How many troops from Paraguay entered the war? O 55,000 O 40,000 O 50,000 O 60,000

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

I’ll give Brainly but pleaseee help

77julia77 [94]

Fruit adult = 26
fruit total = 52
vegetable child = 14
total child = 40
total adult = 50

8 0

3 years ago

A horse walks around a circular track while its trainer stands in the center. The trainer is 14 feet from the horse at all times

max2010maxim [7]

The horse traveled 439.6 feet after walking around the track 5 times

Solution:

Given that, horse walks around a circular track while its trainer stands in the center

The trainer is 14 feet from the horse at all times

Therefore, radius of circular track = 14 feet

The circumference of circle is the distance traveled by horse for 1 lap

The circumference of circle is given as:

$C = 2 \pi r$

Where, "r" is the radius and $\pi$ is a constant equal to 3.14

$C = 2 \times 3.14 \times 14\\\\C = 87.92$

Thus the distance traveled by horse for one time in circular track is 87.92 feet

About how far had the horse traveled after walking around the track 5 times?

Multiply the circumference by 5

$distance = 5 \times 87.92\\\\distance = 439.6$

Thus the horse traveled 439.6 feet after walking around the track 5 times

5 0

3 years ago

Can you plz help me with number 2

Kruka [31]

Answer:

the height is 20

Step-by-step explanation:

you should set a equation first:

12/15=x/25

and then cross multiply

to get x=20

8 0

3 years ago

Read 2 more answers

The cost to produce a product is modeled by the function f(x) = 5x^2 − 70x + 258, where x is the number of products produced. Co

Advocard [28]

The minimum of a quadratic function, with a positive coefficient a, is its vertex.

Let's find the x₀ coordinate.

$f(x) = 5x^2 -70x + 258\\\\x_0=\dfrac{-b}{2a}=\frac{-(-70)}{2*5} =\frac{70}{10} =7$

Now we need to find y₀ coordinate. That will be the minimum of function.

$y_0=5\times7^2-70\times7+258=13$

So, the minimum cost to produce the product is $13

Decompose 5x^2 − 70x + 258 into multipliers

$5x^2 - 70x + 258=(5x^2-70x+245)+13=5(x^2-14+49)+13=\\=5(x-7)^2+13$

Answer: 5(x − 7)^2 + 13; The minimum cost to produce the product is $13.

4 0

3 years ago