Algebra Answers

Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?

Jemima has three boxes whose total weight is 51 1

5 kg. Box B weighs 5 1

2 kg more than box A and box C

weighs 3 1

5 kg more than box B. Choose the correct statement.

[1] Box A weighs 17 5

6 kg.

[2] Box C weighs 21 1

30 kg.

[3] Box A weighs 42 1

2 kg.

[4] Box B weighs 12 1

3 kg.

The equations of three quadratic functions are given below:

(i) y = 2x2 + 12x + 18

(ii) y = −3x2 − 5x + 3

(iii) y = x2 + 2x − 5

Determine the discriminant of each function and the number of x-intercepts that the parabola has. Choose

the correct sentence. The function described in

[1] (i) has no discriminant and the parabola has no x-intercepts

[2] (ii) has a negative discriminant and the parabola has two x-intercepts

[3] (i) has a zero discriminant and the parabola has one x-intercept

[4] (iii) has a positive discriminant and the parabola has one x-intercept

The value of a car when new is R224 000,00. It is estimated that the value of the car will decrease at the

rate of 11% per year. Answer the following questions:

a. Determine the exponential function that describes the value of the car y years after it was bought.

b. Determine the value of the car six years after it was bought.

use pascals triangle to expand the binomical expression (1+2x)^3?

Carl and Dennis are brothers. The sum of their ages is 29. In 6 years' time Carl will be the same age as Dennis was 3 years ago.

3+x² =-3

Multiply out (3x³ + 4x - 5)(2x³ - 8x² + 2) using polynomial long multiplication.

3.Four men are walking late at night. Together they have one flashlight with a weak battery, so that it can only light the immediate vicinity. They come to a bridge, which is so rickety that only two can cross at the same time. Thus, in order to get to the other end of the bridge, two must cross with the flashlight and one must walk back across the bridge to return the flashlight (they cannot risk throwing it), until all are over. The men can walk at different maximum rates. The slowest needs 10 minutes to cross the bridge, the next 5 minutes, the next 2 minutes and the quickest 1 minute. When two walk together, they must proceed at the pace of the slower. They need to get everyone across the bridge in 17-minutes. Can they do it? How?

Solve each of the following problems using the problem solving strategies.

1.This is known as the "Die Hard Problem" because it appears in the film Die Hard with a Vengeance, shown in 1995. But in fact, this and other similar problems. are very old and have been the subject of much study, particularly by computer scientists who have developed various strategies for solving all water-jug problems. In the film, the characters played by Bruce Willis and Samuel L. Jackson must disarm a bomb by placing exactly four gallons of water on a scale. They have water since they are at a fountain, but they have only two jugs, one of which holds five gallons and the other three gallons. Can you solve the problem, and how quickly can you do it?