The equation of a parabola is 12y = (x-1)^2 - 48. Identify the vertex, focus, and directix of the parabola.

Mathematics

1 answer:

dusya [7]3 years ago

8 0

Vertex is (1,-4 )The parabola is going up

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Victor wants to buy fertilizer for his yard. The yard is 45 feet by 55 feet. The direction on the bag of fertilizer say that one

frosja888 [35]

Answer: 2 bags

Step-by-step explanation:

First find the area of the yard.

The area given the units would be:

= Length * Width

= 45 * 55

= ‭2,475‬ ft²

Victor needs enough fertilizer to cover ‭2,475‬ft² but each bag covers only 1,250 ft².

The number of bags needed is therefore:

= ‭2,475‬ / 1,250

= 1.98

= 2 bags

4 0

3 years ago

A six-sided die is rolled two times. What is the theoretical fractional probability that the first number is greater than the se

Alekssandra [29.7K]

Given:

A six-sided die is rolled two times.

To find:

The theoretical fractional probability that the first number is greater than the second number.

Solution:

If a six-sided die is rolled two times, then the total possible outcomes are 36.

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

The outcomes where the first number is greater than the second number are

A = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}

So, the favorable outcomes = 15.

Now, the theoretical fractional probability that the first number is greater than the second number is

$Probability=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$