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4 years ago

Rewrite the equation by completing the square x^2+12x-13=0

Mathematics

1 answer:

mote1985 [20]4 years ago

3 0

Answer:

$(x+6)^{2}-49$

Step-by-step explanation:

In order to complete the square, you want to convert a quadratic from the form -

$ax^{2}+bx+c$

to the form-

$a(x+d)^{2}+e=0$

If you're in a hurry,

$d=\frac{b}{2a}\\e=c-\frac{b^{2}}{4a}$

and you can convert from there.

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Hellppp 70 pointsss

dimulka [17.4K]

y=a.(X-x1)(X-x2)

x1 and x2 are x-intercepts

x1=-3

x2=1

other points: (-1,8) and (0,5)

y=a.(x+3).(x-1)

a=-2

f(x)= -2.(x+3)(x-1)

7 0

3 years ago

Write the equation of the conic section satisfying the given conditions. focus at the pole, e = 3/4, horizontal directrix 2 unit

hjlf

Answer:

The equation in the polar form is;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$

Step-by-step explanation:

e = 3/4 > 1, we have an hyperbola

The polar equation of a conic is of the form;

For vertical directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}$

For horizontal directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}$

Where;

k = Distance from the focus to the directrix = 2

We have;

$r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

$r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

Which gives the equation in the polar form as follows;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$ .

8 0

3 years ago

Which matrix represents the system of equations below? {-2x-7y=3 {7x-6y=12

bekas [8.4K]

Answer:

$\left[\begin{array}{ccc}-2&-7\\7&-6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\12\\\end{array}\right]$

3 0

3 years ago

HELP PLS The function of F is defined by f(x)=x+2 find F(n-4)

GalinKa [24]

Answer:

Step-by-step explanation:

f(n - 4)= n - 4 + 2 = n - 2

7 0

2 years ago

Gabriel is designing equally sized horse stalls that are each in the shape of a rectangular prism. Each stall must be 9 feet hig

ElenaW [278]

Total Volume is given as 1080 cubic feet.

Height is given as 9 feet.

Length is 2 feet longer than the width, so Length = x+2

If the stall is 10 feet wide, then the length would be 10 +2 = 12 feet.

The volume for that would be 10 x 12 x 9 = 1080 cubic feet.

Yes it is possible for the width to be 10 feet.

4 0

3 years ago

Read 2 more answers