Graph the solution of the system of linear inequalities.<br> y + 2x ≥0<br> 3x-2y≤6

Write the standard form equation of the ellipse shown in the graph, and identify the foci.

vlada-n [284]

Answer option A

From the given graph is a Vertical ellipse

Center of ellipse = (-2,-3)

Vertices are (-2,3) and (-2,-9)

Co vertices are (-6,-3) and (2,-3)

The distance between center and vertices = 6, so a= 6

The distance between center and covertices = 4 , so b= 4

The general equation of vertical ellipse is

$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2}=1$

(h,k) is the center

we know center is (-2,-3)

h= -2, k = -3 , a= 6 and b = 4

The standard equation becomes

$\frac{(x+2)^2}{4^2} + \frac{(y+3)^2}{6^2}=1$

$\frac{(x+2)^2}{16} + \frac{(y+3)^2}{36}=1$

Foci are (h,k+c) and (h,k-c)

$c=\sqrt{a^2-b^2}$

Plug in the a=6 and b=4

$c=\sqrt{6^2-4^2}$

$c=\sqrt{20}$

$c=2\sqrt{5}$ , we know h=-2 and k=-3

Foci are $(-2,-3+2\sqrt{5})$ and $(-2,-3-2\sqrt{5})$

Option A is correct

6 0

3 years ago

What is the height of the triangle? 12 units 24 units 36 units 72 units.

konstantin123 [22]

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is $16 \sqrt{3}$ units.

As all the sides are equal thus the $\Delta MNO$ is a equilateral triangle in which the height of the divides the triangle into two equal part of the length $8\sqrt{3}$ at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the $\Delta MRN$ , the length of the hypotenuse is $16 \sqrt{3}$ units and the length of the base is $8\sqrt{3}$ units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

$(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2$

Solve for <em>h,</em>

<em />

<em /> $\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end$ <em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

5 0

2 years ago

A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data isa)4b)13c)17d)20Co

Degger [83]

The mode of the data of sample with 15 values is c) 17.

The mode of any sample of data can be calculated by finding the number that is present highest number of times. Based on this, we will look for the numbers that are present multiple times in the mentioned sample.

17, 18 and 5 are the three numbers that are present more than once. Now, let's see what is the frequency of each of these numbers.

Frequency of 17 - 4

Frequency of 18 - 2

Frequency of 5 - 2

Thus, the number 17 is present maximum number of times and hence is the mode of the data.

Learn more about mode -

brainly.com/question/14532771

#SPJ4

5 0

1 year ago

5. The length of a rectangle is 3 inches less than its width. If the

artcher [175]

Answer:

length is 17 in, width is 20

Step-by-step explanation:

let's shape this as an algebraic equation, where x= the length of one side.

since the width is 3 inches longer than the length, x will be the length and x+3 will be the width.

the perimeter is 74 in, and the perimeter is the added length of all sides. in a rectangle, 2 sides are the length and 2 sides are the width, so:

74 = 2x + 2(x + 3)

let's distribute the 2.

74 = 2x + 2x + 6

now, we combine the x's.

74 = 4x + 6

after this step, subtract 6 from the right to add it to the left side.

68 = 4x

finally, divide both sides by 4.

17 = x

perfect! now that we know the length, we just have to add 3 to find the width.

17 + 3 = 20

5 0

2 years ago

a toy ball expands and contracts. When it is completely closed, it has a diameter of 15.5. Find the volume of the ball when it i

horrorfan [7]

Volume of a sphere is 4/3pi∗r3. r is half the diameter.

3 0

2 years ago

Graph the solution of the system of linear inequalities. y + 2x ≥0 3x-2y≤6