Question

28. Select the expression that is equivalent to x²a.(x - 2)²b.(x-2)(x + 2)2c.x² + 2x + 42d.x²-2x + 4

Answer 1

Given:

• Sule's Sand:

Charge per ton = $5.00

Delivery fee = $200

• Greg's sand pit:

Charge per ton = $12.00

Delivery fee = $50

Let's find the graph which represents this situation.

For Sule's Sand, we have the equation for the total cost:

y = 5.00x + 200

For Greg's sand pit. we have the equation for the total cost:

y = 12.00x + 50

Thus, we have the system of equations:

y = 5x + 200

y = 12x + 50

Now, let's solve the system and find the solution.

Eliminate the equivalent sides and combine the equations:

5x + 200 = 12x + 50

Subtract 200 from both sides:

5x + 200 - 200 = 12x + 50 - 200

5x = 12x - 150

Subtract 12x from both sides:

5x - 12x = 12x - 12x - 150

-7x = -150

Divide both sides by -7:

`\begin{gathered} (-7x)/(-7)=(-150)/(-7) \\ \\ x=21.42 \end{gathered}`

This means both total costs will be the same when the school orders 21.42 tonnes.

PLug in 21.42 for x in either equation:

`\begin{gathered} y=5(21.42)+200 \\ \\ y=307.14 \end{gathered}`

Therefore, both lines will meet at the point:

(x, y) ==> (21.42, 307.14)

Since we have the equations:

y = 5x + 200

y = 12x + 50

Apply the slope-intercept form:

y = mx + b

Where b is the y-intercept.

This means the line representing the first equation will start at the point:

(0, 200)

The line representing the second equation will start at the point:

(0, 50)

Therefore, the correct graph is:

ANSWER: