Algebra Answers

Polynomial Inequalities:

1) (x-5) (x+2) < 0

show your number line and state your answer in interval notation

Synthetic Division:

1. (2x^4 + 7x^3 + x - 12) / (x+ 3)

(show step by step)

Let g(x) be the transformation of f(x)= x2. Write the rule for g(x) using the change described.

1. compression vertically by a factor of 0.5 followed by a reflection

across the x-axis and a vertical shift 3 units down. _____________

2. horizontal stretch by a factor of 3, vertical compression by a factor of 1/3 followed by a horizontal shift right 5 units. ___________

In 10 minutes, a heart can beat 700 times. At this rate, in how many minutes will a heart beat 140 times? At what rate can a hear beat?

Given the equation in X, (m + 1)X^2+ 4(m – 1)X + 4 – m = 0, determine m in each of

the following cases:

a) The equation has a double root, what is the root? (3marks)

b) the equation is of the first degree. What is the root? (3marks)

c) 0 is a root of the equation. What is the other root? (3marks)

d) the equation has two roots of different signs (3marks)

e) the equation has two positive roots. (3marks)

Use substitution y = 2^X to solve for X the equation 2^(2X +1)– 2^(X +1) + 1 = 2X

a) Determine whether set S given below is a basis for ℝ 3 . If not, explain why.

S= {(1,0,0),(0,1,0),(0,0,0)}

b) Find the rank of matrix D given below.

D= [0 3 9 0]

[-2 -1 1 -1]

[0 -1 -3 1]

A car tows a trailer and is restricted to pull a mass of not more than 500kg, the mass of each canned fish is 440g and the mass of each empty box is 27g. There are 15 boxes each contains 36 canned fish, determine the total mass in kg of each box