ACT PREP 2.12

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of all three sides: P = a + b + c.

Front

If a triangle has sides of lengths 6 inches and 9 inches, what is the range for the length of the third side?

Back

The length of the third side must be greater than |6 - 9| = 3 inches and less than 6 + 9 = 15 inches, so it must be between 4 and 14 inches.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you solve the quadratic equation x² + 2x - 8 = 0?

Back

To solve x² + 2x - 8 = 0, factor it to (x + 4)(x - 2) = 0, giving solutions x = -4 and x = 2.

Front

What is the ratio of two quantities?

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second.

Front

If Janelle cuts a board into two pieces in a 2:3 ratio, how do you find the lengths of the pieces?

Back

Let the lengths be 2x and 3x. The total length is 30 feet, so 2x + 3x = 30. Solving gives x = 6, so the pieces are 12 feet and 18 feet.

Front

What is the definition of a solution to an equation?

Back

A solution to an equation is a value that, when substituted for the variable, makes the equation true.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does it mean for a number to be an integer?

Back

An integer is a whole number that can be positive, negative, or zero, but not a fraction or decimal.