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Sample Practice Test Questions
Solve for z:
z2 + 6z - 13 = -z + 5
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
z2 + 6z - 13 = -z + 5
z2 + 6z - 13 - 5 = -z
z2 + 6z + z - 18 = 0
z2 + 7z - 18 = 0
Next, factor the quadratic equation:
z2 + 7z - 18 = 0
(z - 2)(z + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z + 9) must equal zero:
If (z - 2) = 0, z must equal 2
If (z + 9) = 0, z must equal -9
So the solution is that z = 2 or -9
What is \( \frac{4}{6} \) + \( \frac{4}{14} \)?
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 7}{6 x 7} \) + \( \frac{4 x 3}{14 x 3} \)
\( \frac{28}{42} \) + \( \frac{12}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{28 + 12}{42} \) = \( \frac{40}{42} \) = \(\frac{20}{21}\)
On Earth, acceleration due to gravity (g) is approximately __________.
9.8 m/s2
Newton's Law of Univeral Gravitation defines the general formula for the attraction of gravity between two objects: \(\vec{F_{g}} = { Gm_{1}m_{2} \over r^2}\) . In the specific case of an object falling toward Earth, the acceleration due to gravity (g) is approximately 9.8 m/s2.
The mechanical advantage of a third class lever is always:
less than one
A third class lever is designed to multiply distance and speed at the expense of effort force. Because the effort force is greater than the resistance, the mechanical advantage of a third class lever is always less than one.
An example of a third class lever is a broom. The fulcrum is at your hand on the end of the broom, the effort force is your other hand in the middle, and the resistance is at the bottom bristles. The effort force of your hand in the middle multiplies the distance and speed of the bristles at the bottom but at the expense of producing a brushing force that's less than the force you're applying with your hand.
Which of the following is a characteristic of batteries connected in series?
total voltage equals the sum of the individual battery voltages
You can multiply the voltage or the current supplied by individual batteries by connecting them together either in series or in parallel. The characteristics of batteries connected in series are that total voltage equals the sum of the individual battery voltages, total current equals the average of the individual battery currents, the positive terminal of one battery is connected to the negative terminal of the next, and one connection is made between each adjacent battery.
What is \( \frac{-7a^5}{7a^4} \)?
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
The electrical potential difference between two points is called:
voltage
Voltage (V) is the electrical potential difference between two points. Electrons will flow as current from areas of high potential (concentration of electrons) to areas of low potential. Voltage and current are directly proportional in that the higher the voltage applied to a conductor the higher the current that will result.
Someone who has Rh-factor __________ blood cannot receive blood with a __________ type.
negative, positive
Blood transfer is limited by the type and Rh factor of the blood. Someone who has Rh-factor negative blood cannot receive blood with a positive type but a person with Rh-factor positive type blood can receive Rh-negative blood. Type O negative blood is the universal donor because it can be given to a person with any blood type. Type AB positive is the universal recipient meaning someone with this blood type can receive any other type of blood.
All electricity is the movement of which subatomic particles?
electrons
All electricity is the movement of electrons which are subatomic particles that orbit the nucleus of an atom. Electrons occupy various energy levels called shells and how well an element enables the flow of electrons depends on how many electrons occupy its outer (valence) electron shell.