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kvasek [131]
2 years ago
7

Write an equation in slope-intercept form for the line with slope -3/2 and y-intercept 5.

Mathematics
2 answers:
Marina CMI [18]2 years ago
7 0

Answer:

y = -3/2x + 5 totally

Step-by-step explanation:

zhenek [66]2 years ago
4 0

Answer: y = -3/2x + 5

Step-by-step explanation:

<u>Slope-intercept form: y = mx + b</u>

  • m = slope = -3/2
  • b = y-intercept = 5

y = -3/2x + 5

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Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i
serious [3.7K]

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0
2 years ago
I will give brainliest
pshichka [43]

Answer:

They studied for a little more than an our. A

Step-by-step explanation:

Because if you multiply 4 on 2/3 you get 8/12, then add 8/12 and 7/12 together to get 15/12 simplified 1  3/12.

3 0
3 years ago
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How can I determine the question I circled? I’m stuck, please help (look at photo)
Semenov [28]

i dont really know but im guessing use ratios. like 4:total volunteers

or something like that

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3 years ago
Please help me with number 1 to 6 please
Ugo [173]
1.) 144
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3 years ago
Adding parentheses and brackets
eduard

Answer:

what is the question

Step-by-step explanation:

5 0
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