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Alika [10]
3 years ago
7

Suppose you are ordering a calzone from D.P. Dough. You want 4 distinct toppings, chosen from their list of 8 vegetarian topping

s. How many choices do you have for your calzone
Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
6 0

Answer:

1680

Step-by-step explanation:

Number of distinct Toppings wanted = 4

Total number of vegetarian topping = 8

To choose 4 distinct toppings from a total of 8

Using permutation :

nPr : n! (n - r)!

8P4 = 8! / 4!

8P4 = (8*7*6*5)

8P4 = 1680

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4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia
Ad libitum [116K]

The <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its <em>standard</em> form from the coordinates of the foci and a <em>general</em> equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the <em>general</em> equation of the circle into its <em>standard</em> form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0​

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (<em>semi-major</em> distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

5 0
2 years ago
Can someone PLEASE tell me the answer
Kryger [21]

Answer:

the answer is C 36

Step-by-step explanation:

7 0
3 years ago
What number is 30% of 68?
natka813 [3]
30%of 68 = 30/100*68= 3*68/10=204/10=20.4
6 0
3 years ago
Read 2 more answers
What are the first two steps to solve this equation 4(2x - 3) = 1
Alja [10]

Answer:

x=13/8

Step-by-step explanation:

8x-12=1

8x=13

x=13/8

7 0
2 years ago
Read 2 more answers
What is the perimeter of Triangle XYZ?
Svet_ta [14]

Answer:

36

Step-by-step explanation:

From the diagram, the  following is true;

AY = YB = 7

BZ = ZC = 6

XC = XA = 5

perimeter of the triangle is the sum of all the sides

Hence ;

Perimeter = AY+YB+BZ+ZC+XC+XA

Perimeter of the triangle = 7+7+6+6+5+5

Perimeter of the triangle = 36

hence the perimeter of the triangle is 36

7 0
3 years ago
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