Mathematics Flashcards

What is the value of 3x + 5 when x = 4?

Answer: 17

To find the value of the expression 3x + 5 when x = 4, substitute 4 in place of x. First, multiply 3 by 4, which gives 12. Then, add 5 to that result. Therefore, 12 + 5 equals 17.

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 (75) and the denominator (100) by their greatest common divisor, which is 25. This simplification results in the equivalent fraction 3/4.

Solve for y: 2y - 7 = 15

Answer: y = 11

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

What is the area of a rectangle with length 8 units and width 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 multiplied by 5 units. This calculation yields an area of 40 square units.

Which number is a prime number?

Answer: 23

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Of the given options, 23 fits this definition as it can only be divided evenly by 1 and 23. Numbers like 15, 27, and 33 have other divisors besides 1 and themselves, making them composite numbers.

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

Answer: 24 cm

The perimeter of a square is the total distance around its four sides. Since all sides of a square are equal in length, you can calculate the perimeter by multiplying the length of one side by 4. For a square with a side length of 6 cm, the perimeter is 6 cm multiplied by 4, which equals 24 cm.

Simplify: 4² + (10 ÷ 2) × 3

Answer: 31

To simplify the expression 4² + (10 ÷ 2) × 3, follow the order of operations (PEMDAS/BODMAS). First, calculate the exponent: 4² = 16. Next, perform the operation inside the parentheses: 10 ÷ 2 = 5. Then, perform the multiplication: 5 × 3 = 15. Finally, add the results: 16 + 15 = 31.

What is the least common multiple (LCM) of 6 and 8?

Answer: 24

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. To find the LCM of 6 and 8, list their multiples: Multiples of 6 are 6, 12, 18, 24, 30... Multiples of 8 are 8, 16, 24, 32... The smallest number common to both lists is 24.

If a triangle has angles measuring 45° and 45°, what is the measure of the third angle?

Answer: 90°

The sum of the interior angles in any triangle is always 180 degrees. If two angles measure 45° each, their combined sum is 45° + 45° = 90°. To find the measure of the third angle, subtract this sum from 180°: 180° - 90° = 90°. This indicates it is a right-angled isosceles triangle.