Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] T
hink about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint. On the number line below, represent all values of x that meet this constraint.
2 answers:
Answer:
(a) [8, 14]
(b)
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:
Solving the absolute inequality
(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.
Answer:
A. x ± 3 < 11
B. x < 14
C. See the attachment
Step-by-step explanation:
A. Since the value of x is less than 3 units away from 11, we represent it in inequality form as x ± 3 < 11.
B. We now solve this inequality to obtain the values of x which satisfy the constraint.
So, x ± 3 < 11.
x + 3 < 11 and x - 3 < 11
x < 11 - 3 and x < 11 + 3
x < 8 and x < 14
Combining both inequalities,
x < 14
So for x to be less than 3 units away, x must be less than 14.
C. Find the representation on the number line in the attachment.
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Answer: Choice D
This basically says "the nth term is found by computing math, aka evaluating some function, based on the (n-1)th term".
As an example, we could have a function that simply squares the input
Let's say we started at 5. It squares to 25 which in turns squares to 625, and so on. Each new term is based on the old term. Namely, we squared the old n-1 term to get the new nth term.