Algebra 1 Team Decathlon -- Event #6 100 meter hurdle

Front

What is the property of exponents that states \( \frac{1}{a^{-n}} = a^{n} \)?

Back

This property states that the reciprocal of a negative exponent is equal to the positive exponent.

Front

What is the product of \((-7x^2)\) and \((4x^4)\)?

Back

The product is \(-28x^6\). This is found by multiplying the coefficients (-7 and 4) and adding the exponents of x (2 + 4).

Front

How do you solve the equation \(y = mx + b\) for \(x\)?

Back

To solve for \(x\), rearrange the equation to get \(x = \frac{(y - b)}{m}\).

Front

What is the simplified form of \(\frac{x^2y^2z^2}{4y^4}\)?

Back

The simplified form is \(\frac{x^2z^2}{4y^2}\). This is done by reducing the powers of y.

Front

Translate 'Four divided by the sum of a number and twelve' into an algebraic expression.

Back

The expression is \(\frac{4}{(n + 12)}\).

Front

What is the definition of a variable in algebra?

Back

A variable is a symbol, often a letter, that represents one or more numbers.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.

Front

What is the distributive property in algebra?

Back

The distributive property states that \(a(b + c) = ab + ac\). It allows you to multiply a single term by two or more terms inside a parenthesis.

Front

What is the difference between an equation and an expression?

Back

An equation states that two expressions are equal, while an expression is a combination of numbers, variables, and operations without an equality sign.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.