Amaya's test scores in algebra 1 are 78 and 91. she has one more test left and wants to earn a b for the course, which is from 80-89 inclusive. write a compound inequality to represent the situation

Let x be the score Amaya gets on the final test. She wants her average of all 3 tests to be between 80 and 89: 

80 ≤ (78 + 91 + x) / 3 ≤ 89 

Multiply everything by 3: 
240 ≤ 78 + 91 + x ≤ 267 
240 ≤ 169 + x ≤ 267 

Subtract 169 from everything: 
240 - 169 ≤ x ≤ 267 - 169 
71 ≤ x ≤ 98 

 
She needs to score between 71 and 98 to get a B for the course.

The compound inequality expression expressing the required score to obtain a B grade is 80 ≤ (169 + t) ≤ 89

Test scores :

78 and 91

Range of B - grade:

80 - 89

Let the her score in the last test = t

Final average score will be :

(78 + 91 + t) / 3 = (169+t) / 3

To obtain a B grade :

80 ≤ Final average score Final average score ≤ 89

The compound inequality expression can be expressed thus :

80 ≤ Final average score ≤ 89

Therefore, the compound inequality expression is 80 ≤ (169 + t) ≤ 89

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Hello!

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

why?

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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