Mathematics Concepts & Applications Flashcards

If 3x + 5 = 20, what is the value of x?

Answer: 5

To solve the equation 3x + 5 = 20, first subtract 5 from both sides, which gives 3x = 15. Then, divide both sides by 3. This isolates x, resulting in x = 5.

What is the area of a rectangle with a length of 8 units and a width of 5 units?

Answer: 40 square units

The area of a rectangle is calculated by multiplying its length by its width. For a rectangle with a length of 8 units and a width of 5 units, the area is 8 units * 5 units. This calculation yields an area of 40 square units.

Which fraction is equivalent to 0.75?

Answer: 3/4

The decimal 0.75 represents 75 hundredths, which can be written as the fraction 75/100. To simplify this fraction, divide both the numerator and the denominator by their greatest common divisor, which is 25. This simplification results in the equivalent fraction 3/4.

A store offers a 20% discount on a $50 item. What is the final price?

Answer: $40

To find the final price after a 20% discount on a $50 item, first calculate the discount amount: 20% of $50 is (0.20 * 50) = $10. Then, subtract the discount from the original price: $50 - $10 = $40.

What is the perimeter of a square with a side length of 6 units?

Answer: 24 units

The perimeter of a square is the total length of all its sides. Since a square has four equal sides, you can find the perimeter by multiplying the length of one side by four. For a square with a side length of 6 units, the perimeter is 6 units * 4 = 24 units.

Solve for y: 2y − 7 = 15

Answer: y = 11

To solve the equation 2y - 7 = 15, first add 7 to both sides, which gives 2y = 22. Then, divide both sides by 2. This isolates y, resulting in y = 11.

What is 15% of 200?

Answer: 30

To calculate 15% of 200, convert the percentage to a decimal by dividing by 100 (0.15). Then, multiply this decimal by the number: 0.15 * 200. This calculation yields 30.

Which number is a prime number?

Answer: 11

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Of the given options, 11 is a prime number because its only divisors are 1 and 11. Numbers like 9 (divisible by 3), 15 (divisible by 3 and 5), and 21 (divisible by 3 and 7) are composite numbers.

A triangle has angles measuring 45° and 55°. What is the measure of the third angle?

Answer: 80°

The sum of the interior angles in any triangle is always 180 degrees. If two angles measure 45° and 55°, their sum is 45° + 55° = 100°. To find the third angle, subtract this sum from 180°: 180° - 100° = 80°.