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3 years ago

EASY 50 POINTS AND CROWN

Mathematics

2 answers:

Anna11 [10]3 years ago

8 0

The answer for leading coefficient should be 1.

KIM [24]3 years ago

7 0

Answer:

i agree 1

Step-by-step explanation:

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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]

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

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

Aiden borrows a book from a public library. He read a few pages on day one. On day two, he reads twice the number of pages than

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

6 0

2 years ago

Solve the equation <img src="https://tex.z-dn.net/?f=8x%5E2%3D-36" id="TexFormula1" title="8x^2=-36" alt="8x^2=-36" align="absmi

chubhunter [2.5K]

Answer: 4(2x²+9) or $i\frac{3\sqrt{2} }{2}$

Step-by-step explanation:

To solve the equation by factoring, we want to set the equation to zero. In order to have the equation equal to zero, we want to add both sides by 36.

8x²=-36 [add both sides by 36]

8x²+36=0

When it comes to factoring, we want to pull out numbers or variables that are common in each term.

8x²+36=0 [take out a 4 in each term]

4(2x²+9)=0

It may seem that 2x²+9 can be factored further, it actually can't. This tells us that the factored form of the equation is 4(2x²+9)=0.

To solve the equation, we want to find the value of x. We already know the graph does not cross the x-axis because the y-intercept or vertex is (0,9).

4(2x²+9)=0 [divide both sides by 4]

2x²+9=0 [subtract both sides by 9]

2x²=-9 [divide both sides by 2]

x²=-9/2 [square root both sides]

$x=\sqrt{-\frac{9}{2} }$ or $x=i\frac{3\sqrt{2} }{2}$

6 0

3 years ago

Read 2 more answers

Someone please help

OLEGan [10]

Answer:

e= -2

Step-by-step explanation:

1) distribute so you get 6+0.75e=2-1.25e

2) move the variable to one side so you get 6+2e=2

3) subtract the 6: 2e=-4

4) divide by 2: e= -2

4 0

3 years ago

What is equivalent to 3 radical 8

liq [111]

Answer:

C. 8^x/3

Step-by-step explanation:

According to algebraic principles, if n is the root of a number, then that number to the power of 1/n is equal to it. This would mean that n√a = a^1/n.

This would mean that 3√8 = 8^1/3. When there is a power added to a radical expression such as this, that power will go on the denominator. So (3√8)^2 for example is equal to 8^2/3, and in your case, (3√8)^x = 8^x/3

looking back on the fact that this was added 2 days ago i dont think this helped on your quiz

6 0

3 years ago