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bixtya [17]
3 years ago
14

Simply 6^-1(4^-2) plz help

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
6 0

Answer:

  1/96

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

Then ...

6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}

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Leto [7]
A transformation that can be performed on polygon ABCDE is a reflection over the y-axis.
The image of a polygon by a reflection its mirror image. The reflected image has the same size as the original.
It means that polygon ABCDE is congruent to polygon MNPQ.
9 0
3 years ago
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people.
KonstantinChe [14]

Using an exponential function, the inequality is given as follows:

9400(0.857)^t < 6000

The solution is t > 2.9, hence the tax status will change within the next 3 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

A(t) = A(0)(1 - r)^t

A(t) = 9400(1 - 0.143)^t

A(t) = 9400(0.857)^t

The tax status will change when:

A(t) < 6000

Hence the inequality is:

9400(0.857)^t < 6000

Then:

(0.857)^t < \frac{6000}{9400}

\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}

t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}

Since both logs are negative:

t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

More can be learned about exponential functions at brainly.com/question/25537936

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7 0
2 years ago
What is a constant?​
lakkis [162]

Answer:

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.

Step-by-step explanation:

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial. the 3 is a constant term.

5 0
3 years ago
In the adjoining figure, area of trangle ABC is
Zepler [3.9K]

Answer:

PQ=4\ cm

Step-by-step explanation:

see the attached figure with the letter D to better understand the problem

we know that

The segment side AD is the height of triangle ABC

so

Triangles PBQ and ABD are similar by AA Similarity Theorem

The area of triangle ABC is equal to

A=\frac{1}{2}(BC)(AD)

we have

A=48\ cm^2\\BC=12\ cm

substitute

48=\frac{1}{2}(12)(AD)

AD=8\ cm

Remember that

If two triangles are similar  then the ratio of its corresponding sides is proportional

so

\frac{BP}{AB}=\frac{PQ}{AD}

substitute the given values

\frac{BP}{2BP}=\frac{PQ}{8}

\frac{1}{2}=\frac{PQ}{8}

PQ=4\ cm

3 0
3 years ago
Which choice solves the problem?
seropon [69]

D) 209 with a remainder of 4


5 0
3 years ago
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