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sashaice [31]
2 years ago
8

Which expression is equivalent to square root of 9x^2?

Mathematics
2 answers:
-Dominant- [34]2 years ago
7 0
Let's take the square root of this

√(9x^2)

To make this easier, let's use the following property of roots.

√(ab) = √(a) * √(b)

Let's separate the square root into two different square roots.

√(9x^2)
= √(9) * √(x^2)

Now, let's solve for each square root individually.

√(9) = 3
√(x^2) = x

Now, combine them

3 * x = 3x

3x is your answer.

Have an awesome day! :)
wariber [46]2 years ago
6 0
9x^2 can be rewritten as 9*x*x or 3*3*x*x
You can think of 3*3*x*x as 3x*3x which is (3x)^2.

Now we can take the square root of (3x)^2 (which equals 9x^2).

√(3x)^2
The √ and the ^2 cancel out so you are left with 3x.

So, √
9x^2 = √(3x)^2 = 3x.

3x is your answer!
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Emily's piggy bank contains twice as many dimes as nickels. It contains two more quarters than nickels. Emily calculates that if
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Answer:

Emily has 10 nickels, 20 dimes and 12 quarters in her piggy bank

Step-by-step explanation:

The number of dimes in Emily's piggy bank = 2 × The number of nickels

The number of quarters in it = 2 + The number of nickels

Whereby;

The number of quarters = The number nickels

The number of dimes = The number of quarters

The number of nickels = The number of dimes

The total amount = Current amount - $150

Let 'x' represent the number of dimes, let 'y' represent the number nickels, and let 'z' represent the number quarters in Emily's piggy bank, we have;

x = 2 × y

z = 2 + y

The total amount in the piggy bank is therefore;

Total = C = x×0.1  + y×0.05 + z×0.25 = 2·y×0.1 + y × 0.05 + (2 + y) × 0.25 = 0.5·y + 0.5

C = 0.5·y + 0.5

With the second condition, we have;

z = y

x = z

y = x

We get

x × 0.1 + y × 0.05 + z × 0.25 = y ×0.1 + y×0.05 + y×0.25 = 0.4·y = C - 1.5

∴ C = 0.4·y + 1.5

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0.5·y + 0.5 = 0.4·y + 1.5

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y = 10

Therefore;

x = 2×y = 2 × 10 = 20

z = 2 + y = 2 + 10 = 12

Therefore;

The number number of nickels in her piggy bank, y = 10

The number of dimes in her piggy bank, x = 20

The number of quarters in her piggy bank, z = 12

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