex]

[tex]\dfrac{a^2}{c}=2[/tex]

[tex]\dfrac{a^2}{6}=2[/tex]

[tex]a^2=12[/tex]

Now,

[tex]a^2+b^2=c^2[/tex]

[tex]12+b^2=(6)^2[/tex]

[tex]b^2=36-12[/tex]

[tex]b^2=24[/tex]

Putting [tex]h=0,k=0,a^2=12,b^2=24[/tex], we get

[tex]\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1[/tex]

[tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex]

Therefore, the equation of hyperbola is [tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex].

Answer:

the person above has the right answer. I took the test.

Step-by-step explanation:

The person above is correct.

Answer:

18.75 meters

Step-by-step explanation:

8.75 + 0.25(40) = 18.75

Answer:

I do not agree with the student because there is no real solution. Solving the equation only gives possible solutions, but you must check them in the original equation. Checking the solution in the original equation shows that 4 is an extraneous solution.

Step-by-step explanation:

idk if that's the same question i had, but that was the answer for mine. hehehe good luck.

is that on edge?

Answer:

Harry has a score of 30

Step-by-step explanation:

Let us represent their scores as:

Nathan = x

Harry = y

Jack = z

At the end of a football season a coach is adding up everyone's scores

Nathan has scored 11 more than harry

x = y + 11

Harry has scored 10 more then jack.

y = z + 10

z = y - 10

If the total of their scores is 91

x + y+ z = 91

y + 11 + y + y - 10 = 91

3y + 1 = 91

3y = 91 - 1

3y = 90

y = 90/3

y = 30

Since Harry's score is represented as y, Harry has a score of 30

Answer:

y= -1/3x-4

y=2x+2

Step-by-step explanation:

the slope is rise over run

Answer:9

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Multiples of 6:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84

Multiples of 8:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88

Multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Therefore,

LCM(6, 8, 9) = 72

Answer:

Step-by-step explanation:

because we have a kite,

AB=AD

4x=x+15

4x-x=15

3x=15

x=5

Answer:

50

Step-by-step explanation:

Answer: the answer is 50

Step-by-step explanation:

Answer:

x = 48.59 degrees

Step-by-step explanation:

Do sin-1(12/16) and put it in a calculator. After that, you will get your final answer as 48.59 degrees. This requires sin because the opposite angle is 12 for x. The adjacent angle is something else.

Answer:

[tex]\frac{3ab}{2c}[/tex]

Step-by-step explanation:

An algebraic expression is an expression consists of constants, variables, and the algebraic operations: addition, subtraction, multiplication and division.

Given: algebraic expressions are [tex]3ab,2c[/tex].

To divide: [tex]3ab[/tex] by [tex]2c[/tex]

Solution:

[tex]\frac{3ab}{2c}[/tex]

There are no common terms in numerator and the denominator.

So, answer is [tex]\frac{3ab}{2c}[/tex]

Answer:

the value in the five years is  £2,621.44

Step-by-step explanation:

The computation of the value in the five years is given below:

= The value of the second car × (1 - losses percentage)^number of years

= £8,000 × (1 - 0.20)^5

= £8,000 × 0.80^5

= £8,000 ×  0.32768

=  £2,621.44

Hence, the value in the five years is  £2,621.44

We simply applied the above formula so that the correct value could come

And, the same is to be considered

Answer:

64

Step-by-step explanation:

v = s^3

v = (4)^3 [4x4x4]

v = 64

Answer:

The correct answer is 10n ≥ 470.

Step-by-step explanation:

Since, the school club wants to collect at least 500 canned goods, then we know that they don't want to collect any less: they must collet 500 or more canned goods.

They already collected 30 canned goods, therefore we can subtract this quantity from out goal.

500 - 30 = 470

Since there are 10 club members, the number of members multiplied by "n" the minimum amount of canned goods that they can collect, will equal the total amount of canned goods that they need.

Hope this helps! :D

Answer:

10.

Step-by-step explanation:

6+1/3*12=6+4=10

Answer: 10

Step-by-step explanation:

Answer:

12%

Step-by-step explanation:

We can get SI of 3 years = 12005 - 9800 = 2205

SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]

Principal = 12005 - 3675 = 6125

So Rate = (100*3675)/(6125*5) = 12%

Answer:

The widgets should be sold for $26.7 for the company to make the maximum profit.

Step-by-step explanation:

Given the quadratic equation

[tex]f\left(x\right)=-15x^2+801x-59000[/tex]

As the leading coefficient is (-3), so the graph would be a downward Parabola.

Thus, the maximum profit would be at the vertex.

The selling price 'x' can be determined by determining the x-coordinate of the vertex.

In order to calculate the x-coordinate of the vertex, we can find this by

x = -b/2a

where a = -15 and b = 801

x = -801 / 2(-15)

x = -801/-30

x = 801/30

x = 267/10

x = 26.7

Therefore, the widgets should be sold for $26.7 for the company to make the maximum profit.

Answer:

k = ±6

Step-by-step explanation:

guess your question is 4k²–144 = 0??

4k² = 144

k² = 36

k²–36 = 0

(k+6)(k–6) = 0

k+6 = 0 | k–6 = 0

k = –6, k = 6.

Alternatively; k = ±6.

Answer:

True, True, False.

Step-by-step explanation:

A) Rise/Run is 8/1

B) 8 dollars are earned every hour

C) Correct equation is y=8x

Answer:

67 feet

Step-by-step explanation:

Step one:

given

The area of a rectangular warehouse measures 4,288 square feet

The width of the warehouse is 64 feet long.

Required:

the length of the warehouse

Step two:

The expression for the area of a rectangle is

A= L*W

so, for the situation

4,288= L*64

solve for L

divide both sides by 64

L= 4,288/64

L=67 feet

Answer:

-4x^2 - 8......input (x) = 2

Step-by-step explanation:

-4(2^2) - 8 =

-4(4) - 8 =

-16 - 8 =

- 24 <==

i hope this helps you :)

Answer:

D 5x + 13 = 12

Step-by-step explanation:

3 + 5(x + 2) = 12

3 + 5x + 10 = 12

5x = -1

x = -1/5

D) 5x + 13 = 12

5x = 12 - 13 = -1

x = -1/5

Answer: the answer is 13.6 units

Step-by-step explanation:

Answer:

C. 13.6 units

Step-by-step explanation:

i took the quiz on edge

Answer:

5/6 is greater than 4/5

Step-by-step explanation:

4/5 = 0.8

5/6 = 0.833333

Answer:

no

Step-by-step explanation:

5/6 is greater than 4/5

Discount amount = price x discount percentage as a decimal:

Discount amount = 62.00 x 0.15 = 9.30

Discount = $9.30

Answer:

$52.70

Step-by-step explanation:

Question

Juan deposited $2,250 in the bank to celebrate the birth of his son. After three years, he received his statement and the bank said he had $2,587.50 in the account.

How much interest did Juan earn in three years?

How much interest did Juan earn per year?

What was the interest rate?

Answer: GOOD LUCK

337 and 112.33

Answer:

337 and 112.33

Step-by-step explanation:

First answer is 337 u take the difference between the 2 numbers. And the interest is 112.33 per year u divide the interest by 3. I hope this helps.

Answer:

probably 25

Step-by-step explanation: