The correct answer is: [D]: " 7.2 units" .
_______________________________________________________
Explanation:
________________________________________________________
Use the Pythagorean theorem:
a² + b² = c² ;
in which: "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle); and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle; We wish to solve for "c" ;
_______________________________________________
6² + 4² = c² ; Solve for "c" ;
↔ c² = 6² + 4² ;
= (6*6) + (4*4) ;
= 36 + 16 ;
= 52 ;
c² = 52 ;
Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ;
√(c²) = √52 ;
c = √52 ;
At this point, we know the 7² = 49 ; 8² = 64 ; so, the answer is somewhere between "7" and "8" ; yet closer to "7" ; so among the answer choices given;
The correct answer is: [D]: " 7.2 units" .
_________________________________________
However, let use a calculator:
c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
which corresponds to:
___________________________________________
Answer choice: [C]: " 7.2 units" .
___________________________________________
Answer:
The numbers 
such that the average value of 
on the interval [0, b] is equal to 8 are 
and 
.
Step-by-step explanation:
The mean value of function within a given interval is given by the following integral:
If , 
, 
and 
, then:
The roots of this polynomial are determined by the Quadratic Formula:
and .
The numbers such that the average value of on the interval [0, b] is equal to 8 are and .
<h3>
Answer: Choice A) <9,0></h3>
Explanation:
Focus on one of the points in the figure on the left. Let's say we go for the upper left corner point (-7, 4)
Notice it moves to the corresponding image point (2,4). It has shifted 9 units to the right to follow the translation rule 
. We've added 9 to the x coordinate, and the y coordinate stays the same.
This notation can be shortened to <9, 0>
In general, the notation 
is shortened to the translation vector notation 
. In this case, a = 9 and b = 0.
8.54. The last number is low so it can not round up to 5
