Polynomial Arithmetic
Simplify the expression
3 + 2(x+4)(x-4).
2x2 - 29
C = 2πr
What is the formula that represents the radius of a circle in terms of its circumference?
r = C/2π
What is the sum of the roots of the equation
2x2 + 5x - 3 = 0?
-2.5
Jamie has a plan to save money for a trip and puts 5 pennies in a jar today. Tomorrow, she puts the initial amount plus another 5 pennies. Each day she puts 5 more pennies than the previous day. Let f(d) represent the amount of pennies she puts in the jar on day d. What does f(10) = 55 mean?
She puts 55 pennies in the jar on day 10.
Simplify the expression
(3x5 + 8x3) - (7x2 - 6x3).
3x5 + 14x3 - 7x2
P = 2W + 2L
What is the formula that shows how the length of a rectangle can be determined from the perimeter and the width?
L = (P - 2W)/2 or equivalent
What is one solution of the equation
x2 - 21.75x = -15.75?
x = 0.75 or x = 21
The table shows the temperature in degrees F recorded at a weather station hours after midnight yesterday.
h 0 1 2 3
t 45 43 39 40
What is the value of t(2)? Is t(2) > t(1) or is t(2) < t(1)?
39, and t(2) < t(1)
The polynomial (2x - 1)(x2 - 2) - x(x2 - x - 2) can be rewritten in standard form
ax3 + bx2 + cx + d.
What are the values of a, b, c, and d?
a = 1, b = 0, c = -2, d = 2
A = (2πr)h + πr2
What is a formula for h in terms of the other variables that can be used to find the height of a right circular cylindrical pillar?
h = (A - πr2)/2πr
How many solutions does the system of equations have? Be *clear* with your language!
y = 1 - x2
y = 2 - x
No REAL solutions
During a power outage, the temperature inside a house reached 88 F before the AC turned back on. Let f(x) represent the temp. in the house x minutes after the AC came back. What is the meaning of the statement f(30) = 76?
What function statement represents the temperature in the house right when the AC returned?
30 minutes after the AC came back on, the temperature in the house was 76 F. The statement f(0) = 88 represents when the AC returned.
Simplify the expression
-3a(a+b-5)+4(-2a+2b)+b(a+3b-7)
-3a2 + 3b2 - 2ab + 7a + b
V = 2h2L
What is an equation for the height of this rectangular box in terms of the volume and length?
h = √ (V/2L)
x + y = 5
x2 + y = 11
One point of intersection is (3,2). What are the coordinates of the other point?
(-2, 7)
The cost to manufacture x pairs of sunglasses can be represented by the function C(x). Which equation written in function notation represents the cost of $398 to manufacture 4 pairs of sunglasses?
C(4) = 398
The function f is defined as
f(x) = x(x2 - 4) - 3x(x - 2).
What is the equivalent form of the function in the form
f(x) = __(x - __)(x - __)
and what are the zeros of the function?
f(x) = x(x - 2)(x - 1)
x = 0 and x = 2 and 1
A = 16s2 + 25
Solve for s.
s = √ [(A-25)/16] or equivalent
The height, in feet, of a ball above ground t seconds after being thrown is modeled by
-16t2 + 40t + 3. What is the meaning of the 3 in the expression?
The ball was thrown from a height of 3 feet.
The value V of an investment, measured in thousands of dollars, is given by the function V(t), where t represents the number of years since 1995. What is an equation written using function notation that represents an investment with a value of $8,000 in 2005?