When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.
In our case we assume a is not smaller than 7, that is we assume a≥7.
a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:
3a+7≥28,
which is a contradiction because 3a+7 is smaller than 28.
So our assumption is wrong, which means the opposite of it is correct.
Answer: assume a≥7
Answer:
54, 36
Step-by-step explanation:
67+59+x=60*3
126+x=180
x=54
54 cones on Sunday
_____________________________________
180+x=54*4
180+x=216
x=36
36 cones on Monday
Answer:
Step-by-step explanation:
Answer:
x = ±5
Step-by-step explanation:
4x^2 = 100
Divide each side by 4
4/4x^2 = 100/4
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Try this solution:
1. Note, that 100 is divisible by 4, and 999 is not divisible by it, only 996. This is an arithmetic sequence.
2. a1;a2;a3;a4;...a(n) the sequence, where a1=100; a2=104; a3=108; a4=112; ... etc., and a(n)=996. n=?
3. using a formula for n-term of the sequence: a(n)=a1+d(n-1), where a(n)=996; a1=100 and d=4 (according to the condition ' is divisible by 4'). Then 100+4(n-1)=996; ⇒ 4n=900; ⇒ n=225 (including 100).
answer: 225
