Response:
12.
Step-by-step explanation:
We have been given a format for various numbers. Our task is to discover the missing value for our specified format.
Taking the square root of 9 and 16 results in
Moreover, it can be observed that by computing the square root of all figures on the left side of the equation and summing them, we arrive at the right side.
Upon extracting the square roots of 25 and 49 we deduce,[TAG_48]]
Therefore, the missing number in our sequence is 12.
. The 'p' component in this context refers to the distance, specifically the gap from the vertex to either the directrix or the focus. The vertex is centrally positioned between these two points, indicating the focus is located 3 units below the vertex (since the directrix is 3 units above it). Thus, we conclude that p = 3.
Substituting h and k, both being (0, 0), into the equation gives:
resulting in
and when we multiply by -1:
. This result, while not in standard format, aligns with the options provided in your equation. In conclusion:
The focus is positioned at (0, -3), affirming the first statement as correct.
The parabola is inverted, thereby rendering the second statement incorrect.
The value of p can be calculated based on the distances from the vertex to the directrix, making the third statement false.
After incorporating the values for h, k, and p, the fourth statement about the equation is validated as true.
Thus, the fifth option is incorrect.
Using the information that ∠B ≅ ∠C,
we need to demonstrate that sides AB and AC are equal.
This can be shown using a proof by contradiction.
Assume for the sake of argument that AB is not equal to AC.
This means either AB > AC or AB < AC.
Case i: If AB > AC, then according to the triangle axiom, Angle C must be greater than angle B.
However, given that Angle C = Angle B, we see that AB cannot be greater than AC.
Case ii: If AB < AC, then by the triangle axiom, Angle C would have to be less than angle B.
Since Angle C = Angle B, we conclude that AB cannot be less than AC either.
Conclusion:
Therefore, since AB cannot be either greater than or less than AC, we are left with only one possibility, which is that AB = AC.
Thus, from the fact that angle B equals angle C, we deduce that
AB = AC, and AB ≅ AC.
Answer: A container capable of holding 460 grams of oil has a volume of 500 cm³.
Step-by-step explanation:
The density of olive oil is .
An olive farmer aims to bottle 460 grams of oil.
Thus,
The mass of the oil is 460 grams.
It is understood that
Consequently, the volume of the container required for 460 grams of oil is 500 cm³.