The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people.

Question

The variable x represents the number of
.

The variable y represents the number of
.

If y = 9, find the value of x. The committee needs
square tables.

Answer 1

The variable \( x \) represents the number of square tables, and the variable \( y \) represents the number of round tables.

Given the equation:

\[ 150 = 8x + 6y \]

If \( y = 9 \), we can substitute this value into the equation:

\[ 150 = 8x + 6(9) \]

Calculating \( 6 \times 9 \):

\[ 150 = 8x + 54 \]

Now, we can isolate \( x \) by first subtracting 54 from both sides:

\[ 150 - 54 = 8x \] \[ 96 = 8x \]

Next, divide both sides by 8:

\[ x = \frac{96}{8} = 12 \]

The committee needs 12 square tables.

Answer 2

Determine the input value for which the statement
f(x) = 3 and g(x)= 3/2 is true.

From the graph, the input value is approximately______
.

f(x) = 3 and g(x) = 3/2 x – 2

3 = 3/2 x – 2

5 = 3/2 x

The x-value at which the two functions’ values are equal_______
.

The image shows a graph with a grid background. There are two functions plotted: f(x), which is a horizontal line at y = 2, and g(x), which is a diagonal line passing through the points (-1, -2), (1, 0), and (3, 2). The graph has x and y axes labeled, with the x-axis ranging from -5 to 5 and the y-axis ranging from -5 to 5.

Answer 3

To find the input value for which \( f(x) = 3 \) and \( g(x) = \frac{3}{2}x - 2 \) are true, you have already set up the equation:

\[ 3 = \frac{3}{2}x - 2 \]

Now, let's solve this equation step-by-step:

1. Add 2 to both sides:

\[ 3 + 2 = \frac{3}{2}x \] \[ 5 = \frac{3}{2}x \]

2. Multiply both sides by \( \frac{2}{3} \) to isolate \( x \):

\[ x = 5 \cdot \frac{2}{3} \] \[ x = \frac{10}{3} \]

3. Convert \( \frac{10}{3} \) to a decimal:

\[ \frac{10}{3} \approx 3.33 \]

Therefore, the input value for which the statement is true is approximately 3.33.

Next, you want to find the x-value at which the two functions’ values are equal. The horizontal line \( f(x) \) is at \( y = 3 \), and the diagonal line \( g(x) \) intersects \( y = 3 \) as follows:

1. Start with the equation you derived earlier:

\[ \frac{3}{2}x - 2 = 3 \]

2. Add 2 to both sides:

\[ \frac{3}{2}x = 5 \]

3. Multiply both sides by \( \frac{2}{3} \):

\[ x = \frac{10}{3} \]

Consequently, the x-value at which the two functions’ values are equal is also approximately 3.33.

Answer 4

guys answer is 3.5 and 10/3

Answer 5

Let’s go through solving for the \( x \) value again step by step, checking the computations carefully.

You have the equation for \( g(x) \):

\[ g(x) = \frac{3}{2}x - 2 \]

And you set it equal to \( f(x) = 3 \):

\[ 3 = \frac{3}{2}x - 2 \]

Now, let’s solve it correctly:

1. Add 2 to both sides: \[ 3 + 2 = \frac{3}{2}x \] \[ 5 = \frac{3}{2}x \]

2. To isolate \( x \), multiply both sides by \( \frac{2}{3} \): \[ x = 5 \cdot \frac{2}{3} \] \[ x = \frac{10}{3} \approx 3.33 \]

Now, if you stated the answer is \( 3.5 \), it might suggest that there is a specific point in the problem or graph that we are not accounting for correctly.

To find where \( g(x) = 3 \) specifically:

1. Set \( g(x) \) equal to 3 again: \[ \frac{3}{2}x - 2 = 3 \]

2. Add 2 to both sides again: \[ \frac{3}{2}x = 5 \]

3. Now, solve for \( x \) as already calculated: \[ x = \frac{10}{3} \]

At this point, if you are looking for why \( 3.5 \) was mentioned, it may stem from analyzing or interpreting the graph differently or errors in understanding the equations involved.

Please verify the context or any additional data that might lead to a different conclusion. If \( g(x) = 3 \) is computed correctly through the isolated function, it results in \( \frac{10}{3} \) or approximately \( 3.33 \), not \( 3.5 \). If the conditions differ, please elaborate for further assistance!