Algebra Answers

( a) solve for k in the equation -8+44=-20k+80 and explain each step
( b) factorise the following quadratic expressions:
( i) x2 + 14x +24
( ii) t2+12t+35
( iii) m2 + 10m -24
( iv) p2 +8p -84
( v) y2 -4y-32
( vi) x2-7x-18
( vii) v2 - 9v +20
( viii) v2 -12v +32

( c) equate the expression in (b) above to 0 and find the two values of the variables for which the equation will be true

For each of the following number sequence below,
1.state the first term , and write the next four terms of the sequence
2. Find the common difference
3.find the general Th for the sequence
4.write down the input and output value of the five terms of the sequence in a table
5.represent the number sequence on a coordinate plane in a graphic form
6.write down the number sequence of positive multiples of three starting at six
7. 9;14,19;...
8. 3:7;11;....
9. 8;15;22;...
10. 4 ;11,18

The sum of arithmetic progression is 20, the first term being 8 and the common difference is -2. Find the number of terms in the series.

Draw pictures to represent the following:
i) 3/2* 2/3
ii) 25.0 + 01.0 + 1
iii)7/8<12/13

iv) 0.1>0.08
v)1/3 of 2/5

X= {xIx is an even number,1<x>8} write this in set in roster method

1.phiwe bought a packed of bananas she shred half of with her cousin then she shared her half of the bananas equally with her brother again. Now phiwe has 3 bananas. How many bananas were in the packet.
2. Phumza bought 12 metres of curtaining. Some of the material came from a roll with a slight flaw in it and cost R7 per metre instead of the normal R8 per metre. If phumza paid R98,50 altogether, how many metres of the damaged material did she buy?
3.Nancy buys 15 of ribbons . Her sister buys 6 metres of less ribbons but pays twice per metre. Between them the pay R6,00 .what is the price per metre of the two different types of ribbons?
4. You bought 10 shirts , some at R4,00 and some at R4,50 each. If the total cost was R43,50 , how many of each type did you buy?

What type of questions indicate the interpretation of multiplication as scaling?

Which explains whether or not the function represents a direct variation?

This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
This function represents a direct variation because it has a positive, constant rate of change of $10 per hour.
This function does not represent a direct variation because it does not represent the cost for 1 hour.
This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

In Hepburn’s Speed Model, the coefficients of vehicles are indicated for C and D. As the chief of operations in your organization, you are responsible for presenting the yearly budget for the semi trucks in your company’s inventory. Since your safety officer is insisting that each of your drivers must maintain an average speed of 55mph, what would be the vehicle operating cost of your company for each semi-truck in cent per mile?

Using the algebraic expression 2(5x +2y ) + 3x + 6y -10 , identify and explain the following: term , factor , variable, constant and coefficient