All Answers 358315 Answers

there are a lot of resouces on the net.  Here is one.

Don't you know how to do synthetic division?  There are plenty of good You Tube clips on it.

thank you i get it now.

The common ratio is 3, so for the eight term you find 3^8, as the first term also 3. 3^5=6561.

3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3 ⁸  =__________________   ( it is NOT a common FRACTION)

Thanks for your responses, melody. I like the division of the 9x9 dimensioned one into 5 pieces. 

An additional constraint that is implied is that the small square cannot be divided. It *should* be possible to solve, dividing the 9x9 dimensioned square into exactly four sections!

Does anyone have any ideas? (Note that you do NOT need to dissect using lines parallel to the axes. You may very well use diagonals and slanted lines to form triangles, trapezoids, parallelograms, and more!)

Much obliged,

Attq

The altitude to the hypotenuse will divide the original triangle into two isosceles right triangles.

Since the altitude is 4, the base of each of these two new triangles will also be 4, making the base of 

the original triangle 8.

Area  =  1/2 x 8 x 4  =  16

Let  z = a + bi

Then:

1)  |z - 1|  =  | (a + bi) - 1 |  =  | (a - 1) + bi |  =  sqrt( (a - 1)² + (b)² )

2)  |z + 3|  =  | (a + bi) + 3 |  =  | (a + 3) + bi |  =  sqrt( (a + 3)² + b² )

3)  |z - i|  =  | (a + bi) - i |  =  | a + (b - 1)i |  =  sqrt( (a)² + (b - 1)² }

Setting 1) and 2) equal to each other:

     sqrt( (a - 1)² + (b)² )  =  sqrt( (a + 3)² + b² )     --->    (a - 1)² + b²   =   (a + 3)² + b²  

        --->   a² - 2a + 1 + b²  =  a² + 6a + 9 + b²     --->     -8a  =  8     --->     a = -1

Setting 1) and 3) equal to each other:

     sqrt( (a - 1)² + (b)² )  =  sqrt( (a)² + (b - 1)² }     --->    (a - 1)² + (b)²  =  a² + (b - 1)²

       --->     a² - 2a + 1 + b²  =  a² + b² - 2b + 1     --->     a  =  b     --->     b = -1

Is there another answer?  

 |z - 3| = |z + i| = |z - 1 - 2i|.

let z= a+bi

 \(|a+bi - 3| = |a+bi + i| = |a+bi - 1 - 2i| \\  |(a-3)+bi| = |a+(b+1)i| = | (a -1)+(b - 2)i |\\ (a-3)^2+b^2 = a^2+(b+1)^2 = (a-1)^2+(b-2)^2\\ a^2-6a+9+b^2=a^2+b^2+2b+1=a^2-2a+1+b^2-4b+4\\ -6a+9=2b+1=-2a+1-4b+4\\ -6a+8=2b=-2a-4b+4\\ -3a+4=b=-a-2b+2\\~\\ b=-3a+4\\so\\ -3a+4=-a-2(-3a+4)+2\\ -3a+4=-a+6a-8+2\\ -3a+4=5a-6\\ -8a=-10\\ a=1.25\\ b=-3a+4=-3.75+4=0.25\\ z=\frac{5+i}{4} \)

Latex:

|a+bi - 3| = |a+bi + i| = |a+bi - 1 - 2i| \\
 |(a-3)+bi| = |a+(b+1)i| = | (a -1)+(b - 2)i |\\

(a-3)^2+b^2 = a^2+(b+1)^2 = (a-1)^2+(b-2)^2\\
a^2-6a+9+b^2=a^2+b^2+2b+1=a^2-2a+1+b^2-4b+4\\
-6a+9=2b+1=-2a+1-4b+4\\
-6a+8=2b=-2a-4b+4\\
-3a+4=b=-a-2b+2\\~\\
b=-3a+4\\so\\
-3a+4=-a-2(-3a+4)+2\\
-3a+4=-a+6a-8+2\\
-3a+4=5a-6\\
-8a=-10\\
a=1.25\\
b=-3a+4=-3.75+4=0.25\\
z=\frac{5+i}{4}

I answered but i have decided to hide my answer as this is obviously a school competition homework question.

If BD both bisects AC and angle(B), then triangle(ABC) is an isosceles triangle with AB = BC.

Since AB = AC, AB = AC = BC, making the triangle equilateral.

Therefore, angle(A) = 60^o.

Since 44 inches of wire is 2·22 inches of wire, the cost will be 2·66 cents = 132 cents, or $1.32.

Let  A = 1,  B = 2, and  C = 3.

A₆ + B₆  =  C₆     --->     1₆ + 2₆  =  3₆

B₆ + B₆ + C₆  =  AA₆     --->     2₆ + 2₆ + 3₆  =  11₆  

ABC₆  =  123₆     which, in base ten, is:  1·6² + 2·6 + 3  =  51

Line 1:  5x + 8y  =  -9

                     8y  =  -5x - 9

                       y  =  (-5/8)x - 9/8

              The slope of this line is  -5/8.

               This means that the slope of any line perpendicular to it is 8/5.

Line 2:  point = (10, -12)     slope = 8/5

             Point-slope form for a line:  y - y₁  =  m(x - x₁)

                                                        y - -12  =  (8/5)(x - 10)

                                                        y + 12  =  (8/5)(x - 10)

                                                       5y + 60  =  8x - 80

                                                               5y  =  8x - 140

                                                                 y  =  (8/5)x - 28

Can you finish?

12y² - 65y + 42 - 25y  =  12y² - 90y + 42  =  (2y - 14)(6y - 3)

Can you finish? 

Thanks!

There are 16 possibilities, 4 for the numerator and 4 for the denominator.

But, some of these are duplicates; for example:  4/2  =  2/1

I would suggest that you write out the entire list and remove the duplicates.

The formula for the sum of an arithmetic series is:  Sum  =  n(f + l)/2

n = number of terms = 28

f = first term = 25

l = last term =  not yet known

The formula for the last term of an arithmetic series is:  l = f + (n-1)d

f = first term = 25

n = number of terms = 28

d = common difference = 6

----->     l  =  25 + (28 - 1)·6  =  187

Sum  =  28(25 + 187)/2  =  answer ...

lol i feel bad for the rhino

He was composing his answer while this other kid came and typed it

he might be wrong for all i know

\(a_n=25+6\left(n-1\right)\)

The divisors of 5 are 1 and 5. The divisors of 4 are 1, 2, and 4.

Including both the positive and negative possibilities:  1/1,  -1/1,  5/1,  -5/1,  1/2,  -1/2,  5/2,  -5/2,  1/4,  -1/4,  5/4,  -5/4

There are 12 possibilities.