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3 years ago

Which conic section is represented by the following equation? 9x^2 – 5x – 3y^2 – 2y + 4 = 0

Mathematics

2 answers:

zheka24 [161]3 years ago

4 0

Answer:

D. Hyperbola

Step-by-step explanation:

I put B but it was wrong

D is the right answer

stealth61 [152]3 years ago

3 0

Answer:

the awnser is B. Elipse

Step-by-step explanation:

its right on edge 2021

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Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.

4 0

3 years ago

The formula for the size of a file that was downloaded over time t and at an average rate r is r.t.

lakkis [162]

Answer:

The size of file downloaded is 88 megabytes.

Step-by-step explanation:

Given that:

Average rate of downloading the file = $r$

Time taken to download = $t$

Formula for the size of file downloaded = $r.t$

Rate of downloading, $r = 800\ kilobytes/sec$

Time taken, $t$ = 110 seconds

To find:

Size of file downloaded in megabytes = ?

Solution:

First of all, let us apply the given formula to find the size of file downloaded:

Size of file downloaded = $r.t$

Size of file downloaded = 800 kilobytes seconds $\times$ 110 seconds =

88000 kilobytes.

Now, let us convert the unit kilobytes to megabytes to find the answer.

Conversion formula:

1000 kilobytes = 1 megabyte

Let us use unitary method to find the number of megabytes in 88000 kilobytes.

1 kilobytes = $\frac{1}{1000}$ megabytes

88000 kilobytes = $\frac{1}{1000} \times$ 88000 megabytes

$\Rightarrow$ 88 megabytes.

Therefore, the size of file downloaded is 88 megabytes.

5 0

3 years ago

Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a

diamong [38]

Answer: a. 0.4 × 0.15 = 0.060

Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.

For P(A):

P(A') = 1 - 0.6

P(A') = 0.4

For P(B):

P(B') = 1 - 0.85

P(B') = 0.15

To determine probability of A' and B':

P(A' and B') = P(A')*P(B')

P(A' and B') = 0.4*0.15

P(A' and B') = 0.06

Probability of the complement of the event is 0.060

5 0

3 years ago

Solve for h 3/7 = h/14 - 2/7

vodomira [7]

The answer is in attached picture.

Hope this will help u....

4 0

3 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago