Answer:
the Associative Property
Step-by-step explanation:
Notice that the ORDER doesn't change -- a, b, c on both sides. But the GROUPING changes.
Example:
3 + (4 + 5) = (3 + 4) + 5
3 + 9 = 7 + 5
12 = 12
Subtraction does NOT behave this way!
8 - (7 - 1) = 8 - 6 = 2
(8 - 7) - 1 = 1 - 1 = 0
It matters who you associate with! :-)
Answer:
x = 9, Angles are 54°
Step-by-step explanation:
First, we need to find x:
7x-9 = 5x+9
+9 +9
7x = 5x+18
-5x -5x
2x = 18
x = 9
Now, we plug our x value in to find our angles.
5(9) + 9 = 54
Angle B = 54°
7(9) - 9 = 54°
Angle E = 54°
(angles are the same due to AAA property)
Answer:
3/10
Step-by-step explanation:
Multiples of 3: 3,6,9,12,15,18
There are 6 in the numbers 1-20
P(multiple of 3) = number of "multiples of 3" / total
= 6/20
=3/10
Answer:
the original volume is lesser than the new volume by 242.47 in³
Step-by-step explanation:
Volume of a cone is;
V = ⅓πr²h
Where;
r is radius
h is height
For the original chamber;
r = 5.7/2 = 2.85 inches
h = 12 inches
Volume of this original chamber is;
V_orig = ⅓ × π × 2.85² × 12
V_orig = 102.02 in³
In the new design, the chamber is scaled by a factor of 1.5.
Thus;
r_new = 2.85 × 1.5 = 4.275 inches
h_new = 12 × 1.5 = 18 inches
V_new = ⅓ × π × 4.275² × 18
V_new = 344.49 inch³
V_new - V_orig = 344.49 - 102.02 =
Thus, the original volume is lesser than the new volume by 242.47 in³
