Question

1. to promote their streaming service, siriusxm radio offers their subscription for only $2 for the first month and $11 for every month afterward. darra and pax are asked to write an equation for the cost of having a siriusxm subscription for m months. darras equation: $c = 2+11(m - 1)$; pax equation: $c = 11m - 9$. a. what is the same about their equations? what is different? b. who is correct? explain. 2. which of the following expressions is not equivalent to $x^{2}-5x$ for all values of x? a) $x(x - 5)$ b) $7x^{2}-20x - 6x^{2}+15x$ c) $xcdot x - x - x - x - x - x$ d) $-3x-(2x + x^{2})$ 3. on monday, wes recorded a temperature of 65 degrees first thing in the morning. throughout the day, the temperature rose 1.5 degrees per hour. circle one of the expressions below that represents the temperature changes on monday. a) $t = 65+1.5h$ b) $t = 65 - 1.5h$ c) $t = 65h+1.5$ d) $t = 65h - 1.5$ 4. on tuesday, wess thermometer showed a temperature of 60 degrees when he woke up. the temperature then rose 0.75 degrees every hour. write an expression that represents the temperature change on tuesday. use the variables t for temperature and h for hours.

Explanation:

Step1: Analyze problem 1 - similarity and difference

Both equations represent the cost $C$ of the subscription and have the coefficient 11 related to the per - month cost after the first month. The difference is in their form; Darra's is in a more expanded form based on the problem's structure ($2$ for first month and $11$ for remaining months), while Pax's is in a simplified form.

Step2: Analyze problem 1 - correctness

Darra's equation $C = 2+11(m - 1)$:
\[

$$\begin{align*} C&=2+11m-11\\ C&=11m - 9 \end{align*}$$

\]
Pax's equation is $C = 11m - 9$. So both are correct as they are equivalent.

Step3: Analyze problem 2

For option A: $x(x - 5)=x^{2}-5x$.
For option B: $7x^{2}-20x-6x^{2}+15x=(7x^{2}-6x^{2})+( - 20x + 15x)=x^{2}-5x$.
For option C: $x\cdot x-x - x - x - x - x=x^{2}-5x$.
For option D: $-3x-(2x + x^{2})=-3x-2x - x^{2}=-x^{2}-5x
eq x^{2}-5x$.

Step4: Analyze problem 3

The initial temperature is 65 degrees and it rises 1.5 degrees per hour $h$. The temperature $t$ is given by $t = 65+1.5h$. So the answer is A.

Step5: Analyze problem 4

The initial temperature is 60 degrees and it rises 0.75 degrees per hour $h$. The expression for the temperature $t$ is $t = 60 + 0.75h$.

Answer:

1.

• a. Same: Both represent cost $C$ and have coefficient 11. Different: Form of the equations.
• b. Both are correct as they are equivalent.

1. D. $-3x-(2x + x^{2})$
2. A. $t = 65+1.5h$
3. $t = 60 + 0.75h$