Solve 7|3f + 4| = 91 for f. A. –29 or 312⁄3 B. 3 or –17⁄3 C. –3 or 17⁄3 D. –312⁄3 or 29
1 answer:
Answer:
B
Step-by-step explanation:
Given
7 | 3f + 4 | = 91 ← divide both sides by 7
| 3f + 4 | = 13
The absolute value function always returns a positive value, but the expression inside can be positive or negative. Thus there are 2 possible solutions.
Solve 3f + 4 = 13 → 3f = 13 - 4 = 9 ⇒ f = 3
Solve 3f + 4 = - 13 ⇒ 3f = - 13 - 4 = - 17 ⇒ f = -
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
f = 3 : 7| 9 + 4| = 7| 13| = 7 × 13 = 91 ← True
f = -
7 | - 17 + 4| = 7| - 13| = 7 × 13 = 91 ← True
Hence the correct solutions are B
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Answer:
Alandra can fill 60 whole cones
Step-by-step explanation:
The volume of a rectangular prism is V = L × W × H, where
- L is its length
- W is its width
- H is its height
The volume of the cone is V = π r² h, where
- r is the radius of its base
- h is its height
∵ Alandra's rectangular cake pan is 33 cm by 23 cm
∴ L = 33 cm and W = 23 cm
∵ She has enough cake batter to fill it to a depth of 3 cm.
∴ H = 3 cm
→ Find the volume of the batter using the 1st rule above
∵ V = 33 × 23 × 3
∴ V = 2277 cm³
∵ Alandra wants to pour the batter into ice cream cones
∵ She plans to fill each cone to a depth of 9 cm with a diameter of 4 cm
∴ h = 9 cm
∵ r = diameter =
(4)
∴ r = 2 cm
→ Substitute them in the 2nd rule above to find the volume of each cone
∵ V = (π) (2)² (9)
∴ V = 12π cm³
→ To find the number of cones divide the volume of the batter by
the volume of each cone
∵ Number of cones = 2277 ÷ 12π
∴ Number of cones = 60.3993
→ We will take the whole number only because we need the whole cones
∴ Alandra can fill 60 whole cones