How about raising 286 up by 14 to 300 and compensating by lowering 428 by the same 14 Since I know that 14 + 14 is 28 then 28-14 is 14
So 428 - 14 = 414
So now I have 414 + 300 which I can do mentally - the answer is 714 and is also the answer to the original problem 428 + 286
Compensation works very well - bring one number up or down to a rounded number and compensate by doing the opposite to the other - instead of 199 + 457 - try 200 + 456
Same answer and because one of the numbers is nicely rounded, it is easy to add the other.
One more: 207 + 182 becomes 200 + 189 =389 I lowered one by 7 and raised the other one by the same 7.
Let R be the greater radius and r be the smaller radius
A) Area of the sidewalk = R^2 - r^2 - This can be the expression
B) = 3.14
=(R^2-r^2)
=(11^2-9^2)
=(121-81)
=*40
That was the simplified expression
Answer = 3.14 * 40 = 125.6m^2
Each of A, C, and D are rational, so presumably B is the answer here.
A is rational, since
, so
.
C is also rational. If
, then
. This would mean
, and so
.
D is rational by a similar argument. If
, then
. So,
, which means
.
Answer:
B' = 105°
C = 27°
A = 48°
Step-by-step explanation:
Given
B = 105°
C = (2x - 3)°
C' = (5x - 48)°
Rotation = 90°
Before solving the requirements of this question, it should be noted that rotation do not change the angle of shapes.
i.e. an angle retain its measurements pre and after rotation.
Solving (a): The measurement of B'
Using the analysis above.
B' = B
Recall that
B = 105°
So:
B' = 105°
Solving (b): A and C
First, I'll solve for C.
Using the same analysis above.
C = C'
Substitute values for C and C'
5x - 48 = 2x - 3
Collect like terms
5x - 2x = 48 - 3
3x = 45
Multiply both sides by ⅓
⅓*3x = ⅓*45
x = 15
Substitute 15 for x in
C = (2x - 3)°
C = 2 * 15 - 3
C = 30 - 3
C = 27°
Solving for A
The sum of angles (A, B and C) is represented as:
A + B + C = 180
Substitute values for B and C
A + 105° + 27° = 180°
A + 132° = 180°
Collect like terms
A = 180° - 132°
A = 48°
It seems that "d" or the common difference is a number that makes the sequence go into the larger positive realm of numbers. Therefore, 2*(7+30d)=7+80d. d=35/100. Now just do 7 + 40(35/100) = 21. 21 is your answer!
