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Math Knowledge

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

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

General Science

When compared to eukaryotic cells, prokaryotic cells are:

less complex

Cells are classified into one of two groups based on whether or not they have a nucleus. Eukaryotic cells have a nucleus, prokaryotic cells do not have a nucleus and therefore have a less complex structure than eukaryotic cells.

General Science

In the food chain, bacteria and fungi convert the organic matter in the dead bodies of plants and animals into simple nutrients. Bacteria and fungi are:

decomposers

Decomposers (saprotrophs) are organisms such as bacteria and fungi that break down the organic matter in the dead bodies of plants and animals into simple nutrients.

General Science

In the heart, the __________ artery and vein manage blood flow to the lungs.

pulmonary

The two largest veins in the body, the venae cavae, pass blood to the right ventricle which pumps the blood to the lungs through the pulmonary artery. Blood picks up oxygen in the lungs and returns it to the left atrium via the pulmonary vein.

Mechanical Comprehension

What type of load acts on a relatively small area of a structure?

concentrated load

A concentrated load acts on a relatively small area of a structure, a static uniformly distributed load doesn't create specific stress points or vary with time, a dynamic load varies with time or affects a structure that experiences a high degree of movement, an impact load is sudden and for a relatively short duration and a non-uniformly distributed load creates different stresses at different locations on a structure.

Mechanical Comprehension

If the green box weighs 25 lbs. and 75 lbs. of force is applied 5 ft. from the fulcrum at the blue arrow, how far from the fulcrum would the green box need to be placed to balance the lever?

15 ft.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{75 lbs. \times 5 ft.}{25 lbs.} \) = \( \frac{375 ft⋅lb}{25 lbs.} \) = 15 ft.

Word Knowledge

The con man's fraud involved selling swampland to gullible investors.

deceit

Trick.

Electronics Information

The valence shell of a semiconductor is how full of electrons?

half full

Semiconductors have valence shells that are exacly half full and can conduct electricity under some conditions but not others. This property makes them useful for the control of electrical current.

Word Knowledge

Mediate most nearly means:

arbitrate

To come between parties in order to reconcile.

General Science

The hottest of Earth's atmospheric layers is which of the following?

thermosphere

Temperatures again increase with altitude in the thermosphere which is the hottest (4,530 °F / 2,500 °C) atmospheric layer due to direct exposure to the Sun's radiation. However, the gas in this layer is highly diluted so even though the atoms of gas may be very high in temperature, there are too few of them to effectively transfer much heat.