2a Let              

  1    2   −1
A   =        4  k    −2
0    0   −1

−k      2     k − 4
B =       4     −1       −2
0       0     k − 8

 
i    Express AB in the simplest form
ii     Find the inverse of A in terms of k, stating the condition under which A−1 exist
x  0 
iii     Given that X = y and C =  46 , k=5 use the inverse of A to solve the equation AX=C

2b Given that a and b are positive, solve the simultaneous equation
a = 3b log3 a + log3 b = 2
10 marks 2c P (x) = x3 + x2 + ax + b. If P(x) is divided by (x                                        2), the remainder is                                              7 and If P(x) is divided by
(x + 1), the remainder is 32. Find the value of a and b
3a A transformation is defined by the 2 × 2 matrix
A   = a b a a + b a
 
where a and b are scalars. If n is an odd integer, prove that
An     =  bn−1A​

Daryl factors the polynomial p(x)=x3+x2−26x+24 to rewrite it as p(x)=(x+6)(x−4)(x−1). which equations must be true? there may be more than one correct answer. select all correct answers. p(1)=0 p(−4)=0 p(−1)=0 p(6)=0 p(4)=0 p(−6)=0

1. how do you convert the repeating, nonterminating decimal 0. to a fraction? explain the process as you solve the problem.

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96