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Levart [38]
3 years ago
13

Solve for c: 2(4c-7) is greater than or equal to 8(c-3)

Mathematics
1 answer:
loris [4]3 years ago
3 0

2(4c-7)\geq8(c-3)\ \ \ \ |\text{use distributive property}\\\\(2)(4c)-(2)(7)\geq(8)(c)-(8)(3)\\\\8c-14\geq8c-24\ \ \ \ |-8c\\\\-14\geq-24\ \ \ TRUE\\\\\text{therefore your answer is}\ x\in\mathbb{R}\ (all\ real\ numbers)

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Step-by-step explanation:

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If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),
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Step-by-step explanation:

<u>Step 1:  Solve using the first point</u>

<em>(2, 28)</em>

28 = a(2)^3 + b(2)^2 + c(2) + d

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<u>Step 2:  Solve using the second point</u>

<em>(-1, -5)</em>

-5 = a(-1)^3 + b(-1)^2 + c(-1) + d

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<u>Step 3:  Solve using the third point</u>

<em>(4, 220)</em>

220 = a(4)^3 + b(4)^2 + c(4) + d

220 = 64a + 16b + 4c + d

<u>Step 4:  Solve using the fourth point</u>

<em>(-2, -20)</em>

-20 = a(-2)^3 + b(-2)^2 + c(-2) + d

-20 = -8a + 4b - 2c + d

<u>Step 5:  Combine the first and fourth equations</u>

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8 = 8b + 2d

8 - 8b = 8b - 8b + 2d

(8 -8b)/2 = 2d/2

4 - 4b = d

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-5 + 5 = -a + b - c + d + 5

0 + c = -a + b - c + c + d + 5

c = -a + b + d + 5

<u>Step 7:  Substitute d with the stuff we got in step 5</u>

c = -a + b + (4 - 4b) + 5

c = -a + b + 4 - 4b + 5

c = -a - 3b + 9

<u>Step 8:  Substitute d and c into the first equation</u>

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6 / 6 = (6a - 6b) / 6

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1 + b = a

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220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)

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a = b + 1

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c = 0

<u>Step 12:  Find d using b = 2</u>

d = 4 - 4b

d = 4 - 4(2)

d = 4 - 8

d = -4

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