Algebra Answers

9: If your starting salary were $40,000 and you received a 3% increase at the end of every year for 15 years, what would be the total amount, in dollars, you would have earned over the first 16 years that you worked?
Round your answer to the nearest whole dollar, and express your answer without using commas.
Answer: $_______

10: In a geometric sequence, the term ^a + 1 can be smaller than the term ^a n
A: False
B: True

: What is the value of the fourth term in a geometric sequence for which a^1 = 15 and r = 1/3
Express your answer as a fraction.
Answer:_______


: The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3. What is the common ratio in this sequence?
Answer:___________

: What is the sum of the first five terms of a geographic series with a^1 = 20 and r = ¼
Express your answer as an improper fraction in lowest terms without using spaces.
Answer:_____

A contractor needs to order the glass for a window. The window is in the shape of an isosceles triangle and the height of the window is 2.5 times the base width. If the width of the base must be 85 cm, what is the largest window area the contractor can use?

According to Descartes' rule of signs, how many possible negative real roots could the following polynomial function have?
f(x) = 3x^4 – 5x^3 – 5x^2 + 5x + 2

A: Two or Zero
B: Three
C: Four
B: Three or One

: Identify the relative minimum value for the function shown below.
g(x) = x^3 – 3x^2 + 2
Answer:________

1: In a ___ sequence, the ratio between consecutive terms is constant.

: What is the equation for the vertical asymptote of the function shown below?
f(x) = 3x^4 – 3
------------
2x – 5

A: y = x^3 – 2
B: x = 3/2
C: x = 3/5
D: x = 5/2

: The number 4 is an upper bound for the set of roots of this polynomial function
f(x) = 3x^4 – 5x^3 – 5x^2 + 5x + 2
A: True
B: False

: Which of the following correctly describes the domain of the function shown below?
r(x) = 2x
---------
x^2 – 1

A: {x:x = ± 1}
B: {x:x + 1}
C: All real numbers
D: {x:x=0}

A furniture company is faced with the following the price-demand function,
revenue function, and cost function:

p(x) = 90 − 5x
R(x) = xp(x)
C(x) = 250 + 15x
where p(x) is the price in dollars at which x hundred chairs can be sold and
R(x) and C(x) are in thousands of dollars.

a. Give the revenue R for producing 1200 chairs.
b. Find the production level that gives the break-even point.
c. Find the production level that gives the maximum revenue and the maximum
profit.

Consider the quadratic function f(x) = −4x^2 − 8x − 3

a. Describe the transformations we would apply to the basic function g(x) = x^2
to obtain f.

b. What is the vertex and axis of symmetry

13: According to the fundamental theorem of algebra, how many zeros does the polynomial below have. f(x) = x^5 – 12x^3 + 7x – 5
Answer:_____

14: If you know that 7 - √5 is a root of a polynomial function, then the name given to 7 + √5 , which is another root of that same function, is the radical________?

15: Give the equation of the horizontal asymptote of the function shown below.
g(x) = 2x/ x + 5

A: x=2
B: y= 2/5
C: y = 2
D: y = -5

10: Find the remainder of the division problem shown below.
(x^4 + x^3 – 3x – 3) ÷ (x-2)
Answer:________

12: Is the term (x+2) a factor of the polynomial shown below?
f(x) = x^3 – 10x^2 + 27x – 12

A: Yes, the remainder is 0.
B: Yes, the remainder is -114.
C: No, but the remainder is 0.
D: No, but the remainder is -114.

1: What is the degree of the following monomial?

-2f^2 g^3 h^5
Answer:_______

2: which of the following expressions is a polynomial?

A: f(x) = -2.1x^7 + 3x^2 + 17/2x

B: f(x) = -1/5x^2 + 4.5x + 2^x

C: f(x) = 4/x - 11x^2

D: f(x) = -3x^4 + 8x^2 – 2√x + 1

3: What is the leading coefficient of this polynomial?
f(x) = 3x^2 – 1/5x^5 + 7x^10
Answer:_____

4: What is another name for this polynomial, based on the number of terms it contains?
g(x) = 5x^9 + 17x^5
Answer:____

5: Based on its degree, what kind of polynomial is this?
h(x) = -x^2 + 2x – 5
Answer:________

6: For the polynomial shown below, find f(1)
f(x) = 3x^4 – x^3 + 4x – 2
Answer:_______