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Veseljchak [2.6K]
3 years ago
10

Simplify the expression using the distributive property.

Mathematics
1 answer:
MatroZZZ [7]3 years ago
6 0

Answer:

-9x-14

Step-by-step explanation:

Using distributive property, we can simplify the expression to x - 2 - 10x - 12

Then we can combine like terms and get -9x - 14

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The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm.
valentina_108 [34]

Answer:

h = 9x

Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

           ii. for the sphere, radius = 3x cm

           iii.  volume of the cylinder = volume of the sphere

volume of a cylinder is given as;

volume = \frac{1}{3}\pir^{2}h

where: r is its base radius and h the height

volume of the given cylinder = \frac{1}{3}\pi x (2x)^{2} x h

                                              = \frac{1}{3}\pi x 4x^{2} x h

                                              = \frac{4}{3}\pix^{2} h

volume of a sphere = \frac{4}{3}\pir^{3}

where r is the radius.

volume of the given sphere =  \frac{4}{3}\pi x (3x)^{3}

                                         =  \frac{4}{3}\pi x 9 x^{3}

                                         = 12\pix^{3}

Since,

volume of the cylinder = volume of the sphere

Then we have;

\frac{4}{3}\pix^{2} h = 12\pix^{3}

4\pix^{2} h = 36\pix^{3}

subtract x^{2} from both sides

4\pih = 36\pix

divide both sides by 4\pi

h = \frac{36\pi x}{4\pi }

  = 9x

h = 9x

5 0
2 years ago
Rewrite the expression with rational exponents as a radical expression.
nexus9112 [7]

Answer:

If the expression is 4x^\frac{3}{7}, then the answer is the first option.

If the expression is (4x)^\frac{3}{7}, then the answer is the third option.

Step-by-step explanation:

Remember that when you have a radical expression in the form \sqrt[n]{x}, you can rewrite as:

=x^\frac{1}{n}

Then:

- If the expression is 4x^\frac{3}{7}, then you can rewrite it in the following radical form:

=4\sqrt[7]{x^3} (This form matches with the first option.)

- If the expression is (4x)^\frac{3}{7}, then you can rewrite it in the following radical form:

=\sqrt[7]{(4x)^3} (This form matches with the third option).

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Which function represents a parabola that opens downward and intersects the x-axis at (3,0) and (-4,0)?
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