Complete question is;
Which of the following can be reduced to a single number in standard form?
A) 3√3 + 5√8
B) 2√5 + 5√45
C) √7 + √9
D) 4√2 + 3√6
Answer:
Only option B) 2√5 + 5√45 can be reduced to a single number
Explanation:
A) For 3√3 + 5√8;
Let's simplify it to get;
3√3 + 5√(4 × 2)
From this, we get;
3√3 + (5 × 2)√2 = 3√3 + 10√2
This is 2 numbers and not a single number. Thus it can't be reduced to a single number in standard form.
B) 2√5 + 5√45
Simplifying to get;
2√5 + 5√(9 × 5)
This gives;
2√5 + (5 × 3)√5 = 2√5 + 15√5
Adding the surds gives;
17√5.
This is a single number and thus can be reduced to a single number
C) For √7 + √9
Simplifying, to get;
√7 + 3.
This is 2 numbers and not a single number. Thus it can't be reduced to a single number in standard form.
D) 4√2 + 3√6
Thus can't be simplified further because both numbers inside the square root don't have factors that are perfect squares.
Thus, it remains 2 numbers and not a single number and can't be reduced to a single number in standard form.
Answer:
138.46 ft
Explanation:
When the ball is dropped until the moment it hits the water, the ball moves in a uniform acceleration motion. Therefore, the equation that describes the movement of the ball is:
Where X is the distance that the ball has fallen at a time t. 
is the initial velocity, which is 0 ft/s as the ball was simply dropped. 
is the initial position, we will say that this value is 0 in the position where the ball was dropped for simplicity, and it increases as the ball is falling. Now, we replace x with 16 feets and solves for t:
The velocity that the ball will have at the moment the ball that the ball hits the water will be:
The time that will take the ball to reach the bottom from the top of the lake will be t = 5.3s - 1s = 4.3s. And as the ball will travel with constant velocity equal to 32.2 ft/s^2, the depth of the lake will be:
The correct option is <u>D</u>.
Qualitative observations are observations that are made using our senses of sight, hearing, smell, taste and feel. These observations do not involve numbers or measurements of any kind.
The student's observations regarding the squirrel as is mentioned in options A, B and C involve measurements. Therefore these are not qualitative observations.
Option D, however, is made on the basis of sight, where the student observes the squirrel moving in a zigzag manner.
Therefore, of all the three observations, the student's observation that the squirrel ran in a zigzag pattern is the qualitative observation.
