Question

name the initial value, rate of change, type of inequality symbol, and where you shade. solve each problem algebraically

Answer 1

Given:

Number of new words to learn everyday = 2

Number of words he can spell already = 10

Let's write an inequality to determine the number of whole days it will take for him to be able to spell at least 75 words.

Apply the slope intercept form:

y = mx + b

Where m is the rate of change and b is the initial value.

We have the inequality:

`75\leq2x+10`

Where:

Initial value = 10

Rate of change = 2

Let's solve for x.

Subtract 10 from both sides:

`\begin{gathered} 75-10\leq2x+10-10 \\ \\ 65\leq2x \end{gathered}`

Divide both sides by 2:

`\begin{gathered} (65)/(2)\leq(2x)/(2) \\ \\ 32.5\leq x \\ \\ x\ge32.5\approx33 \end{gathered}`

Therefore, it will take him aa minimum of 33 days to be able to spell at least 75 words.

ANSWER:

33 days