Free ASVAB Practice Tests

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

Drag is friction that opposes movement through a fluid like liquid or air. The amount of drag depends on the shape and speed of the object with slower objects experiencing less drag than faster objects and more aerodynamic objects experiencing less drag than those with a large leading surface area.

Soldering is a process by which two or more items (typically metal) are joined together by melting a filler metal (solder) into the joint. An electrically powered soldering iron or soldering gun is used to melt the solder which is an alloy of lead and tin that has a melting point below the melting point of the items being joined. A chemical cleaning agent called flux is also used to clean the surfaces before soldering.

Momentum is a measure of how difficult it is for a moving object to stop and is calculated by multiplying the object's mass by its velocity:  \(\vec{p} = m\vec{v}\).  Like velocity, momentum is a vector quantity as it expresses force applied in a specific direction.

Electricity is delivered from power stations to customers as AC because it provides a more efficient way to transport electricity over long distances. Most households use electricity with a frequency of 60Hz.

Mantle makes up 84% of the Earth's volume and has an average thickness of approximately 1,800 miles (2,900 km). It is dense, hot, and primarily solid although in places it behaves more like a viscous fluid as the plates of the upper mantle and crust gradually "float" along its circumference.

In a four-stroke cycle engine there is always one piston delivering power, one exhausting gases, one drawing in the air-fuel mixture, and one compressing that mixture.

Because this lever is in equilibrium, we know that the effort force at the blue arrow is equal to the resistance weight of the green box. For a lever that's in equilibrium, one method of calculating mechanical advantage (MA) is to divide the length of the effort arm (E_a) by the length of the resistance arm (R_a):

MA = \( \frac{E_a}{R_a} \) = \( \frac{7 ft.}{8 ft.} \) = 0.88

When a lever is in equilibrium, the torque from the effort and the resistance are equal. The equation for equilibrium is R_ad_a = R_bd_b where a and b are the two points at which effort/resistance is being applied to the lever.

In this problem, R_a and R_b are such that the lever is in equilibrium meaning that some multiple of the weight of the green box is being applied at the blue arrow. For a lever, this multiple is a function of the ratio of the distances of the box and the arrow from the fulcrum. That's why, for a lever in equilibrium, only the distances from the fulcrum are necessary to calculate mechanical advantage.

If the lever were not in equilibrium, you would first have to calculate the forces and distances necessary to put it in equilibrium and then divide E_a by R_a to get the mechanical advantage.

Ball peen hammers are most commonly used in automotive repair. They have rounded heads and are used to drive punches and chisels.