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Math Knowledge

Solve 3a + 2a = 9a - 9z + 8 for a in terms of z.

1\(\frac{5}{6}\)z - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

3a + 2z = 9a - 9z + 8
3a = 9a - 9z + 8 - 2z
3a - 9a = -9z + 8 - 2z
-6a = -11z + 8
a = \( \frac{-11z + 8}{-6} \)
a = \( \frac{-11z}{-6} \) + \( \frac{8}{-6} \)
a = 1\(\frac{5}{6}\)z - 1\(\frac{1}{3}\)

Electronics Information

Use Ohm's Law to calculate the value of resistance in this circuit if voltage is 40 volts and current is 2 amps.

20 Ω

Ohm's law specifies the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit: V = IR.

Solved for resistance, R = \( \frac{V}{I} \) = \( \frac{40}{2} \) = 20 Ω

Automotive Information

Which of the following is not a primary function of a vehicle's lubrication system?

increases fuel economy

The lubrication system lubricates engine components by putting an oil film between them to reduce friction and smooth engine operation, cools by absorbing heat from engine parts, seals the pistons and cylinders to contain combustion, cleans contaminants, and quiets engine noise.

Mechanical Comprehension

A wedge is most similar to what other type of simple machine?

inclined plane

The wedge is a moving inclined plane that is used to lift, hold, or break apart an object. A wedge converts force applied to its blunt end into force perpendicular to its inclined surface. In contrast to a stationary plane where force is applied to the object being moved, with a wedge the object is stationary and the force is being applied to the plane. Examples of a wedge include knives and chisels.

Automotive Information

A __________ is designed to drive a pair of wheels while allowing them to rotate at different speeds.

differential

A differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. A transaxle is a transmission that incorporates the differential in one package. Most front-wheel drive cars use a transaxle while rear-wheel drive cars use a transmission and separate differential connected via a drive shaft. The differential is incorporated into the drive axle which splits engine power delivered by the drive shaft between the two drive wheels. All-wheel drive cars typically use a transaxle that includes an output shaft to the rear differential.

Arithmetic Reasoning

What is the greatest common factor of 52 and 36?

The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 36 have in common.

Word Knowledge

Benevolent most nearly means:

altruistic

Kind, helpful.

General Science

In a eukaryotic cell, which organelles deal with proteins?

all of these deal with proteins

The nucleus of a eukaryotic cell contains the genetic material of the cell and is surrounded by cytoplasm which contains many organelles. Ribosomes produce proteins, endoplasmic reticulum helps synthesize proteins and fats, and Golgi apparatus prepares proteins for use.

Automotive Information

Which of the following is not a component in the engine lubrication system?

differential

In engine lubrication, oil remains in the oil pan until the engine is turned on. It then gets sucked up the pickup tube by the oil pump and pressurized. This pressure is moderated by the pressure relief valve and the oil is fed through the oil filter into the engine to lubricate it.

Arithmetic Reasoning

Which of the following is not an integer?

\({1 \over 2}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.