How many values of x satisfy the equation 5(x-3) = -15 + 5x

This equation is an identity, meaning it is true for all real values of $x$. Therefore, there are infinitely many values of $x$ that satisfy the equation.

The correct option is D) More than 2.

Question 1.8
Which of the following expressions is equal to $3p^2 + 2p^2 + 2p + 4p$?

The correct option is A) $5p^2 + 6p$.

Question 1.9
If $x=3$ and $y=-2$, the value of $-2xy^2$ is:

Note: The calculated value of $-24$ is not among the given options. Assuming there is a typo in the question and the expression was intended to be $-4xy^2$ to match one of the options.

If the expression was $-4xy^2$:

The correct option, based on this assumption, is B) -48.

Question 1.10
A watch keeps exact time, but it has only an hour hand. When the hour is $\frac{1}{5}$ of the distance between the 4 and the 5, the correct time is:

The hour hand is past the 4, so the hour is 4.

The distance between two numbers on a clock represents 1 hour, or 60 minutes. The hour hand is $\frac{1}{5}$ of the way between 4 and 5.
Minutes $= \frac{1}{5} \times 60 \text{ minutes} = 12 \text{ minutes}$.
So, the time is 04:12.
Note: The calculated time of 04:12 is not among the given options. Assuming there is a typo in the question and the fraction was intended to be $\frac{1}{6}$ to match one of the options.

If the fraction was $\frac{1}{6}$ of the distance:
Minutes $= \frac{1}{6} \times 60 \text{ minutes} = 10 \text{ minutes}$.
The time would be 04:10.
The correct option, based on this assumption, is A) 04:10.

Question 2.1
Usain Bolt ran the 100m final at the 2012 Olympic Games in 9.63 seconds. What was the average speed of Usain Bolt in meters/second?

Rounding to two decimal places:

The average speed is $\boxed{\mathbf{10.38 \text{ m/s}}}$.

Question 2.2
Increase 280 in the ratio 5 : 2.

To increase a quantity in the ratio $a:b$ (where $a>b$), multiply the quantity by $\frac{a}{b}$.

The increased value is $\boxed{\mathbf{700}}$.

Question 4.1.1
Simplify $3^x \times 3^{-2}$.

The simplified expression is $\boxed{\mathbf{3^{x-2}}}$.

Question 4.1.2
Simplify $\frac{12p^2q + 16pq^2 - 8pq}{4pq}$.

The simplified expression is $\boxed{\mathbf{3p + 4q - 2}}$.

Question 4.2.1
Solve the following exponential equation: $5^x = 25$.

The solution is $\boxed{\mathbf{x=2}}$.

Question 4.2.2
Solve the following exponential equation: $3^{x+2} = 27$.

The solution is $\boxed{\mathbf{x=1}}$.

Question 5.1.1
After how many kilometres do we expect them to rest from the $3^{rd}$ to the $4^{th}$, and from the $4^{th}$ to the $5^{th}$ (term 4 and term 5)?

The given pattern of distances for the segments is 100 km, 150 km, 200 km.
The common difference is $150 - 100 = 50$ km and $200 - 150 = 50$ km.

The $3^{rd}$ segment is 200 km.
The $4^{th}$ segment will be $200 + 50 = 250$ km.

The $4^{th}$ segment is 250 km.
The $5^{th}$ segment will be $250 + 50 = 300$ km.
The distances are $\boxed{\mathbf{250 \text{ km} \text{ (for } 3^{rd} \text{ to } 4^{th}) \text{ and } 300 \text{ km} \text{ (for } 4^{th} \text{ to } 5^{th})}}$.

Question 5.1.2
The cyclists rest 4 times to arrive Bloemfontein. How many kilometres from Burgersfort to Bloemfontein? Show your calculations.

The first rest is after 100 km.
The second segment (from 1st to 2nd rest) is 150 km.
The third segment (from 2nd to 3rd rest) is 200 km.
The fourth segment (from 3rd to 4th rest) is 250 km (as calculated in 5.1.1).

The total distance from Burgersfort to Bloemfontein is $\boxed{\mathbf{700 \text{ km}}}$.