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liberstina [14]
2 years ago
14

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4. In which direction does the parabola

open? up down right left.
Mathematics
1 answer:
zaharov [31]2 years ago
7 0

The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

<h3>What is a directrix?</h3>

A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.

As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.

As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.

Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

Learn more about Directrix:

brainly.com/question/2629634

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Answer:

5

Step-by-step explanation:

Subtract 5 to both sides when plugging in 10 for y.  

10=x+5 \\-5      -5⇒5=x

8 0
3 years ago
How do i calculate? All the way to s_75. It’s so long
mina [271]

Answer:

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Step-by-step explanation:

The sum can be broken into parts that you know. Here, one of those parts is the sum of numbers 1 to n. That sum is given by n(n+1)/2.

\displaystyle S_{75}=\sum\limits_{n=1}^{75}{(67-2n)}=\sum\limits_{n=1}^{75}{67}-2\sum\limits_{n=1}^{75}{n}\\\\=75\cdot 67-2\dfrac{75(75+1)}{2}=75(67-76)\\\\=\bf{-675}

__

Another way to do this is to realize the sequence of numbers is an arithmetic sequence with a first term of 65 and a last term of 67-2·75 = -83.

The sum of an arithmetic sequence is found by multiplying the number of terms by their average value. Their average value is the average of the first and last terms.

The average value of those 75 terms is (65 +(-83))/2 = -9, so their sum is ...

  75(-9) = -675

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Answer:

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