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vodka [1.7K]
4 years ago
7

Find the standard form of the equation of the parabola with the given characteristics

Mathematics
1 answer:
lord [1]4 years ago
5 0

Answer:

Step-by-step explanation:

The standard equation of a parabola is

y² = 4ax

where, a is the focus,

The coordinates of the centre of parabola is (0,0)

coordinates of focus is (a, 0)

It is symmteric about the x axis

the equation of directrix is x = -a.

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Describe how to convert from vertex form to standard form. (10 points
Anton [14]

Answer:

  "simplify" it

Step-by-step explanation:

To convert from vertex form to standard form for a quadratic, eliminate parentheses and collect terms. In short, "simplify" it.

7 0
3 years ago
PLEASE HELP I WILL GIVE A LOT OF POINTS!
vazorg [7]

9514 1404 393

Answer:

  (2.27, 0.96)

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.

For example, the line perpendicular to side AC can be found as ...

  (∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)

  ∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)

For side AC, we want the point to be B(4, 5), so the equation is ...

  7(x -4) -3(y -5) = 0

  7x -3y -13 = 0

Similarly, the altitude to side AB can be written as ...

  (∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)

  8(x -3) +3(y +1) = 0

  8x +3y -21 = 0

__

By the "cross multiplication method", the solution to these equations is ...

  x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27

  y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96

The orthocenter is near (2.27, 0.96).

__

A graphing application confirms this result.

_____

<em>Additional information about the cross multiplication method</em>

For the general form equations ...

  • ax +by +c = 0
  • dx +ey +g = 0

The "cross multiplication method" has you write the array ...

  \begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}

and form the "cross products" in groups of four coefficients:

  D = ae -db, X = bg -ec, Y = cd -ga

Then the solution to the set of equations is ...

  1/D = x/X = y/Y   ⇒   x = X/D, y = Y/D

__

<em>Additional note</em>

Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.

3 0
3 years ago
A local television station for a city with a population of 500,000 recently conducted a poll where they invited viewers to call
Scilla [17]

Answer:

b. Invalid, because the sample may not be representative of the population.

Step-by-step explanation:

A sample of around 10% of the population is needed to be representative.

In this question:

We have a population of 500,000, and a sample of 10,000.

10,000/500,000 = 1/50 = 0.02 = 2% of the population, so not representative, and option b is correct.

8 0
2 years ago
What is the solution of the system <br> 3x + 2y =18 <br> Y= -2/3x + 12
laiz [17]

Answer:

3x + 2y =18


Y= -2/3x + 12

3x + 2(-2/3x+12) = 18

3x + (-4/3x+24) = 18

3x + -1 1/3x +24 =18

1 2/3x +24 = 18

1 2/3x = -6

5/3x = -6

x = -3.75

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Given g(x) is a linear function and passes through the points (3,2) and (5,-1),
Slav-nsk [51]

Answer:

-3/2

Step-by-step explanation:

here it goes. (-1)- (2) / (5)-(3)

7 0
3 years ago
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