A rectangular box has dimensions 12 in, 4 in, and 4 in. If the first two dimensions is decreased and the last dimension is increased by the same amount, a second box is formed, and its volume is five-eight of the volume of the first box. Determine the dimensions of the second box.
1. Dimensions of the first box.
2. Volume of the first box.
3. Volume of the second box.
(Hint: five-eighths of the volume of the first box)
4. First dimension of the second box.
(Note: use variables to indicate decrease)
5. Second dimension of the second box.
(Note: use variables to indicate decrease)
6. Third dimension of the second box.
(Note: use variables to indicate increase)
7. Working equation for the dimension of the second box.
8. Dimensions of the second box. (Show complete solution)
Answer Box
(12 – x) in
(x + 4) in
10 in x 2 in x 4 in
14 in³
(x – 4) in (4 – x) in
(12-x) (4–x) (4+x)= 192
120 in³
(x-12) (x–4) (x+4)= 20
20 in³
192 in³
(x – 12) in
12 in x 4 in x 4 in 16 in³
(12-x) (4–x) (4+x)= 120
(4 + x) in
NONSENSE=REPORT
CORRECT ANSWER=BRAINLIEST
1. Dimensions of the first box.
2. Volume of the first box.
3. Volume of the second box.
(Hint: five-eighths of the volume of the first box)
4. First dimension of the second box.
(Note: use variables to indicate decrease)
5. Second dimension of the second box.
(Note: use variables to indicate decrease)
6. Third dimension of the second box.
(Note: use variables to indicate increase)
7. Working equation for the dimension of the second box.
8. Dimensions of the second box. (Show complete solution)
Answer Box
(12 – x) in
(x + 4) in
10 in x 2 in x 4 in
14 in³
(x – 4) in (4 – x) in
(12-x) (4–x) (4+x)= 192
120 in³
(x-12) (x–4) (x+4)= 20
20 in³
192 in³
(x – 12) in
12 in x 4 in x 4 in 16 in³
(12-x) (4–x) (4+x)= 120
(4 + x) in
NONSENSE=REPORT
CORRECT ANSWER=BRAINLIEST
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Answer:
1.) 12 in x 4 in x 4 in
2.) 192 in³
3.) 120 in³
4.) (12 – x) in
5.) (4 - x) in
6.) (4 + x) in
7.) (12-x) (4–x) (4+x)= 120
8.) 10 in x 2 in x 6 in
Step-by-step explanation:
(12-x) (4-x)(4+x) = 120
(12-x) (16-x²) = 120
192 - 12x² - 16x + x
= 120
x
- 12x² - 16x = -72
say x =2
(2)
- 12 (2)² - 16(2) = -72
8 - 48 - 32 = -72
-72 = -72, ok
therefore, the dimension are
(12-x) = 12-2 = 10 in
(4–x) = 4-2 = 2 in
(4+x) = 4+2 = 6 in