4 Americans can arrange themselves in 4! ways.similarly ,3 Frenchmen can arrange themselves in 3! ways.3 Englishmen can arrange themselves in 3! ways.now these 3 groups of same nationality people can be arranged among themselves in 3! ways.so total number of ways = 3!4!3!3!

6 0

3 years ago

What adds up to -54 and multiplies to -16

Kaylis [27]

X + y = -54
xy = -16

$xy = -16$
$\frac{xy}{x} = \frac[-16}{x}$
$y = \frac{-16}{x}$

$x + y = -54$
$x + \frac{-16}{x} = -54$
$\frac{x^{2}}{x} + \frac{-16}{x} = -54$
$\frac{x^{2} - 16}{x} = -54$
$x^{2} - 16 = -54x$
$x^{2} + 54x - 16 = 0$
$x = \frac{-(54) \± \sqrt{(54)^{2} - 4(1)(-16)}}{2(1)}$
$x = \frac{-54 \± \sqrt{2916 + 64}}{2}$
$x = \frac{-54 \± \sqrt{2980}}{2}$
$x = \frac{-54 \± 59.6}{2}$
$x = -27 \± 29.8$
$x = -27 + 29.8$ $or$ $x = -27 - 29.8$
$x = 2.8$ $or$ $x = 56.8$

x + y = -54
  2.8 + y = -54
- 2.8 - 2.8
y = -56.8
(x, y) = (2.8, -56.8)

or

  x + y = -54
  -56.8 + y = -54
+ 56.8 + 56.8
y = 2.8
  (x, y) = (-56.8, 2.8)

The two numbers that add up to -54 and multiply to -16 are -56.8 and 2.8.

8 0

3 years ago

1.The coordinates of the vertices of △RST are R(−4, −1) , S(−1, −1) , and T(−4, −2) .

Tju [1.3M]

RS points east; R'S' points north, so there has been a rotation 90° CCW.

After that rotation, point S would be at (1, -1). It is actually at (1, 1), so has been shifted 2 units upward.

A sequence that does the desired mapping is

c. rotation of 90° CCW about the origin
b. translation 2 units up

8 0

4 years ago