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andrezito [222]
2 years ago
9

Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).

Mathematics
1 answer:
defon2 years ago
3 0

Answer:

y − 7 = − 6 /11 ⋅ ( x + 7 )

Step-by-step explanation:

Find the point-slope form.

Point-slope formula: y-y₁=m(x-x₁)

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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
Need help Thank you very much
Brrunno [24]

Answer:

A is right I believe

Step-by-step explanation:

a: 5x

b: 2x

c: 1/5x

d: 1/2x

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3 years ago
The radius of a circle is 1 m. Find the circumference to the nearest tenth.
soldier1979 [14.2K]

Answer:

sorry :( I need points :((((((

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3 years ago
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Help me with this problem please:)
elena-14-01-66 [18.8K]
The area of the square is 4
and the area of the triangle is 2

4+2=6

the area is 6
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Cara wants to buy a television that cost $500 including taxes to pay for the television he would use a payment plan that require
PtichkaEL [24]

Answer:

Result

brainly.com/question/22157981Step-by-step explanation:

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