All categories

1 year ago

Prove 2(2x+4)= 16 2(2x) by using the laws of exponents. boris9

Mathematics

1 answer:

storchak [24]1 year ago

7 0

The prove that the equation can be verified using the laws of exponents.

<h3>What is the proof of the equation given; 2^(2x+4)= 16 × 2^(2x)?</h3>

It follows from the task content that the equation given is; 2^(2x+4)= 16 • 2^(2x).

It follows from the laws of indices ; particularly, the product of same base numbers.

The evaluation is therefore as follows;

2^(2x+4)= 16 • 2^(2x)

2^(2x) • 2⁴ = 16 • 2^(2x)

2^(2x) • 16 = 16 • 2^(2x)

Hence, since LHS = RHS, it follows that the expression is mathematically correct.

You might be interested in

Twenty toothpicks, each 6 cm long, form a figure consisting of six equilateral triangles and a rectangle as shown. What is the t

Roman55 [17]

The total area of the figure is 139.20 square centimeters

Areas

The area of a shape is the amount of space it occupies

<h3>Composite figure</h3>

The figure (see attachment) is a composite figure, and the total area is the sum of the areas of each shape that makes up the complete figure

The shape has 6 equilateral triangles, each of which has an area of:

$A_1 = \sqrt{\frac{3s^2}{4}}$

Where:

$s = 6$ --- the length of each toothpick

The area of the rectangle is then represented as:

$A_2 =3s \times s$

$A_2 =3s^2$

So, the total area of the figure is:

$Total = 6A_1 + A_2$

This gives

$Total =6 \times \sqrt{\frac{3s^2}{4}} + 3s^2$

Substitute 6 for s

$Total =6 \times \sqrt{\frac{3(6)^2}{4}} + 3(6)^2$

$Total =6 \times \sqrt{27} + 108$

$Total =6 \times 5.20+ 108$

$Total =139.20$

Hence, the total area of the figure is 139.20 square centimeters

Read more about areas at:

brainly.com/question/21135654

7 0

2 years ago

find the magnitude of two forces f1 and f2 such that at right-angle to each other, their resultant is √13N. Also, if the two for

serious [3.7K]

This can be solved a couple of ways. One way is to use the Pythagorean theorem to write equations for the magnitude from the components of the forces. That is what was done in the graph here.

Another way is to use the Law of Cosines, which lets you make direct use of the angle between the vectors.
.. 13 = a^2 +b^2 -2ab*cos(90°)
.. 19 = a^2 +b^2 -2ab*cos(120°)
Subtracting the first equation from the second, we have
.. 6 = -2ab*cos(120°)
.. ab = 6

Substituting this into the first equation, we have
.. 13 = a^2 +(6/a)^2
.. a^4 -13a^2 +36 = 0
.. (a^2 -9)(a^2 -4) = 0
.. a = ±3 or ±2

The magnitudes of the two forces are 2N and 3N, in no particular order.