How do you write 40% as a fraction or whole number in simplest form?

Which hyperbola’s asymptote rectangle has the greatest perimeter?

Vitek1552 [10]

Answer:

The greatest perimeter is in (D) ⇒ the perimeter = 60 units

Step-by-step explanation:

* In the hyperbola

- The standard form of the equation of a hyperbola with

center (h , k) and transverse axis parallel to the x-axis is

(x - h)²/a² - (y - k)²/b² = 1

∵ the length of the transverse axis is 2a

∵ the length of the conjugate axis is 2b

∴ The perimeter of asymptote rectangle is 2(2a + 2b)

* Lets check the answers to find the greatest perimeter

A) (x - 4)²/11² - (y + 2)²/3² = 1

* Compare it with the standard form equation

∵ a = 11 ⇒ 2a = 22

∵ b = 3 ⇒ 2b = 6

∴ The perimeter = 2(22 + 6) = 56

B) (x - 2)²/4² - (y + 1)²/10² = 1

* Compare it with the standard form equation

∵ a = 4 ⇒ 2a = 8

∵ b = 10 ⇒ 2b = 20

∴ The perimeter = 2(8 + 20) = 56

C) (x + 5)²/5² - (y - 3)²/9² = 1

* Compare it with the standard form equation

∵ a = 5 ⇒ 2a = 10

∵ b = 9 ⇒ 2b = 18

∴ The perimeter = 2(10 + 18) = 56

D) (x - 7)²/8² - (y - 2)²/7² = 1

* Compare it with the standard form equation

∵ a = 8 ⇒ 2a = 16

∵ b = 7 ⇒ 2b = 14

∴ The perimeter = 2(16 + 14) = 60

* The greatest perimeter is in (D)

4 0

3 years ago

Read 2 more answers

How could you represent the following scenarios on a graph ?

Tcecarenko [31]

Answer:

Step-by-step explanation:

Johnny mows lawns after school and earns $10 per hour.

Let the number of hours h mows = x

Total earning of Johnny = $10x

If the earning is represented by the variable 'y' equation representing the total earnings will be.

y = 10x

Table for Input output values,

x 0 1 2 3 4

y 0 10 20 30 40

3 0

3 years ago

Plz help ?!?!?!!?!?!?!??!

lord [1]

15 Im sure its 15 I re calculated just to be sure

5 0

3 years ago

Using the information in the diagram, what is the height of the tree to the nearest foot?

Ray Of Light [21]

The answer is 80 ft.

Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other.

The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:

to solve for x, all you need to do is cross multiply then divide.

The answer is then 80ft.

Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two.

160ft/2 = 80ft.

5 0

3 years ago

Use matrices to write the equation of the function in the form y = mx + b that contains the points

Fofino [41]

The line has a slope of -6 and a y intercept of 7.

The linear equation is given by:

y = mx + b;

where m is the slope of the line, b is the y intercept, y, x are variables.

The equation of the line passing through the points (6.-29) and (-4,31) is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-29)=\frac{31-(-29)}{-4-6}(x-6)\\\\y+29=-6(x-6)\\\\y=-6x+7$