Algebra Answers

given 4b-a=4 and ab=8 when the equations are solved for a and b simultaneously, one of the values of a is

On a scale drawing of a park, a triangular area has side lengths 8cm, 15cm, and 17cm. If the triangular area of the actual park has a perimeter of 160m, what is the length of its shortest side?

2=x-3/2

The development budget of a municipality in Ghana includes expenditure on Feeder Roads, Schools and Water supply. The expenditure on roads, schools and water supply

are in the ratio 7:15:2. If the expenditure on roads is GH¢28,000,000.00, Find the expenditure on;

(i) Schools

(ii) Water supply

(iii) What is the total budget for these three projects.

(b)The cost of maintaining the municipality libraries is GH¢900,000.00 and this is met from the expenditure on schools. What percentage correct to three significant figures, of the expenditure on schools is spent on maintaining libraries.

C. After making a down payment of GH¢4000 for an automobile, the municipality paid GH¢400 per month for 36 months with interest charged at 12% per year compounded

monthly on the unpaid balance.

(i) What was the original cost of the car?

(ii) What portion of the Municipality’s total car payments went toward interest

charges?

Three students, A, B and C, received a Stadio Mathematics award for their top performance. They have decided to split the award as follows: i. Student A receives R10 000 plus 1 5 of what then remains; ii. Student B then receives R16 000 plus 1 4 of what then remains; and iii. Student C then receives the rest, which is R18 000. How much is the original monetary award? Which student receives the most money?

After a long Saturday soccer match. Stadio soccer players decided to go to a local restaurant for a meal. They agreed to equally split the total cost of the meal. After everything was eaten, the cost, amounting to R28.80, arrived at the table. Three of the players noticed that they had left their cash at home. However, the remaining players agreed to pay R0.80 more to cover the missing amount. How many players were originally going to pay for this meal?

A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 128 responses, but the responses were declining by 25% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 11 days after the magazine was published, to the nearest whole number

Pew Research Center reported that among mothers, family size is shrinking. Suppose we are to randomly select one mother (age 40 to 44) and record the number of children she has. Here is a probability model.

Number of Children

1

2

3

4+

Probability

0.22

0.41

0.24

0.13

(a) Explain why this is a valid probability model.

(b) Explain why events “have 1 child” and “have 2 children” are mutually exclusive

For each of the following write the event using proper notation and find the probability:

(c) Find the probability that a randomly selected mother has less than 2 children.

(d) Find the probability that a randomly selected mother has 1 or 2 children. 

(e) Find the probability that a randomly selected mother does not have 4 or more children.

Complete the square of the terms inside the square brackets:

ax² + bx + c = a [x2 + ( b/a) x + c/a]

Evaluate the following polynomial expression using Horner’s rule. Assume the value of x

is 3.

𝑃(𝑥) = 10x⁵ + 6x⁴+ 3x³ − 6x² + 8𝑥 + 15

Show all the intermediate steps.