Linear Equations and Functions
What is the slope of the line passing through the points (2,5) and (6,9)?
4/4 = 1
Solve the quadratic equation for x:
x^2 - 5x + 6 = 0
x = 2
x = 3
A population of bacteria doubles every 4 hours. Initially, there are 200 bacteria in the culture.
1) Write an exponential function P(t) that models the population of bacteria after t hours.
1) P(t) = 200 * 2^t/4
Given the functions in the image:
https://photos.google.com/photo/AF1QipNbSyA8u606LFxa_Sk7MAAfKb76NBchrKDJsx32
f(g(x)) = 2x^2 + 1
Simplify the expression:
https://photos.google.com/search/_tra_/photo/AF1QipPKr9MrMRdBKOsV_WBasMUTqcKQ5LcV_H1pamCb
4xy^6
Write the equation of a line in slope-intercept form that passes through the point (3, -2) and has a slope of m = 4.
y = 4x - 14
Solve the quadratic equation using the quadratic formula:
3x^2 - 7x + 2 = 0
x = 2
x = 1/3
A population of bacteria doubles every 4 hours. Initially, there are 200 bacteria in the culture. The given function is:
P(t) = 200 * 2^t/4
How long will it take for the population to reach exactly 10,000 bacteria?
Approximately 22.58 hours
The function h(x) is given as:
https://photos.google.com/photo/AF1QipPxxe-L2uIzPTp0dN8QF97TloiIqmPv-9VlzXxg
f(x) = sqrt(x)
g(x) = 3x^2 + 5
Simplify the expression:
https://photos.google.com/photo/AF1QipPa5rMx1WmfxeZSwKF1WCq7Iz_VNTxVefUT3MYF
6y
A small business charges a flat fee of $50 for a repair service, plus an additional charge per hour of work.
1) Write a linear equation that represents the total cost, C, of a repair job as a function of the hours worked, h, given that the cost for 4 hours of work is $150.
2) If one customer is charged $175 and another is charged $275, how many total hours did the two customers' repairs take?
The total number of hours worked for the two customers is 14 hours.
Find the quadratic equation for the graph, f(x).
Graph:
https://photos.google.com/photo/AF1QipOQx8e-UQ907bS85w7NaOgcgfBf5zUYSmqf4wz8
-2x^2 + 8x - 3
Use the definition of logarithm to solve the following equation:
https://photos.google.com/photo/AF1QipPd8AoGwlrfRnO1gAxqG8oHClUlWMNvzNWhKgJt
x = -1.45
Find the inverse of the function:
f(x) = 2x+3 pretend this is a fraction.
---------
x - 4
The science quad at Julian's school measures 120ft by 90ft. Julian begins walking at a constant rate diagonally from the Northwest corner of the quad to the Southeast corner and this takes him 20 seconds.
1) Find the parametric equations (x(t), y(t))
x(t) = 6t
y(t) = -9/2 + 90
Find the point(s) of intersection between the line
y = 2x + 4 and the function f(x) = x^2 - x - 6
The functions intersect at the coordinates:
(5,14) and (-2,0)
A ball is thrown vertically upward from the top of a building. If the ball is thrown with an initial velocity of 48 ft/s from a building 32 ft tall:
1) Write the equation for the height of the ball as a function of time.
2) Find the maximum height the ball reaches algebraically.
1) h(t) = -16t^2 + 48t + 32
2) 68 feet at 1.5 seconds.
Use the definition of logarithm to solve the following equations:
https://photos.google.com/photo/AF1QipNm8bF6ecTQ7mjcPKvmFfjBNmfg50bU0_O7ovW2
4.49
Find the inverse function f(x), which determine the weight of a shipment based on its cost. f(x) represents dollars and x represents weight of the shipment in pounds.
1)
y = 10x + 25
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5
2) If the cost of a shipment is $35, what is the weight of the shipment?
A soccer field measures 100 yards long (north-south) and 60 yards wide (east-west). A player starts at the southwest corner of the field and runs diagonally to the northeast corner which took them 25 seconds.
1) Write parametric equations (x(t), y(t)).
2) What are the player's coordinates after 10 seconds.
1) x(t) = 2.4t y(t) = 4t
2) (24, 40)
A delivery company charges a base fee for a package and an additional cost per mile. A customer paid $20 for a delivery over 10 miles, and another customer paid $35 for a delivery over 25 miles. However, for deliveries exceeding 50 miles, the company charges an extra flat fee of $10.
1) Write a piecewise linear function f(x) that represents the total delivery cost, where x is the number of miles.
2) What is the total cost for a 60-mile delivery?
3) At what mileage does the cost of delivery reach $100?
1) f(x) = { x + 10 if <= 50
{ x + 20 if x > 50
2) Cost for a 60-mile delivery is $80.
3) Mileage for a $100 delivery is 80 miles.
A farmer is building a rectangular pen along a river, using the river as one side of the pen. The farmer has 240 feet of fencing available to enclose the other three sides (two widths and one length).
1) Write an equation for the area of the pen as a function of the width.
2) What width maximizes the area of the pen?
3) What is the maximum area?
1) A(w) = -2w^2 + 240w
2) w = 60 feet
3) 7200 square feet
The population of a city grows according to the formula:
P(t) = 50,000 * e^0.03t
1) How many years will it take for the population to double?
2) If the population reaches 80,000, how long has it been growing?
1) Approximately 23.10 years.
2) Approximately 15.67 years.
The functions f(x) and g(x) are defined as:
https://photos.google.com/photo/AF1QipPNICAJAnpB1O5uuSz4aPDLRjNvE4gNhSOFdOq8