Math Flashcards

10 people can paint a building in 5 days. If each person paints as quickly as the others then how much of the building could 7 people paint in 5 days?

Answer: 7\/10

If 10 people can paint a building in 5 days, the total work required is 10 people * 5 days = 50 'person-days'. This represents painting the entire building (1 unit of work). If 7 people work for 5 days, they complete 7 people * 5 days = 35 'person-days' of work. The fraction of the building painted is the ratio of work done to total work required: 35/50, which simplifies to 7/10.

How many meters are there in 21 feet? Note: In the metric system of units: 1 meter = 100 centimeters and 1 meter:1 foot = 3.25:1

Answer: 6.4615

The given conversion factor is 1 meter = 3.25 feet. To convert 21 feet to meters, divide the number of feet by the conversion factor: 21 feet / (3.25 feet/meter). Performing this calculation gives approximately 6.461538 meters. Rounded to four decimal places, this is 6.4615 meters.

What is the x value such that y =15 - 3x and y = 0?

Answer: 5

To find the x-value when y = 0, substitute y = 0 into the equation y = 15 - 3x. This yields 0 = 15 - 3x. Add 3x to both sides to get 3x = 15. Finally, divide by 3 to solve for x: x = 15 / 3 = 5.

Put these four fractions in order from smallest to largest: 1\/4, 2\/3, 4\/7, 1\/2

Answer: 1\/4, 1\/2, 4\/7, 2\/3

To order the fractions, convert them to decimals: 1/4 = 0.25, 2/3 ≈ 0.667, 4/7 ≈ 0.571, and 1/2 = 0.5. Arranging these decimal values from smallest to largest gives 0.25, 0.5, 0.571, 0.667. This corresponds to the original fractions in the order: 1/4, 1/2, 4/7, 2/3.

On a number line what is the distance between -3\/7 and -2\/3 ?

Answer: 5\/21

The distance between two numbers on a number line is the absolute value of their difference. Calculate |-2/3 - (-3/7)| = |-2/3 + 3/7|. To combine these fractions, find a common denominator, which is 21. Convert the fractions: -2/3 = -14/21 and 3/7 = 9/21. Then, |-14/21 + 9/21| = |-5/21| = 5/21.

A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.

Answer: 5 seconds

The rocket reaches the platform when its height h is 0. Set the equation to 0: -t^2 + 3t + 10 = 0. Multiply by -1 to get t^2 - 3t - 10 = 0. Factor the quadratic equation: (t - 5)(t + 2) = 0. This gives two solutions: t = 5 or t = -2. Since time cannot be negative in this context, the rocket takes 5 seconds to reach the platform.

In the diagram below, which line has a positive slope?

Answer: AC

A line has a positive slope if it rises as you move from left to right across the graph. Without the specific diagram, we infer that line AC is the one that exhibits this characteristic. This means that for any two points on line AC, the y-coordinate increases as the x-coordinate increases.

In the diagram below, what are the coordinates of the mirror image of the point B in the x-axis?

Answer: (3,-2)

When a point is reflected across the x-axis, its x-coordinate remains unchanged, while its y-coordinate changes sign. If the mirror image of point B in the x-axis is (3, -2), then the original coordinates of point B must have been (3, 2). The x-coordinate stays 3, and the y-coordinate changes from 2 to -2.

Which is the best simplification of (24 x 32) \/ (2 x 3)?

Answer: 23 x 3

To simplify the expression (2^4 * 3^2) / (2 * 3), apply the rules of exponents for division: a^m / a^n = a^(m-n). For the base 2 terms, 2^4 / 2^1 = 2^(4-1) = 2^3. For the base 3 terms, 3^2 / 3^1 = 3^(2-1) = 3^1, or simply 3. Combining these simplified terms yields 2^3 * 3.

Which of the following is the same as 10x2 - 11x + 3?

Answer: (5x - 3)(2x - 1)

To determine which factored form is equivalent to 10x^2 - 11x + 3, multiply out each option using the FOIL method (First, Outer, Inner, Last). For option B, (5x - 3)(2x - 1) expands to (5x * 2x) + (5x * -1) + (-3 * 2x) + (-3 * -1). This simplifies to 10x^2 - 5x - 6x + 3, which combines to 10x^2 - 11x + 3, matching the original expression.