The answer is -16 - 10i.
Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)
Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²
Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i
Conditional probability formula is:P ( A and B ) = P ( A ) · P ( B / A )0.46 = P ( A ) · 0.31P ( A ) = 0.46 : 0.31P ( A ) = 1.48And this is impossible because 0 ≤ P ( A ) ≤ 1The student obviously made a mistake.
Answer:
To convert 1 meter into yards
Using the given facts : 100 centimeters in a meter, 2.54 centimeters in an inch, 12 inches in a foot, and 3 feet in a yard.
we can write these as;
and
1 ft = 12 inches
3 ft = 
Since,
1 inches = 2.54 cm
36 inches = 91.44 cm
Also,
1 m = 100 cm
or
1 cm = 
then;
91.44 cm = 
⇒ 1 yards = 0.9144 m
Divide both sides by 0.9144 we get;
1 meter = 
yards.
Therefore, the answer is, 1 m = 1.1 yards (nearest to tenth)
First transformation.
Duadrilateral ABCD has vertices with such coordinates:
- A(15,10);
- B(15,20);
- C(20,15);
- D(20,5).
Apply a rotation by 90°counterclockwise around point A to this quadrilateral, then
- A(15,10)→A'(15,10);
- B(15,20)→B'(5,10);
- C(20,15)→C'(10,15);
- D(20,5)→D'(20,15).
Second transformation.
1. A reflection across the y axis has a rule:
(x,y)→(-x,y).
Then
- A'(15,10)→A''(-15,10);
- B'(5,10)→B''(-5,10);
- C'(10,15)→C''(-10,15);
- D'(20,15)→D''(-20,15).
2. A translation 20 units down has a rule:
(x,y)→(x,y-20).
Then
- A''(-15,10)→G(-15,-10);
- B''(-5,10)→H(-5,-10);
- C''(-10,15)→I(-10,-5);
- D''(-20,15)→J(-20,-5).
Answer: first blank -B, second blank - B.
