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Ira Lisetskai [31]
3 years ago
7

Find the length of the side of a square with area 225 square units

Mathematics
1 answer:
Anestetic [448]3 years ago
4 0
A = l^{2};
Then, 225 = l^{2};
l^{} =  \sqrt{225} = 15 unit;
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Match the numerical expressions to their simplest forms.
Aloiza [94]

Answer:

(a^6b^1^2)^\frac{1}{3} = a^2b^4

\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}} = a^3b^2

(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4} = a^2b

(\frac{a^3}{ab^-^6})^\frac{1}{2} = ab^3

Step-by-step explanation:

Simplify each of the expressions:

1

(a^6b^1^2)^\frac{1}{3}

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

(a^6b^1^2)^\frac{1}{3}

a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}

Simplify,

a^2b^4

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}

Rewrite as square roots:

\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}

Simplify,

\sqrt{a^5b^3}*\sqrt{ab}

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

\sqrt{a^5b^3*ab}

Simplify,

\sqrt{a^6b^4}

Since this operation is taking the square root, divide the exponents in half to do this operation:

a^3b^2

3

(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

(\frac{a^8}{b^-^4})^\frac{1}{4}

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

(a^8b^4)^\frac{1}{4}

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

\sqrt[4]{a^8b^4}

SImplify, divide the exponents by (4) to simulate taking the quartic root,

a^2b

4

(\frac{a^3}{ab^-^6})^\frac{1}{2}

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}

(a^2b^6)^\frac{1}{2}

Rewrite to the half-power as a square root,

\sqrt{a^2b^6}

Simplify, divide all of the exponents by (2),

ab^3

7 0
3 years ago
He<br> Find the volume of this cylinder. Use 3 for pi<br> V = ?
Alborosie

Answer:

30in^3

Step-by-step explanation:

3x1^2x10=

3x1x10=

30

30in^3

3 0
2 years ago
Read 2 more answers
Find the slope given the points (-5-3) and (2 4)
Anna35 [415]

Answer:

1

Step-by-step explanation:

I graphed and got the answer.

5 0
3 years ago
Question Help In 2005, it took 20.29 currency units to equal the value of 1 currency unit in 1917. In 1990, it took only 13.10 c
bezimeni [28]

Answer:

The amount it took in 2011 to equal the value of 1 currency unit in 1917 was of 24.091 currency units.

The amount it took in 2019 to equal the value of 1 currency unit in 1917 was of 28.031 currency units.

Step-by-step explanation:

The value needed to equal the value of 1 currency unit in 1917, in x years after 1990, is given by:

V(x) = 0.4925x + 13.7485

a) Use this function to predict the amount it will take in 2011 and in 2019 to equal the value of 1 currency unit in 1917​

2011 is 2011 - 1990 = 21 years after 1990, so we have to find V(21).

V(21) = 0.4925*21 + 13.7485 = 24.091

The amount it took in 2011 to equal the value of 1 currency unit in 1917 was of 24.091 currency units.

2019 - 1990 = 29, so we also to find V(29).

V(29) = 0.4925*29 + 13.7485 = 28.031

The amount it took in 2019 to equal the value of 1 currency unit in 1917 was of 28.031 currency units.

8 0
2 years ago
What is it? I am not sure
earnstyle [38]

Answer: I think its A

Step-by-step explanation: maybe

5 0
2 years ago
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