Unit 1
Algebra Review
Algebra Review
7(x + 10) – 8 = –6(x – 7) + 9
–11/13
An assembly line manufactures I-beams at a rate of 51 feet per second. Convert this speed to miles per hour (MPH), rounded to one decimal place.
34.8
Let h(t) be the height above ground, in feet, of a rocket t seconds after launching. Explain the meaning of h(2) = 350.
The rocket is 350 feet high 2 seconds after launch.
The temperature, f(t) of a cup of coffee, in degrees Celsius, after t minutes can be determined by the equation f(t) = 55(0.9)t + 20.
• What is the initial temperature of coffee?
• When will the coffee reach 26°C ?
• Initial Temperature: 20°C
• Approx. 21 minutes
Find a coterminal angle and a reference angle for the following angles:
• 495°
• 7𝝅/3
• 135°; 45°
• 𝝅/3
(x4y0)2 ⋅ x3
x11
The temperature of a solution is 29.1°C. Convert that to degrees Fahrenheit, one decimal place, using F = 95C + 32.
84.4°
A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) = −4.9t2 + 221t + 279.
Find the find the two times the rocket reaches 300 meters. Round to three decimal places.
0.095 seconds, 45.007 seconds
Rewrite the equation in exponential form.
log9(729) = y
What is the value of y?
9y = 729
y =3
Using a calculator, determine the value of cos(2𝜋/7). Round the value to four decimal places.
0.6235
x2 − 4x + 29 = 0
2 ± 5i
The electrical current, in amperes, in a circuit varies directly as the voltage. When 12 volts are applied, the current is 4 amperes. What is the current when 36 volts are applied?
12 amperes
The number of chirps heard by crickets in a minute can be used to estimate the temperature of the air, in degrees Fahrenheit. Using linear regression, estimate the temperature if 140 chirps are heard.
Chirps Temperature
81 54.5
97 59.5
103 63.5
123 67.5
150 72
182 78.5
195 83
y = 0.230666x + 37.67858
70 chirps (exact answer 69.97)
Solve for x. Leave the answer in exact (fractional or radical) form.
log (13x) = 1
10/13
Find the length of an arc that subtends a central angle of 8° in a circle of radius 18 meters. Round to 2 decimal places.
2.51 meters
Write the number 7.55 × 10−4 as a whole number or decimal.
0.000755
y varies inversely as x. If x = 3 then y = 7. Find y when x = 2.
10.5
On Black Friday, the price per unit in dollars of a cell phone production is modeled by p = 50 − 0.0175x, where x is in thousands of phones produced, and the revenue is represented by thousands of dollars is R = x ⋅ p.
Find the production level that will maximize revenue.
1429 thousands of phones
Write log5(25xy2) as a sum and/or difference of logarithms. Express powers as factors.
2 + log5x + 2log5y
A radio tower is 120 feet tall. A guy wire is attached from the top of the tower to an anchor point which is 30 feet from the base of the tower. Find the length of guy wire (in feet) and the angle A between guy wire and ground (in degrees). Round your answers to 2 decimal places.
Guy wire: 123.69 feet
Angle A: 75.96
Multiply, writing the final answer in scientific notation.
(6.1 × 1013) (5.4 × 1033)
3.294 × 1047
Hooke's law states that the distance that a spring is stretched by hanging object varies directly as the mass of the object. If the distance is 180 cm when the mass is 27 kg, what is the distance when the mass is 8 kg? Round to 2 decimal places.
53.33 cm
Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought four notebooks and four thumb drives for $84. Lisa bought three notebooks and two thumb drives for $49. Solve using a system of linear equations, using x for the price of a notebook and y as the price of a thumb drive.
4x + 4y = 84
3x + 2y = 49
Solution: $7 for notebook, $14 thumb drive
Solve for x:
log(x+4) − log(x+1) = 1
−2/3
(Why is this negative answer acceptable and not extraneous? When is an answer extraneous under the domain for logarithms?)
Use the Law of Cosines to find all three angles and all three sides of a triangle, given:
Angle A = 47°, b = 10, c = 9
a = 7.6
Angle B = 73.2°
Angle C = 59.6°