Determine the rational roots of 2x^5-11x^4+14x^3-2x^2+12x+9=0. Select all that apply.

Find the volume of a pyramid with a square base, where the perimeter of the base is

Liula [17]

Answer:

33.4 m^3

Step-by-step explanation:

The edge length of the base is 1/4 of the perimeter, so is ...

(10.3 m)/4 = 2.575 m

Then the area of the base is the square of this, or ...

B = (2.575 m)^2 = 6.630625 m^2

The volume is ...

V = (1/3)Bh = (1/3)(6.630625 m^2)(15.1 m) ≈ 33.4 m^3

The volume of the pyramid is about 33.4 cubic meters.

3 0

3 years ago

Select the correct answer.

maksim [4K]

it should be A. 3/4

8 0

2 years ago

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Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function

Yanka [14]

Answer:

120

Step-by-step explanation:

A: D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

B: D: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

C: D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

D: D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

7 0

3 years ago

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If the absolute value of x is 4, what is the value of x?

natima [27]

The absolute value of x is 4

4 0

3 years ago

Which is equivalent to V180x11 after it has been simplified completely?

inna [77]

Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

7 0

3 years ago

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