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olganol [36]
3 years ago
5

7 square root of 3 end root minus 4 square root of 6 end root plus square root of 48 end root minus square root of 54

Mathematics
1 answer:
Levart [38]3 years ago
5 0
7\sqrt3-4\sqrt6+\sqrt{48}-\sqrt{54}\\\\=7\sqrt3-4\sqrt6+\sqrt{16\cdot3}-\sqrt{9\cdot6}\\\\=7\sqrt3-4\sqrt6+\sqrt{16}\cdot\sqrt3-\sqrt9\cdot\sqrt6\\\\=7\sqrt3-4\sqrt6+4\sqrt3-3\sqrt6\\\\=\boxed{11\sqrt3-7\sqrt6}
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a recipe calls 1 2/3 cups of brown sugar for the granola bars and 1 q/3 cups of brown sugar for the topping. Dara has 3 1-4 cups
sp2606 [1]

Answer:

yes, she does have enough

Step-by-step explanation:

3 1/4 - 1 1/3 - 1 2/3

=1/4

4 0
2 years ago
Samantha is making soup. To make the broth, she combines 2/3 cup of vegetable stock and 2/3 cup of chicken stock. Boiling the br
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2/3 cup + 2/3 cup = 1 1/3 cups
1 1/3 cups - 1/4 = 1 1/8 cups

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3 years ago
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
Which would be included in a probability model for rolling a cube with faces numbered 1 through 6. Select all that apply.
scoundrel [369]

Answer:

Step-by-step explanation:

8 0
3 years ago
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Sally has 3 /4 of a yard of ribbon. she uses 1/8 yard of ribbon to make each bow. does she have enough ribbon to make 7 bows?
tekilochka [14]

Answer:

No

Step-by-step explanation:

3/4 of a yard is equal to 6/8 of a yard. If Sally wants 7 ribbons, she needs at least 7/8 yards of ribbon.

3 0
3 years ago
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