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Arithmetic Reasoning

If \( \left|x + 9\right| \) - 3 = 7, which of these is a possible value for x?

-19

First, solve for \( \left|x + 9\right| \):

The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal + 10 or -10 for \( \left|x + 9\right| \) to equal 10:

x + 9 = 10
x = 10 - 9
x = 1

x + 9 = -10
x = -10 - 9
x = -19

So, x = -19 or x = 1.

General Science

Heat is always transferred from __________ to __________ environments.

warmer, cooler

Heat is always transferred from warmer to cooler environments and conduction is the simplest way this transfer can occur. It is accomplished through direct contact between materials and materials like metals that transfer heat efficiently are called conductors while those that conduct heat poorly, such as plastic, are called insulators.

Arithmetic Reasoning

What is \( \frac{-7a^5}{7a^4} \)?

-a

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7a^5}{7a^4} \)
\( \frac{-7}{7} \) a^{(5 - 4)}
-a

Mechanical Comprehension

What is the mechanical advantage of this inclined plane if the length of the ramp is 24 ft. and the height of the green box is 8 ft.?

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In this case, the effort distance is the length of the ramp and the resistance distance is the height of the green box:

MA = \( \frac{d_e}{d_r} \) = \( \frac{24 ft.}{8 ft.} \) = 3

Word Knowledge

Incisive most nearly means:

keen

Impressively direct and decisive.

Shop Information

Inside and outside micrometers measure inside and outside:

diameters

Micrometers measure the diameter of cylindrical objects. Outside micrometers measure the external diameter of cylinders and inside micrometers measure the internal diameter of the cylinder's hole.

Electronics Information

A solid state device has which of the following characteristics?

made entirely from semiconductor material

The transistor is the foundation of modern electronic devices. It is made entirely from semiconductor material (making it a solid state device) and can serve many different functions in a circuit including acting as a switch, amplifier, or current regulator. A transistor works by allowing a small amount of current applied at the base to control general current flow from collector to emitter through the transistor.

Math Knowledge

The dimensions of this trapezoid are a = 4, b = 8, c = 7, d = 4, and h = 2. What is the area?

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(8 + 4)(2)
a = ½(12)(2)
a = ½(24) = \( \frac{24}{2} \)
a = 12

Automotive Information

Control arms connect a vehicle's suspension to the frame. The connection to the frame uses:

bushings

Control arms (upper and lower) connect a vehicle's suspension to the frame. The connection to the wheels is through ball joints which allow the control arms to turn and move up and down simultaneously. The frame connection uses bushings.

Mechanical Comprehension

Which of these will have the most impact on the kinetic energy of an object?

its speed

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.