Answer:
Same-side Interior Angles theorem justifies ∠ 11 + ∠ 10 =180°
Step-by-step explanation:
To Prove:
∠ 11 + ∠ 10 =180°
Proof:
Consider lines are Parallel,then
Corresponding Angles are Equal
∴ ∠ 10 = ∠ 12 say (equation 1)
Now by Linear Pair postulate we have,
∴ ∠ 11 + ∠ 12 = 180° say (equation 2)
Now by replacing ∠12 by ∠ 10 from equation 1 in equation 2 we get
∴ ∠ 11 + ∠ 10 = 180°
Hence proved the above statement.
Answer:
The answer to this question is 19.
Step-by-step explanation:
Given that :
f(x)=13.
f'(x)=3. 1 ≤ x ≤ 3.
Integrate
∫f'(x) dx=∫3 dx
f(x)=3x+c 1 ≤ x ≤ 3.
f(1)= 3+c
c=13-3 =10.
f(x)=3x+10 1 ≤ x ≤ 3.
now ,
f(3)=3(3)+10=19.
So f(3) is at least 19.
Answer:
-7
Step-by-step explanation:
Answer:
They can be seated in 120 differents ways.
Step-by-step explanation:
Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)
It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:
<u> 5 </u>*<u> 4 </u>* <u> 3 </u> * <u> 2 </u> * <u> 1 </u> = 120
1st place 2nd Place 3rd place 4th Place 5th Place
Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.
Finally, they can be seated in 120 differents ways.
This is probably the answer I’m not 100% sure
