In ∆DEF, DE = 18, EF = 16, and DF = 12. Find m∠F.

∠F=78.58484226°

Step-by-step explanation:

a²=b²+c² - 2bc cosA

DE²=EF²+DF² - 2(EF)(DF)cos∠F

18²=16²+12²-2(16)(12)cos∠F

324=256+144-384cos∠F

324-400=-384cos∠F

76=384cos∠F

0.197916=cos∠F

∠F=cos⁻¹(0.197916)

∠F=78.58484226°

why can't you?

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40