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4 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!

Mathematics

1 answer:

dimulka [17.4K]4 years ago

6 0

Answer:

the absolute value inequality in the form |x-b|c that has the solution set x≤−9 or x≥−5. lol jk

Step-by-step explanation:

|x−b|=c

Since we need three conditions that need to be met, we will opt for presenting three different expressions as a solution.

Case 1

One solution: x=−9

One expression that satisfies this condition is

(c = 0, b = -9 )

|x + 9|=0

|-9 + 9|=0

Case 2

All numbers such that x≤5

The solutions that satisfy this case can be found in the attached picture below, (they were obtained with a mathematical solver.)

Case 3

All numbers such that x≤-14

i pretty sure this is it.

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3 years ago

Read 2 more answers

A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin

Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

$x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2} or \frac{30-21.21 }{2}\\ = \frac{51.21 }{2} or \frac{8.79}{2}\\ = 25.605 or 4.395$

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

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3 years ago