If the area of triangle ABD is 12 square units, what is the area of Rectangle ABCD?

What makes a NUMBER rational is the ability to have a perfect square root, cube root, or have these components: Perfect square/cube, whole number, repeating (pattern) decimal, termination decimal, and I think one more that I can't remember.

The properties of the rational exponents are given and a rational equation is of the form b = aˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the rational exponent equation be A

Now , the properties of the exponent equations are

mᵃ×mᵇ = mᵃ⁺ᵇ

The powers of the exponents are added together

mᵃ / mᵇ = mᵃ⁻ᵇ

The powers of the exponents are subtracted together

( mᵃ )ᵇ = mᵃᵇ

The powers of the exponents are multiplied together

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

Any number raised to the power of 0 is 1

m⁻ᵃ = ( 1 / mᵃ )

Hence , the exponents are solved

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Final answer:

Rational exponents have properties that help to simplify expressions and solve mathematical problems. These properties include the product rule, the quotient rule, and the power rule. Utilizing these rules, especially in scientific notation, helps provide concise computations for very large or small numbers.

Explanation:

Properties of Rational Exponents

The properties of rational exponents play a key role in simplifying expressions and solving mathematical problems. Here are three key properties:

• Product Rule: When you multiply two numbers with the same base, you should add the exponents. This is expressed as: a^m * a^n = a^(m+n).
• Quotient Rule: When you divide two numbers with the same base, you should subtract the exponents. This rule is reflected in: a^m / a^n = a^(m-n).
• Power Rule: When you raise a power to a power, you should multiply the exponents: (a^m)^n=a^(mn).

These properties are crucial for solving problems. For example, scientific notation, which is used to represent very large or small numbers, employs these properties of exponents. In scientific notation, numbers are expressed as a product of a digit term and an exponential term. This method is useful for making computations convenient and precise.

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The required simplified solution of the given expression is 11x -8.

Given that,
To determine the simplified expression that is equivalent to the 3(x-2)+2(4x-1).

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
3(x-2)+2(4x-1)
Applying the distributive law in order to multiply the 3 and 4 in the respective parenthesis.
= 3x - 6 + 8x - 2
= 11x - 8

Thus, the required simplified solution of the given expression is 11x -8.

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The amount borrowed from each friend by Keith will be $6.

What is the solution to the equation?

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Keith borrowed a total of $30 by borrowing the same amount of money from 5 different friends.

Let the amount borrowed from each friend be x. Then the equation will be

5x = 30

Divide the equation by 5, then the value of the variable x will be

x = 30 / 5

x = $6

The amount borrowed from each friend by Keith will be $6.

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Answer:

$6

Step-by-step explanation: