1.

Question

The linear equation represented on the coordinate plane shows the average temperature increase in a city since the year 2000

Select all the statements that are true for the linear equation.

(3 points)
Responses

y = 0.2x + 15 represents the linear equation
y = 0.2x + 15 represents the linear equation

The average increase in temperature each year is 1°C.
The average increase in temperature each year is 1°C.

In the year 2010 the temperature was 17 ° C.
In the year 2010 the temperature was 17 ° C.

If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029
If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029

The average increase in temperature every 5 years is 1°C.

Answer 1

Let's analyze the linear equation given:

\( y = 0.2x + 15 \)

Here, \(y\) represents the average temperature, and \(x\) represents the number of years since 2000.

1. The average increase in temperature each year is 1°C.

   • This statement is false. The slope of the equation is 0.2, which means the average increase in temperature each year is 0.2°C, not 1°C.

2. In the year 2010 the temperature was 17 °C.

   • To find the temperature in 2010, we substitute \(x = 10\) (since 2010 is 10 years after 2000): \[ y = 0.2(10) + 15 = 2 + 15 = 17°C \]
   • This statement is true.

3. If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029.

   • The average increase each year is 0.2°C, thus the temperature in 2030 will only be 0.2°C higher than in 2029. Therefore, this statement is false.

4. The average increase in temperature every 5 years is 1°C.

   • To determine the increase in temperature over 5 years, we can calculate: \[ y = 0.2(5) + 15 = 1 + 15 = 16°C \text{ (in 2005)} \] \[ y = 0.2(10) + 15 = 17°C \text{ (in 2010)} \]
   • The increase from 2005 to 2010 is \(17°C - 16°C = 1°C\). Thus, the average increase in temperature every 5 years is 1°C, making this statement true.

Final Responses:

• True Statements:

  • In the year 2010 the temperature was 17 °C.
  • The average increase in temperature every 5 years is 1°C.

• False Statements:

  • The average increase in temperature each year is 1°C.
  • If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029.

Answer 2

Which equations have the solution set of {14, −5}
?

Select all that apply.

(3 points)
Responses

(x − 14)(x − 5) = 0
(x − 14)(x − 5) = 0

(4x − 1)(x+5)=0
(4x − 1)(x+5)=0

(x − 14)(x + 5) = 0
(x − 14)(x + 5) = 0

(x + 14)(x + 5) = 0
(x + 14)(x + 5) = 0

(4x + 2)(x + 5) = 0
(4x + 2)(x + 5) = 0

(8x - 2)(x + 5) = 0
(8x - 2)(x + 5) = 0

(2x - 8)(x - 5) = 0

Answer 3

To determine which equations have the solution set of \({14, -5}\), we need to factor each equation or solve for \(x\) and see if they yield the same solutions.

1. \((x - 14)(x - 5) = 0\)

   • Solutions: \(x - 14 = 0 \Rightarrow x = 14\) and \(x - 5 = 0 \Rightarrow x = 5\)
   • Not a solution set of \({14, -5}\).

2. \((4x - 1)(x + 5) = 0\)

   • Solutions: \(4x - 1 = 0 \Rightarrow 4x = 1 \Rightarrow x = \frac{1}{4}\) and \(x + 5 = 0 \Rightarrow x = -5\)
   • Not a solution set of \({14, -5}\).

3. \((x - 14)(x + 5) = 0\)

   • Solutions: \(x - 14 = 0 \Rightarrow x = 14\) and \(x + 5 = 0 \Rightarrow x = -5\)
   • This is a valid solution set of \({14, -5}\).

4. \((x + 14)(x + 5) = 0\)

   • Solutions: \(x + 14 = 0 \Rightarrow x = -14\) and \(x + 5 = 0 \Rightarrow x = -5\)
   • Not a solution set of \({14, -5}\).

5. \((4x + 2)(x + 5) = 0\)

   • Solutions: \(4x + 2 = 0 \Rightarrow 4x = -2 \Rightarrow x = -\frac{1}{2}\) and \(x + 5 = 0 \Rightarrow x = -5\)
   • Not a solution set of \({14, -5}\).

6. \((8x - 2)(x + 5) = 0\)

   • Solutions: \(8x - 2 = 0 \Rightarrow 8x = 2 \Rightarrow x = \frac{1}{4}\) and \(x + 5 = 0 \Rightarrow x = -5\)
   • Not a solution set of \({14, -5}\).

7. \((2x - 8)(x - 5) = 0\)

   • Solutions: \(2x - 8 = 0 \Rightarrow 2x = 8 \Rightarrow x = 4\) and \(x - 5 = 0 \Rightarrow x = 5\)
   • Not a solution set of \({14, -5}\).

Summary of Valid Statements

• The only equation that has the solution set of \({14, -5}\) is:
  • \((x - 14)(x + 5) = 0\).