a) To find the volume of a cube, you cube the side length.
So, that will be V = 9/2³ = 729/8 in³.
b) To find the volume of a rectangular prism, you multiply the length by the width by the height.
So, that is V = 18 * 9 * 9/2 = 729 in³.
c) To find how many times the smaller box can go into the larger one, you divide the larger one's volume over the smaller one's.
That is <em>729/(729/8) = 729*8/729 = </em><em>8 boxes</em><em>.</em>
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
given the 2 equations
x + y = 4 → (1)
y = 3x → (2)
Substitute y = 3x into (1)
x + 3x = 4
4x = 4 ( divide both sides by 4 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = 3 × 1 = 3
solution is (1, 3 )
The [# of sides (n) - 2] × 180° is the formula for the sum of interior angles (IAs) in a regular polygon. And so that sum of all IAs ÷ IA = n
Each central angle is opposite of one side.
And all of the central angles add up to 360°, therefore 35×n = 360
35n/35 = 360/35 = 10.29, but we need to verify: each 35° central angle forms an isosceles triangle with a side of the polygon, and each opposite angle (x) is 1/2 of an interior angle. All 3 angles of a triangle sum to 180°, and 2 angles (x) are equal in an isosceles, so
x + x + 35 = 180
2x + 35 = 180
2x = 145
2x/2 = 145/2
x = 72.5
And each x is 1/2 of an interior angle (IA), therefore 2x = IS
IA = 2 (72.5) = 145
(n - 2) × 180° = IA × n
(n - 2) × 180° = 145n
(n - 2) × 180°÷180 = 145n/180
n - 2 = 29n/36
36n/36 - 72-36 = 29n/36
(36n/36 - 72-36)×36 = (29n/36)×36
36n - 72 = 29n
36n - 29n = 72
7n = 72
7n/7 = 72/7
n = 10.29
Are you sure the central angle was 35, not 36°?? Because we don't get a whole number as the # of sides. How can we have 0.29 of a side?
10 square units.
The quadrilateral is 2 x 2 = 4
Triangle a 2 x 2 = 4; divided by 2 = 2
Triangle b 4 x 2 = 8; divided by 2 4
4 + 2 + 4 = 10 units squared
