Respuesta :

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it

[tex]71<a(18)<76[/tex]

we can divide both sides by 18

[tex]\frac{71}{18} <b<\frac{76}{18}[/tex]

now, we can simplify it

[tex]3.944<a<4.222[/tex]

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 8

[tex]\frac{71}{8} <b<\frac{76}{8}[/tex]

now, we can simplify it

[tex]8.875<a<9.5[/tex]

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it

[tex]71<a(8)<76[/tex]

we can divide both sides by 12

[tex]\frac{71}{12} <b<\frac{76}{12}[/tex]

now, we can simplify it

[tex]5.9166<a<6.333[/tex]

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 7

[tex]\frac{71}{7} <b<\frac{76}{7}[/tex]

now, we can simplify it

[tex]10.14285<a<10.857[/tex]

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it

[tex]71<a(5)<76[/tex]

we can divide both sides by 5

[tex]\frac{71}{5} <b<\frac{76}{5}[/tex]

now, we can simplify it

[tex]14.2<a<15.2[/tex]

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE


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