Mathematics Knowledge Flashcards

Which of the following angles is obtuse?

Answer: 130 degrees

An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. Among the given options, 130 degrees is the only angle that falls within this range. The other options represent acute angles (less than 90 degrees) or a right angle (exactly 90 degrees).

Y2-49 = 0. Y could equal:

Answer: 7

The equation Y² - 49 = 0 can be solved by adding 49 to both sides, resulting in Y² = 49. To find Y, take the square root of both sides. The square root of 49 is 7, so Y could equal 7 (or -7, but 7 is the only positive option provided).

If a circle has a diameter of 1.5 feet, what is its circumference?

Answer: 1.5 π

The circumference of a circle is calculated using the formula C = πd, where 'd' is the diameter. Given that the diameter is 1.5 feet, substitute this value into the formula. Therefore, the circumference is 1.5π feet.

Solve for the value of x in the following system: 2x + 4y = 15 3x - 4y = 10

Answer: 5

This system of equations can be solved using the elimination method. Notice that the 'y' terms have opposite coefficients (+4y and -4y). Adding the two equations together eliminates 'y': (2x + 4y) + (3x - 4y) = 15 + 10, which simplifies to 5x = 25. Dividing both sides by 5 gives x = 5.

What is the value of x in the rhombus seen in the figure?

Answer: 145 degrees

In a rhombus, consecutive angles are supplementary, meaning they add up to 180 degrees. If one angle is 35 degrees, the adjacent angle (x) will be 180 - 35 degrees. Therefore, x = 145 degrees.

Charles walked all the way around a crop circle and found that traveled 5.5 miles. If he had walked directly through it and passed the center, how much shorter would he have walked?

Answer: 3.75 miles

Charles walked the circumference of the crop circle, which is 5.5 miles. The distance he would have walked directly through the center is the diameter. Using the circumference formula C = πd, we can find the diameter: d = C/π = 5.5 / 3.14 ≈ 1.75 miles. The difference in distance is the circumference minus the diameter: 5.5 - 1.75 = 3.75 miles.

Simplify the expression: 3x + 6.5x2 = ?

Answer: This expression cannot be simplified.

To simplify an algebraic expression, you can only combine 'like terms'. Like terms have the same variable raised to the same power. In this expression, '3x' has 'x' to the power of 1, while '6.5x²' has 'x' to the power of 2. Since the powers of 'x' are different, these terms cannot be combined, and the expression remains as is.

What is the perimeter of the rhombus shown in the figure?

Answer: 40 cm

A rhombus is a quadrilateral where all four sides are equal in length. The figure indicates one side length is 10 cm. To find the perimeter, you multiply the side length by 4. Therefore, the perimeter is 10 cm * 4 = 40 cm.

A rectangular plot of land is measured to be 130 feet by 220 feet. Its total area is:

Answer: 28,600 square feet

The area of a rectangle is calculated by multiplying its length by its width (Area = Length × Width). For a plot of land measuring 130 feet by 220 feet, the area is 130 feet × 220 feet. This calculation yields 28,600 square feet.

How much water could a container hold that measures 8cm by 12cm by 10cm?

Answer: 960 mL

To find the volume of a rectangular container, multiply its length, width, and height: Volume = 8cm × 12cm × 10cm = 960 cm³. Since 1 cubic centimeter (cm³) is equivalent to 1 milliliter (mL), the container can hold 960 mL of water.

If a square is cut in half across its diagonal, the formed triangles will have angles of:

Answer: 45-45-90

When a square is cut in half across its diagonal, it forms two congruent right-angled triangles. Since all angles in a square are 90 degrees and the diagonal bisects two of these angles, the two non-right angles in each triangle will be 45 degrees. Thus, the formed triangles are 45-45-90 right triangles.

What is the area of an isosceles right triangle that has one leg that measures 4 cm?

Answer: 8 cm

An isosceles right triangle has two equal legs and a right angle. If one leg measures 4 cm, the other leg also measures 4 cm. The area of a right triangle is (1/2) * base * height. In this case, both the base and height are 4 cm, so the area is (1/2) * 4 cm * 4 cm = 8 cm².

A given rectangle has an area of 24 square feet. Which of the following cannot be one of its side lengths?

Answer: All of the above can be a side length.

The area of a rectangle is found by multiplying its length and width. If the area is 24 square feet, any side length must be a factor of 24. 24 is divisible by 4 (24/4=6), by 8 (24/8=3), and by 10 (24/10=2.4). Since all given options can be a factor of 24, all of them can be a side length.

The base of a right triangle is 1 foot, and the interior angles are 45-45-90. What is its area?

Answer: 0.5 foot squared

A right triangle with 45-45-90 interior angles is an isosceles right triangle, meaning its two legs are equal in length. If the base is 1 foot, then the height is also 1 foot. The area of a triangle is calculated as (1/2) * base * height, so the area is (1/2) * 1 foot * 1 foot = 0.5 square foot.

The circumference of a circle is 20 cm. What is the approximate radius of the circle?

Answer: 3.2 cm

The formula for the circumference of a circle is C = 2πr, where 'r' is the radius. Given the circumference is 20 cm, we can set up the equation 20 = 2πr. To find 'r', divide 20 by 2π: r = 20 / (2 * 3.14) = 20 / 6.28 ≈ 3.18 cm. The closest approximate radius is 3.2 cm.

What is the distance between the points (2,4) and (-1, 8)?

Answer: 5

The distance between two points (x1, y1) and (x2, y2) is found using the distance formula: √((x2-x1)² + (y2-y1)²). Plugging in the points (2,4) and (-1,8): √((-1-2)² + (8-4)²) = √((-3)² + (4)²) = √(9 + 16) = √25. The distance is 5.

Which of the following statements about trapezoids is true?

Answer: A trapezoid can have 4 angles which are not equal to one another.

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. Unlike parallelograms, its non-parallel sides can have different lengths, and its angles are not necessarily equal. Therefore, a trapezoid can indeed have four angles that are all different from one another.

Two parallel lines are intersected by a third line, which is perpendicular to the first parallel line. The value of another angle made by the intersecting lines is:

Answer: 90 degrees

When a transversal line is perpendicular to one of two parallel lines, it forms a 90-degree angle with that line. Because the two main lines are parallel, the transversal will also be perpendicular to the second parallel line. Therefore, all angles formed at the intersections will be 90 degrees.