05 Algebra and Applied Math Free Online FlashCards

What is a variable?

A variable is a symbol, such as $x$, that represents an unknown or changing value.

What rule keeps an equation balanced while solving it?

Perform the same operation on both sides to keep the equation balanced and isolate the variable.

When can you combine like terms?

Combine terms with the same variable raised to the same power. For example, $5x+2-3x+6=2x+8$.

How does a rate differ from a ratio?

A ratio compares quantities by division; a rate compares quantities with different units, such as miles per hour.

If 4 notebooks cost $12, what do 7 notebooks cost at the same price?

The proportion $\frac{4}{12}=\frac{7}{x}$ gives $4x=84$, so $x=21$.

What is 15% of 80?

Convert the percent to a decimal and multiply: $0.15\times80=12$.

How do you calculate percentage increase or decrease?

Divide the change by the original amount, then multiply by 100 to express the result as a percentage.

Which inequality symbols represent “at least” and “no more than”?

“At least” translates to $\geq$, while “no more than” translates to $\leq$.

A service costs $18 plus $6.50 per hour. How many hours total $44?

Set up $18+6.50h=44$. Solving gives $h=4$ hours.

What relationship connects distance, rate, and time?

Distance equals rate multiplied by time: $d=rt$.

How can a conversion factor change units without changing a quantity?

Multiply by a conversion factor equal to 1, such as $\frac{60\text{ min}}{1\text{ hr}}$, so the unwanted unit cancels.

What should you check before interpreting a graph?

Check the title, labels, units, scale, and time period; an axis may start above zero or use uneven intervals.