$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}}$

$\bf \rule{34em}{0.25pt}\\\\ \cfrac{1}{x^{-\frac{3}{6}}}\implies x^{\frac{3}{6}}\implies x^{\frac{1}{2}}\implies \sqrt[2]{x^1}\implies \sqrt{x}$

5 0

2 years ago

Translate this phrase into an algebraic expression. 73 less than twice Jose's height Use the variable to represent Jose's height

Luba_88 [7]

Answer:

x-73

Step-by-step explanation:

Let x=Jose's height. If it says "less than," then that is subtraction. Since Jose's height is not defined, there is no specific number that can be used to describe "73 less than twice Jose's height," so I use the variable x, and then subtract 73.

8 0

2 years ago

the volume of a cone is 120 cubic centimeters. the height of the cone is 4.5 centimeters. determine the radius of a cone

kolbaska11 [484]

<h3> given:</h3>

$v = 120 \: {cm}^{3}$

$h = 4.5 \: cm$

the radius of the cone.

<h3>solution:</h3>

$r = \sqrt{3 \frac{v}{\pi \: h} }$

$r = \sqrt{3 \times \frac{120}{\pi \times 4.5} }$

$r = 5.04627 \: cm$

$r = 5.05 \: cm$

hence, the radius of the given cone is 5.05 centimeters.

7 0

2 years ago

Help me with this question Please I need help

34kurt

Answer:

384 cm²

Step-by-step explanation:

The shape of the figure given in the question above is simply a combined shape of parallelogram and rectangle.

To obtain the area of the figure, we shall determine the area of the parallelogram and rectangle. This can be obtained as follow:

For parallelogram:

Height (H) = 7.5 cm

Base (B) = 24 cm

Area of parallelogram (A₁) =?

A₁ = B × H

A₁ = 24 × 7.5

A₁ = 180 cm²

For rectangle:

Length (L) = 24 cm

Width (W) = 8.5 cm

Area of rectangle (A₂) =?

A₂ = L × W

A₂ = 24 × 8.5

A₂ = 204 cm²

Finally, we shall determine the area of the shape.

Area of parallelogram (A₁) = 180 cm²

Area of rectangle (A₂) = 204 cm²

Area of figure (A)

A = A₁ + A₂

A = 180 + 204

A = 384 cm²

Therefore, the area of the figure is 384 cm²

3 0

2 years ago