Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

(b) Using a scale of [tex]$2 \text{ cm}$[/tex] to 1 kilogram on the [tex]$x$[/tex]-axis and [tex]$2 \text{ cm}$[/tex] to [tex]$GHc 20$[/tex] on the [tex]$y$[/tex]-axis, copy and complete the table below for the relation [tex]$y = 20x + 20$[/tex], and draw the graph for the relation.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
[tex]$y$[/tex] & 40 & 60 & 80 & 100 & 120 & 140 & 160 & 180 & 200 \\
\hline
\end{tabular}

(i) From the graph, find the weight of meat that can be bought with [tex]$GHc 90$[/tex].

(ii) From the graph, find the cost of [tex]$3.5 \text{ kg}$[/tex] of meat.

(iii) Using the relation, how many kilograms of meat can be bought at a cost of [tex]$GHc 240$[/tex]?

Sagot :

GinnyAnswer
Alright, let's tackle this question step-by-step:

### Step 1: Completing the Table
Given the relation \( y = 20x + 20 \), we can fill in the missing \( y \)-values for \( x = 1, 2, 4, 6, 8 \).

For each \( x \):
1. \( x = 1 \):
[tex]\[ y = 20(1) + 20 = 40 \][/tex]

2. \( x = 2 \):
[tex]\[ y = 20(2) + 20 = 60 \][/tex]

3. \( x = 4 \):
[tex]\[ y = 20(4) + 20 = 100 \][/tex]

4. \( x = 6 \):
[tex]\[ y = 20(6) + 20 = 140 \][/tex]

5. \( x = 8 \):
[tex]\[ y = 20(8) + 20 = 180 \][/tex]

So, the completed table is:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\( x \) & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
\( y \) & 40 & 60 & 80 & 100 & 120 & 140 & 160 & 180 & 200 \\
\hline
\end{tabular}

### Step 2: Drawing the Graph
Use the table with \( x \)-values from 1 to 9 and their corresponding \( y \)-values to plot points on a graph.

1. Use a scale of 2 cm for each unit on the \( x \)-axis (representing 1 kg).
2. Use a scale of 2 cm for each GH¢ 20 units on the \( y \)-axis.

For example:
- Plot the point \( (1, 40) \) at 2 cm on the \( x \)-axis and 4 cm on the \( y \)-axis.
- Plot \( (2, 60) \) at 4 cm on the \( x \)-axis and 6 cm on the \( y \)-axis, and so on.

Connect these points to form a straight line, which represents the relation \( y = 20x + 20 \).

### Step 3: Solving the Problems

#### (i) Weight of Meat that can be Bought with GH¢ 90
From the relation \( y = 20x + 20 \), solve for \( x \) when \( y = 90 \):

[tex]\[ 90 = 20x + 20 \][/tex]
[tex]\[ 70 = 20x \][/tex]
[tex]\[ x = \frac{70}{20} \][/tex]
[tex]\[ x = 3.5 \][/tex]

So, the weight of meat that can be bought with GH¢ 90 is 3.5 kg.

#### (ii) Cost of 3.5 kg of Meat
To find the cost of 3.5 kg of meat, use the relation \( y = 20x + 20 \):

[tex]\[ y = 20(3.5) + 20 \][/tex]
[tex]\[ y = 70 + 20 \][/tex]
[tex]\[ y = 90 \][/tex]

So, the cost of 3.5 kg of meat is GH¢ 90.

#### (iii) Kilograms of Meat that can be Bought at a Cost of GH¢ 240
From the relation \( y = 20x + 20 \), solve for \( x \) when \( y = 240 \):

[tex]\[ 240 = 20x + 20 \][/tex]
[tex]\[ 220 = 20x \][/tex]
[tex]\[ x = \frac{220}{20} \][/tex]
[tex]\[ x = 11 \][/tex]

So, 11 kg of meat can be bought at a cost of GH¢ 240.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.