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3 years ago

Which exponent makes this statement true? 1/5^9= 5^?

Mathematics

1 answer:

Aleks04 [339]3 years ago

5 0

Answer:

The exponent -9 makes the given statement true.

Step-by-step explanation:

We have been given an incomplete mathematical statement and we need to figure out the exponent for 5 on the right hand side to complete the statement.

The given incomplete statement is $\frac{1}{5^{9}}=5^{?}$ .

Let us rewrite the left hand side of the expression by moving the exponential term to the numerator using exponent property. As per this property, if we shift an exponential term from denominator to numerator (or vice versa), the sign of exponent changes.

Therefore, we get:

$5^{-9}=5^{?}$

Now that we have common bases on both the sides, we can equate the exponents. And upon equating the exponents, we can see that the 'question mark' should be replaced by -9 in order for statement to be true.

Therefore, exponent -9 on the right hand side will make the statement true.

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Read 2 more answers

There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r

zhannawk [14.2K]

Answer:

Step-by-step explanation:

The first cave has 7 times more bats than the last cave. So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves. So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats. Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end. If cave #45 has b bats, then caves #39-#44 have 77−b bats. And since caves #38-44 have 77 bats, then cave #38 has b bats. Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

x = 12

There are at most 12 bats in the 30th cave.

8 0

3 years ago

7. A cylindrical tank can hold 2279.64 cubic feet of water. The radius of the tank is 11 feet. What is the height of the tank?

aliina [53]

Answer:

r = 8.12

Step-by-step explanation:

The volume for a cylinder is V=πr^2h therefore,

v = 2279.64

h = 11ft

r = ?

2279.64 = πr^2 * 11

$\frac{2279.64}{11}= {\pi r^2} \\$

207.24 = πr^2

$\frac{207.24}{\pi} =r^2\\\\66 = r^2\\\\\sqrt{66} = r\\\\\\8.12 = r$

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2 years ago

Which number has an absolute value that is equal to the absolute value of 32?

Gennadij [26K]

Answer:

-32

Step-by-step explanation:

The absolute value of a number is its distance from 0. Since distance is always positive the absolute value is the same number but positive. So the absolute value of -32 and 32 would both be 32 because they have the same distance from 0.

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