Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. a(n) = 1 + (n - 1) (-5.7) a)1, –21.8, –56 b)–5.7, –21.8, –51.3 c)0, –17.1, –51.3 d)1, –16.1, –50.3

D) 1, -16.1, -50.3

Step-by-step explanation:

For calculate the first term of the sequence we replace n by 1 in the equation, then:

A(n)=1+(n-1)(-5.7)

A(1)=1+(1-1)(-5.7)

A(1)=1

At the same way we can calculate the fourth term of the sequence replacing n by 4 in the equation, then:

A(n)=1+(n-1)(-5.7)

A(4)=1+(4-1)(-5.7)

A(4)=1 + 3*(-5.7)

A(4)=-16.1

Finally, the tenth term of the sequence can be calculate replacing n by 10, so:

A(n)=1+(n-1)(-5.7)

A(10)=1+(10-1)(-5.7)

A(10)= 1 + 9*(-5.7)

A(10)=-50.3

Then, the first, fourth and tenth term of the sequence is 1, -16-1 and -50.3 respectively.

if x = 1, then the answer is 3.5

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: