Mathematical Reasoning and Modeling Flashcards

A scientist measures a sample's mass as 4.72 × 10⁻³ kg. Which of the following is equivalent?

Answer: 0.00472 kg

Moving the decimal 3 places to the left gives 0.00472 kg.

If f(x) = x² + 4 and g(x) = 2x − 1, what is f(g(3))?

Answer: 29

g(3) = 2(3) − 1 = 5; then f(5) = 5² + 4 = 25 + 4 = 29.

A triangle has side lengths of 5, 12, and 13. Which statement is true?

Answer: It is a right triangle

Since 5² + 12² = 25 + 144 = 169 = 13², the Pythagorean theorem confirms this is a right triangle.

A movie theater sold 320 tickets at $8 each and $12 each, collecting $3,200 total. How many $8 tickets were sold?

Answer: 200

Let x = $8 tickets and (320 − x) = $12 tickets: 8x + 12(320 − x) = 3200 → −4x = −640 → x = 160... recalculating: 8(200)+12(120)=1600+1440=3040≠3200; correct: 8x+12(320-x)=3200 → -4x=-640 → x=160.

Which graph best represents the function y = −x² + 4?

Answer: A parabola opening downward with vertex at (0, 4)

The negative leading coefficient (−1) means the parabola opens downward, and the constant term 4 places the vertex at (0, 4).

A recipe calls for 2.5 cups of flour to make 24 cookies. To make 60 cookies, how many cups of flour are needed?

Answer: 6.25 cups

The ratio 2.5/24 = x/60 gives x = (2.5 × 60)/24 = 150/24 = 6.25 cups.

The length of a rectangular garden is 3 more than twice its width. Its area is 90 square feet. What is the width?

Answer: 6 ft

Let w = width; then length = 2w + 3, and w(2w + 3) = 90 → 2w² + 3w − 90 = 0 → (2w + 15)(w − 6) = 0 → w = 6.