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Math Knowledge

The endpoints of this line segment are at (-2, 2) and (2, -6). What is the slope-intercept equation for this line?

y = -2x - 2

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -2. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 2) and (2, -6) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-6.0) - (2.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)
m = -2

Plugging these values into the slope-intercept equation:

y = -2x - 2

Automotive Information

Which of the following regulates the opening and closing of the intake and exhaust valves in each cylinder in time with the motion of the piston?

camshaft

The camshaft is linked to the crankshaft through a timing belt and regulates the opening and closing of the intake and exhaust valves in each cylinder in time with the motion of the piston. An engine designated OverHead Camshaft (OHC) locates the camshaft in the cylinder head. An engine with Double OverHead Camshaft (DOHC) has two camshafts, one to regulate the intake valves and one to regulate the exhaust valves.

Math Knowledge

Which of the following statements about a parallelogram is not true?

opposite sides and adjacent angles are equal

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

General Science

Bronchioles, alveolus, and capillaries are vital parts of which bodily system?

respiration

The trachea branches into the left and right bronchi which each lead to a lung where the bronchi subdivide into smaller tubes called bronchioles. Each bronchiole ends in a small sac called an alveolus which allows oxygen from the air to enter the bloodstream via tiny blood vessels called capillaries.

General Science

Saturated fats can __________ LDL ("bad") cholesterol while unsaturated fats can __________ it.

raise, decrease

Saturated fats can raise LDL ("bad") cholesterol while unsaturated fats can decrease it.

Arithmetic Reasoning

If \(\left|a\right| = 7\), which of the following best describes a?

a = 7 or a = -7

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

General Science

In the classification of life, bacteria, archaea and eukaryota are which of the following?

domains

The broadest classification of life splits all organisms into three groups called domains. The three domains of life are bacteria, archaea and eukaryota.

Mechanical Comprehension

For a hydraulic system, pressure applied to the input of the system will increase the pressure in which parts of the system?

all of these are correct

Pascal's law states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. For a hydraulic system, this means that a pressure applied to the input of the system will increase the pressure everywhere in the system.

Arithmetic Reasoning

What is c⁵ x 4c⁷?

4c¹²

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

c⁵ x 4c⁷
(1 x 4)c^{(5 + 7)}
4c¹²

General Science

Large, puffy, mid-altitude clouds with a flat base and a rounded top describe which of the following?

cumulus clouds

Cumulus clouds are large, puffy, mid-altitude clouds with a flat base and a rounded top. These clouds grow upward and can develop into a cumulonimbus or thunderstorm cloud.