Evaluating & Linear Equations
if f(x) = x2-3x+10
what would f(4) be?
f(4) = 14
Solve and graph the inequality: 2x + 7 < 15.
x < 4 (open circle)
Write a system of equations for: A total of 15 coins (nickels and dimes) equals $1.10
n + d = 15
5n + 10d = 110
Solve for x:
x^2-9x + 20
x = 5
x = 4
A population of 500 triples every year. Write the exponential model:
y = a(b)^x
y = 500(3)^x
Solve for x: 5x - 12 = 3x + 8
x = 10
Solve the inequality and graph:
3(2x-4) ge 8x +2
x le -7 (closed)
Adult tickets are $10 and child tickets are $6. If 30 tickets were sold for $260, how many of each were sold?
A = 20 C = 10
Solve for x:
2x^2-5x-3
x = 3
x = -0.5 or -1/2
You deposit $5,000 into an account with 4% annual interest. How much is in the account after 8 years (round to nearest cent)?
$6842.85
Solve for x: 4(x - 2) + 6 = 22.
x = 6
Solve for x:
|x + 8| = 15
x = -23
x = 7
At a cafe, 2 coffees and 3 muffins cost $14.50.
4 coffees and 1 muffin cost $14.00.
Find the price of one coffee.
c = 2.75
Find the vertex of:
x^2 - 6x +5
(3, -4)
A car worth $25,000 depreciates by 12% each year. What is its value after 5 years (round to nearest cent)?
$13193.30
Solve for x: 6x + 5 = 2(3x + 2)
No solutions (parallel lines)
Solve for x:
|2x - 5| = 11
x = 8
x = -3
Two numbers sum to 49. The first number is 4 more than twice the second. Find both numbers
y = 15
x = 34
Solve by completing the square:
x^2 + 6x -2
x = -3 +- sqrt11
A substance has a half-life of 4 hours. If you start with 100g, how much remains after 12 hours?
12.5 or
25/2
2/3x-5 = 1/4x+10
Solve for x
x = 36
Solve and check for extraneous solutions:
|3x - 12| = x + 2
x = 7 and x = 5/2
A coffee shop owner wants to make a 10-pound "House Blend" that costs $12 per pound. He mixes "Morning Roast" ($10 per pound) with "Midnight Roast" ($15 per pound). How many pounds of each does he need?
Midnight Roast = 4
Morning roast = 6
Find max height and time
y = -t^2 + 8t
Max height of 16ft at 4 seconds
Compare two investments: Plan A offers 5% annual interest on $2,000. Plan B offers 4.5% interest compounded semi-annually on $2,200. Which is worth more after 10 years?
Plan B is worth more by $175.33