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Arithmetic Reasoning

What is \( 5 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)

17\( \sqrt{7} \)

To add these radicals together their radicands must be the same:

5\( \sqrt{28} \) + 7\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
10\( \sqrt{7} \) + 7\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

10\( \sqrt{7} \) + 7\( \sqrt{7} \)
(10 + 7)\( \sqrt{7} \)
17\( \sqrt{7} \)

Word Knowledge

Civility most nearly means:

courtesy

Politeness.

Math Knowledge

This diagram represents two parallel lines with a transversal. If d° = 140, what is the value of z°?

For parallel lines with a transversal, the following relationships apply:

angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with d° = 140, the value of z° is 40.

General Science

Examples of tertiary consumers include:

sharks

Tertiary consumers eat primary consumers and secondary consumers and are typically carnivorous predators. Tertiary consumers may also be omnivores. Examples include wolves, sharks, and human beings.

General Science

Which of the following is a decomposer?

fungi

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

Convert 0C° to F°.

To convert from C° to F° use:

\(F° = {9 \over 5}C° + 32\)

\(F° = {9 \over 5}(0) + 32\)

\(F° = 0 + 32 = 32\)

Electronics Information

The formula specifying Ohm's law is which of the following?

V = IR

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

General Science

In the foood chain, producers serve as a food source for other organisms. Typical producers are plants that can make their own food through photosynthesis and certain bacteria that are capable of converting inorganic substances into food through:

chemosynthesis

Producers (autotrophs) serve as a food source for other organisms. Typical producers are plants that can make their own food through photosynthesis and certain bacteria that are capable of converting inorganic substances into food through chemosynthesis

Mechanical Comprehension

Tension is a force that does which of the following?

stretches an object

Tension is a force that stretches or elongates something. When a cable or rope is used to pull an object, for example, it stretches internally as it accepts the weight that it's moving. Although tension is often treated as applying equally to all parts of a material, it's greater at the places where the material is under the most stress.

General Science

During continental drift, the drifting plates move across which of the following?

liquid mantle

The crust and the rigid lithosphere (upper mantle) is made up of approximately thirty separate plates. These plates more very slowly on the slightly more liquid mantle (asthenosphere) beneath them. This movement has resulted in continental drift which is the gradual movement of land masses across Earth's surface. Continental drift is a very slow process, occurring over hundreds of millions of years.