What is a solution to (x-3)(x+9)=-27

-6

0

Step-by-step explanation:

By observation we can see one solution is x=0 since this will give us

(0-3)(0+9)=(-3)(9)=-27 which is the result on the right hand side.

Now this is a quadratic equation so it should have another solution. This one doesn't seem as obvious to me.

The goal normally is to get 0 on side and factor if possible or use quadratic formula.  There is also completing the square.

So I'm going to multiply (x-3)(x+9) using foil.

First: x(x)=x^2

Outer: x(9)=9x

Inner: -3(x)=-3x

Last: -3(9)=-27

Combine like terms:

x^2+6x-27

So the equation is:

x^2+6x-27=-27

Add 27 on both sides:

x^2+6x+0=0

x^2+6x=0

Factor x out:

x(x+6)=0

In order for these equation to be true one of the left hand factors need to be 0.

Let's find when x is 0, well that is when x=0.

Let's find when x+6 is 0.

x+6=0 can be solved by subtracting 6 on both sides:

x=-6

The solutions are -6 and 0.

We already checked x=0.

Let's check x=-6:

Plugging in -6 where x is in the given equation:

(-6-3)(-6+9)

(-9)(3)

-27 which is the same as right hand side.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.