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Morgarella [4.7K]

3 years ago

10

Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system? (2

points)
No Solutions
Infinite Solutions
(3.2)
(9,2)

1 answer:

Aneli [31]3 years ago

4 0

Answer:

No solutions

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

Find the equation of the directrix of the parabola x2=+/- 12y and y2=+/- 12x

PIT_PIT [208]

Answer:

x^2 = 12 y equation of the directrix y=-3
x^2 = -12 y equation of directrix y= 3
y^2 = 12 x equation of directrix x=-3
y^2 = -12 x equation of directrix x= 3

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

x^2 = 12 y
x^2 = -12 y
y^2 = 12 x
y^2 = -12 x

For each part the value of directrix will be different.

For x² = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x² = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y² = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y² = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

5 0

3 years ago

How can knowing how to represent proportional relationships in different ways be useful to solving problems

Anna35 [415]

Answer:

appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

$\dfrac{A}{B}=\dfrac{C}{D}$

is equivalent to the equation obtained by "cross-multiplying:"

AD = BC

This equation can be written as proportions in 3 other ways:

$\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}$

Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

a) put the unknown quantity in the numerator

b) give that unknown quantity a denominator of 1, if possible.

__

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

<u>Example</u>:

x/4 = 3/2

Usual method:

2x = 4·3

x = 12/2 = 6

Multiplying by the denominator:

x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

__

<u>Example 2</u>:

x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

x/1 = 4/2 . . . . . . written with 1 in the denominator

x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

8 0

3 years ago