Answer:
The equation
represents the equation of the parabola with focus (-3, 3) and directrix y = 7.
Step-by-step explanation:
To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).
Using the distance formula
, we find that the distance between (x, y) is

and the distance between (x, y) and the directrix y = 7 is
.
On the parabola, these distances are equal so, we solve for y:

The answer would be $175
Multiply the most by the number of tickets
Answer:
Area of the triangle is 10 square units
Step-by-step explanation:
Recall that the formula for the area of a triangle is: "base x height / 2", and in this case, we can consider the triangle's base as the segment that joins the vertices (5, 4) and (5, 8) which gives a segment length of 4 units. The height of the triangle is then the distance between the third vertex (0,7) and the base, which is exactly 5 units. Then the area becomes:
Area = 4 x 5 / 2 = 10 square units.
Answer:
B. The maximum occurs at the function's x-intercept.
Step-by-step explanation:
Given table:

From inspection of the table, we can see that:
and
This indicates <u>symmetry</u>.
The line of symmetry is the mid-point between the two x-values.
Therefore, the <u>line of symmetry</u> is x = -4
The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a <u>maximum</u>.
As the y-value of the vertex is 0, the maximum occurs at the function's <u>x-intercept</u>.
Answer:
Let x be the percentage score he got in fifth test,
According to the question,
His score in first, second, third and fourth test are 80%, 84%, 76% and 77% respectively,
Thus, the average of his total score in the five test,
= 
But, Again according to the question,
The average of the five grades as greater than or equal to 80%
That is,

⇒ 
⇒ 
⇒ 
Thus, the least score he can get in the fifth test is 83.