number
l'ere. IND
1 Which of the following shows the commutative property of addition?
A. 9 +09
B. 18 x 65 65 x18 C. 6 + 25 + 25 + 6 D. 4(3 + 12) 403) + 402)
A2. What is the additive inverse of a negative integer?
A. Zero
B. Same integer C. Alway's positive D. Always negative
3. Which of the following is a TRUE statement?
A. 24 - 8 - 8 -- 24 B 4(24 + 6) = 4(6+24) C. 23 - (5-6) - (23-5) - 6 D. 12(32 x 24) - 12/24 x 32)
4. Which of the following numbers is the multiplicative identity for whole numbers?
A 3
B. 2
C. 1
D, 0
5. What is the equivalent expression when 4 x 32 is expressed in commutative property?
A. 32 x 4
B, 32 + 4
C, 32 x 1
D, 32 + 1
6. Which of the following statements shows the closure property of addition?
A. 2(3) - 3(2)
B. - 63 +92 - 29 C. 67 x 1 = 67
D. 92 + 0 = 92
7. Which of the following is the equivalent expression of 4(10 - 7) when expressed in distributive property?
A. 7(10) -4
B. 4(10) - 4(7) C. (4. 10) (4 - 7) D. (4+ 10) (4 + 7)
8 What is the result when we multiply any number by zero?
A. 2
B. 1
C. 0
D. - 1
9 Which of the following illustrates the associative property for multiplication?
A. 3(9+11) = 3(9) +3(11)
C. 15 + 6 = 6 + 15
B. (2 x 6) x 24 = 2 x (6 x 24) D. 17(45) - 45(17)
10. When (19+ 2) + 14 is expressed to associative property, which of the following expressions is this equal to?
A. 2(14 + 19) B. 19(2 + 14)
C. 19+ (2 + 14) D. (19+ 2) + (2 4 14
11197999
l'ere. IND
1 Which of the following shows the commutative property of addition?
A. 9 +09
B. 18 x 65 65 x18 C. 6 + 25 + 25 + 6 D. 4(3 + 12) 403) + 402)
A2. What is the additive inverse of a negative integer?
A. Zero
B. Same integer C. Alway's positive D. Always negative
3. Which of the following is a TRUE statement?
A. 24 - 8 - 8 -- 24 B 4(24 + 6) = 4(6+24) C. 23 - (5-6) - (23-5) - 6 D. 12(32 x 24) - 12/24 x 32)
4. Which of the following numbers is the multiplicative identity for whole numbers?
A 3
B. 2
C. 1
D, 0
5. What is the equivalent expression when 4 x 32 is expressed in commutative property?
A. 32 x 4
B, 32 + 4
C, 32 x 1
D, 32 + 1
6. Which of the following statements shows the closure property of addition?
A. 2(3) - 3(2)
B. - 63 +92 - 29 C. 67 x 1 = 67
D. 92 + 0 = 92
7. Which of the following is the equivalent expression of 4(10 - 7) when expressed in distributive property?
A. 7(10) -4
B. 4(10) - 4(7) C. (4. 10) (4 - 7) D. (4+ 10) (4 + 7)
8 What is the result when we multiply any number by zero?
A. 2
B. 1
C. 0
D. - 1
9 Which of the following illustrates the associative property for multiplication?
A. 3(9+11) = 3(9) +3(11)
C. 15 + 6 = 6 + 15
B. (2 x 6) x 24 = 2 x (6 x 24) D. 17(45) - 45(17)
10. When (19+ 2) + 14 is expressed to associative property, which of the following expressions is this equal to?
A. 2(14 + 19) B. 19(2 + 14)
C. 19+ (2 + 14) D. (19+ 2) + (2 4 14
11197999
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Answer:
W = original width of cardboard (cm)
L = original length of cardboard (cm) = 12 + W
h = height of box = 5 cm
l = length of box (cm) = L - 2*h
w = width of box = W - 2*h
v = volume of box (cm^3) = l*w*h = 1900
v = (L-2*h)(W-2*h)*h = L*W*h - 2*L*h^2 - 2*W*h^2 + 4*h^3 = 1900
h = 5 cm, insert into equation, Note: h^2 = (5 cm)^2 = 25 cm^2 and 2*25 cm^2 = 50 cm^2
and 4*h^3 = 4*125 cm^3 = 500 cm^3 , Insert with results below:
(5 cm)*L*W - (50 cm^2)*L - (50 cm^2)*W + 500 cm^3 = 1900 cm^3
or simplifying: (5 cm)*L*W - (50 cm^2)*(L + W) = 1400 cm^3
or w/o units: 5*L*W - 50*(L+W) = 1400 mathematical statement as volume
To solve for unknown L and W,
Simplify by dividing through each term by 5 cm:
L*W - (10 cm)*(L + W) = 280 cm^2 mathematical statement using 2 unknown variable
or w/o units" L*W - 10*(L+W) = 280
To find the original cardboard length (L) and width (W):
L = 12 cm + W
Substitute L = 12 cm +W and solve for W:
(12 cm + W)*W - (10 cm)*[(12 cm + W) + W] = 280 cm^2
(12 cm)*W + W^2 - 120 cm^2 + (20 cm)*W = 280 cm^2
(12 cm)*W + (20 cm)*W + W^2 = 280 cm^2 + 120 cm^2 = 400 cm^2
simplify and rearrange as standard quadratic equation and solve:
W^2 + (32 cm)*W - 400 cm^2 = 0 where: [ -b +/- √(b^2 - 4*a*c)]/2*a a = 1 b = 32 c = -400
therefore, only use positive root: W = [-32 + √( 32^2 - 4*1*(-400) )/2*1 = 9.612 cm
L = 12 cm + W = 12 cm + 9.612 cm = 21.612 cm
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