Mathematics Grade 12

1. Solve for [tex]$x$[/tex]:

[tex]\[
\begin{array}{ll}
1.1 & (3x - 2)^2 = 5 \\
1.2 & 23 = -9 \\
1.3 & z^2 - 3x^2 - x + 3 = 0 \\
1.4 & 2x^2 + 9x - 550 = 0
\end{array}
\][/tex]

2. Solve for [tex]$x$[/tex] and [tex]$y$[/tex] simultaneously:

[tex]\[
y - x + 3 = 0 \quad \text{and} \quad y^2 - x = 6 + y
\][/tex]

3. If [tex]$\pi$[/tex] and [tex]$n$[/tex] are rational numbers such that [tex]$\sqrt{\pi} + \sqrt{\pi} = \sqrt{7 + \sqrt{48}}$[/tex], calculate a positive value of [tex][tex]$m^2 + m^2$[/tex][/tex].

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Please let me know if you need further clarifications or corrections.



Answer :

Let's look at the problem and break down the solution:

Olivia initially starts with an amount of money and spends some of it on buying bagels. To find out how much money she has left, we will follow these steps:

1. Identify the initial amount of money Olivia has:
Olivia starts with 23 units of money.

2. Determine the number of bagels Olivia bought:
Olivia purchased 5 bagels.

3. Find out the cost of each bagel:
Each bagel costs 3 units of money.

4. Calculate the total amount of money spent on bagels:
To find out how much Olivia spent on the bagels, we multiply the number of bagels by the cost of each bagel.
[tex]\[ \text{Total money spent on bagels} = \text{number of bagels} \times \text{cost per bagel} \][/tex]
Substituting the given values:
[tex]\[ \text{Total money spent on bagels} = 5 \times 3 = 15 \][/tex]
So, Olivia spent 15 units of money on bagels.

5. Calculate the amount of money Olivia has left:
To find out how much money Olivia has left, we subtract the money spent on the bagels from her initial amount of money.
[tex]\[ \text{Money left} = \text{initial amount of money} - \text{money spent on bagels} \][/tex]
Substituting the given values:
[tex]\[ \text{Money left} = 23 - 15 = 8 \][/tex]
So, after buying the bagels, Olivia has 8 units of money left.

Therefore, Olivia spent 15 units of money on bagels, and she has 8 units of money left.