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3 years ago

Describe how to simplify the expression 3^-6/3^-4

Mathematics

2 answers:

Kaylis [27]3 years ago

5 0

Answer:

The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression is

$\frac{3^{-6}}{3^{-4}}$

In the above expression we have common base 3 but the exponents are different.

According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.

$\frac{a^m}{a^n} =a^{m-n}$

Use this rule in the given expression.

$\frac{3^{-6}}{3^{-4}}=3^{-6-(-4)}$

$\frac{3^{-6}}{3^{-4}}=3^{-2}$

Therefore the correct option is d.

love history [14]3 years ago

4 0

The awnser is D, just took the quiz.

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Given: Elmwood St. and Oak Dr. are the same distance. All intersections are perpendicular.

vlabodo [156]

Answer:

The above result is proved with the help of Pythagoras theorem and explained below.

Step-by-step explanation:

Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.

In triangle ADC,

By applying Pythagoras theorem, we get

$AC^{2}=AD^{2}+DC^{2}$ → (1)

In triangle ABC,

$AC^{2}=AB^{2}+BC^{2}$ → (2)

Now, from eq (1) and (2)

Peach Tree Dr. is the same distance as Sycamore Ln.

$AD^{2}+DC^{2} = AB^{2}+BC^{2}$

⇒ $DC^{2} = AB^{2}$ (∵ AD=BC)

⇒ DC=AB (∵Distance can never negative)

Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.

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3 years ago

A boat is 400 feet away from one dock and 500 feet away from the another dock. the angle between the paths is 45°. what is the a

FinnZ [79.3K]

Answer:

The approximate distance between the docks is 357 feet

Step-by-step explanation:

Let the distance between docks be d.

This is the opposite side to 45° angle of triangle with other sides 400 ft and 500 ft.

Use the law of cosines to find the value of d:

$d = \sqrt{400^2+500^2-2*400*500*cos45} =357$ (rounded)

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2 years ago

Factorise completely;<br>y(ay-x)+x(y-ax)

Kay [80]

Answer:

$ay2 - xy + xy - ax2$

ay2- ax2

5 0

3 years ago

La suma de las edades de tres personas es 127años. La mayor tiene 30 años mas que la menor y la del intermedio 26 menos que la m

Over [174]

Answer:

La mayor tiene 61 años.

Step-by-step explanation:

Sea x,y,z la edad de la mayor, intermedio y la menor respectivamente.

Tenemos las siguientes ecuaciones:

$x+y+z=127$ (la suma de las edades es 127)

$x = z+30$ (la mayor tiene 30 años más que la menor)

La frase "y la del intermedio 26 menos que la menor" no tiene sentido, puesto que esto implicaría que la del intermedio es menor que la menor. Luego se asume que la frase ha de ser "y la del intermedio 26 menos que la mayor"

$x-26 = y$ (la del intermedio tiene 26 menos que la mayor).