geno3141

All letters have rotational symmetry if you allow a rotation of 360^o.

The only letter in that group of have a rotation less than 360^o is the letter Z, which has rotational symmetry of 180^o.

The formula for slope:  m  =  (y₂ - y₁) / (x₂ - x₁)

For this problem  (x₁, y₁)  =  (1, -19)   --->   x₁ = 1,  y₁ = -19

                            (x₂, y₂)  =  (-2, -7)   --->   x₂ = -2,  y₂ = -7

Placing these numbers into the formula:  m  =  (-7 - -19) / (-2 - 1)   --->   m  =  12 / -3   --->   m  =  -4

9x + 9  =  45 + 5x

First, get all the variables to one side by subtracting 5x from both sides:

9x - 5x + 9  =  45 + 5x - 5x

4x + 9  =  45

Now, get all numbers to the other side by subtracting 9 from both sides:

4x + 9 - 9  =  45 - 9

4x  =  36

Finally, divide both sides by 4:

4x/4  =  36/4

x  =  9

-2(7 - n) + 4

First:  use the distributive property:  -2(7 - n)  =  (-2)(7) - (-2)(n)  =  -14 + 2n:

-14 + 2n + 4

Now:  add like terms:  -14 + 4  =  -10

-10 + 2n

Factored:

3x² - 21x  =  3x(x - 7)

6x + 8  =  2(3x + 4)

x³ - 14x² + 49  =  <can't be factored>

15x + 20  =  5(x + 4)

To divide fractions, multiply by the reciprocal, so:

=  [3x(x - 7)] / [2(3x + 4)]  times  [5(x + 4] / [ x³ - 14x² + 49 ]

=  [15x(x - 7)(x +4)] / [2(3x + 4)(x³ - 14x² + 49)]

   ...   nothing cancels  ...

One way to find the area of a parallelogram is the use the formula:  Area  =  (a)(b)(sin(C))

where  a  and  b  are the lengths of two adjacent sides and  C  is the size of the included angle.

Since a rhombus is a parallelogram:  a = 6,  b = 6,  and  C = 120^o .

Area  =  (6)(6)(sin(120))  =  31.18  (approximately)

Since all 4 sides are equal, this is a rhombus.

The diagonals of a rhombus intersect at their midpoint.

If the midpoint is labeled "X", then AX = 7  and  BX = 24.

Also, the diagonals of a rhombus are perpendicular to each other; this means that triangle AXB is a right triangle with a right angle at corner X.

Using the Pythagorean Theorem:  AX² + XB²  = AB²     --->     (7)² + (24)²  =  (AB)²      --->     49 + 576  =  (AB)²

     --->     625  =  (AB)²     --->     AB = 25

Since all four sides are equal, the perimeter  =  4 x 25  =  100

To change a graph into the inequality, write

the left-hand value first 

then either a "<" sign (if the left-hand endpoint circle is open) or a "<=" sign (if the left-hand endpoint circle is filled in)

then an "x"

finally either a "<" sign (if the right-hand endpoint circle is open) or a "<=" sign (if the right-hand endpoint is filled in).

Thus, the answer is C)

Another way to do this is to place the original problem in the form:  ax² + bx + c  =  0

and then find the value of the discriminant:  b² - 4ac  (the portion under the square root sign in the quadratic formula).

If this value is zero, there will be one answer; if this value is positive, there will be two (unequal) real answers; if this value is negative there will be two (unequal) imaginary answers.

5  =  17x² - 200x     --->     subtract 5 from both sides and exchange the sides    --->     17x² - 200x - 5  =  0

So,  a = 17,   b = -200,  and  c = -5

b² - 4ac  =  (-200)² - 4(17)(-5)  =  40340

Since this value is positive, there will be two, unequal, real answer.

Add down the columns, you will get:  3x²  =  432

Divide by 3:                                          x²  =  144

Find the square root:                             x  =  12  or  x  =  -12

If  x = 12:  substitute into the first equation:  (12)² + y²  =  289

                                                                       144 + y²  =  289

                                                                                 y²  =  145

To solve this, find the square root; but the instructions say that you should find b, which is this number:  145.

The answer is (B)  145.