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gregori [183]
3 years ago
7

Which expression is equivalent to 4^6 ⋅ 4^−8?

Mathematics
1 answer:
grin007 [14]3 years ago
5 0

Answer:

\dfrac{1}{4^2}

Step-by-step explanation:

The exponents add:

  4^6·4^-8 = 4^(6-8) = 4^-2

A negative exponent means the same as the reciprocal of the opposite positive exponent.

  4^-2 = 1/4^2

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How do I find an absolute value function from a graph?
elixir [45]
You count how many places the number is away from 0. try writing it out in an equation it would help
8 0
3 years ago
Kelly was asked to determine whether △KLN is congruent to △MNL. She noted that KL ≅ MN, LM ≅ KN, and that the three pairs of cor
Art [367]

Answer:

<h2>Kelly is wrong, with this congruent parts, we can conclude that triangles are congruent.</h2>

Step-by-step explanation:

To demonstrate congruent triangles, we need to use the proper postulates. There are at least 5 postulates we can use.

  • Angle-Angle-Side Theorem (AAS theorem).
  • Hypotenuse-Leg Theorem (HL theorem).
  • Side-Side-Side Postulate (SSS postulate).
  • Angle-Side-Angle Postulate (ASA postulate).
  • Side-Angle-Side Postulate (SAS postulate).

In this case, Kelly SAS postulate, because the corresponding sides-angles-sides are congruent, i.e., KL ≅ MN and LM ≅ KN, also, all corresponding angles are congruent.

So, as you can see, only using SAS postulate, the congruency can be demonstrated. (Refer to the image attached to see an example of SAS postulate)

8 0
3 years ago
Find the number of ways of arranging the numbers
Doss [256]

First of all, note that all integers are either 0,1, or 2 modulo 3 (if you're not familiar with this terminology, it means that every integer is either a multiple of 3, or it is 1 or 2 away from a multiple of 3).

So, we can think of our numbers as

\begin{array}{c|c}x&x\mod 3\\0&0\\1&1\\2&2\\3&0\\4&1\\5&2\\6&0\\7&1\\8&2\\9&0\end{array}

In order to make sure that the sum of any three adjacent numbers is divisible by 3, we have to make sure that any group of 3 three adjacent numbers contains a 0, a 1 and a 2. This is possible only if we arrange our 9 numbers in 3 groups of 3 numbers containing 0,1 and 2 exactly once, repeating always the same pattern.

For example, we could arrange our numbers following the pattern

0,1,2,0,1,2,0,1,2

or

2,0,1,2,0,1,2,0,1

We have 3!=6 possible patterns. Suppose for example that we choose the pattern

0,1,2,0,1,2,0,1,2

One possible way of following this pattern would be the arrangement

3,1,2,6,4,5,9,7,8

In fact, we substituted every '0' with a multiple of 3 (3, 6 or 9), every '1' with a number 1 away from a multiple of 3 (1, 4 or 7) and every '2' with a number 2 away from a multiple of 3 (2, 5 or 8).

This means that, once we fix a patter, we have 3 choices for the first 3 slots, 2 choices for the next 3 slots, and the final slot will be fixed. So, we have

3\cdot 3\cdot 3\cdot 2 \cdot 2 \cdot 2 = 216

possible ways of following a fixed pattern. Since the number of patterns was 6, we have

216\cdot 6 = 1296

possible arrangements.

7 0
3 years ago
Read 2 more answers
2/3
Veronika [31]

Answer:

2/3

4

3.

An airplane is flying from New York City to Los Angeles. The distance it travels in

miles, d, is related to the time in seconds, t, by the equation d = 0.15t.

d= 0.15

1

0.157

t

(seconds)

1

30

d

(miles)

0.15

0.15 x 1

0.15 x 30

12.75

a.

How fast is it flying? Be sure to include the units.

b.

How far will it travel in 30 seconds?

C.

How long will it take to go 12.75 miles?

4.

Crater Lake in Oregon is shaped like a circle with a diamet

Step-by-step explanation:

7 0
3 years ago
The sum of two consecutive odd integers is 84. Find the two integers.
Rudik [331]

Answer: n + (n + 2) = 84

Step-by-step explanation:

If n is the smallest integer, the other integer must be two more than that, because it has to be odd. The two numbers add up to 84, so the other side of the equation is 84.

5 0
3 years ago
Read 2 more answers
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