11, 13, and 16. sorry if im wrong, and i hope this helps.
Comment
There are 4 terms in this series
That's because the summation (Sigma) goes from 3 to 6 inclusive. So k takes on values of 3,4,5,6
You could use this summation formula
Formula
Sum = (a + L)n/2
Substitution
a is the first term.
k = 3 for the first term
a = -5k + 20
a = -5(3) + 20
a = -15 + 20
a = 5
For the last term k = 6
L = -5(6) + 20
L = -30 + 20
L = - 10
Sum
Sum = (5 - 10)*4/2
Sum = -5 * 2
Sum = -10
Comment
You may wonder how come the last term and the sum are the same. The reason to be found by figuring out the 4 terms and adding them together.
When k = 3, -5k + 20 = -15 + 20 = 5
When k = 4, -5k + 20 = -20 + 20 = 0
When k = 5, -5k + 20 = -25 + 20 = -5
When k = 6, -5k + 20 = -30 + 20 = -10
Sum = 5 + 0 - 5 - 10 = - 10
Conclusion.
It is an accident of the numbers.
Answer: - 10 = the Sum
Answer:
3. 63°
4. x = 13
Step-by-step explanation:
3. The exterior angle is equal to the sum of the opposite interior angles.
118° = (4x +7)° + (6x -9)°
120 = 10x . . . . . . . . . divide by °, add 2
12 = x
m∠K = (6x -9)° = (6·12 -9)°
m∠K = 63°
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4. Corresponding angles are congruent, and the sum of angles in a triangle is 180°.
74° + (5x)° + (3x+2)° = 180°
8x = 104 . . . . . . . . . . . . . . . divide by °, subtract 76
x = 13 . . . . . . . . . . . . . . . . . .divide by 8
Answer:
Step-by-step explanation:
x + 2y = 14 ...............(1)
6x + 3y = 21 ..............(2)
Solve for x in equation 1
When x + 2y = 14
Therefore x = 14 - 2y ...................(3)
Now put equation 3 in equation 2 and solve
6x + 3y = 21 .............(2)
6(14 - 2y) + 3y = 21
Open the bracket and resolve
84 - 12y + 3y = 21
-9y + 84 =21
Now collect the like terms
-9y + 84 = 21
-9y = 21 - 84
-9y = -63
Divide through by -9 to get y
y = -63/-9
y = 7
Substitute for y in equation( 3 )to x
x= 14 - 2y............(3)
So, x = 14 - 2(7)
x = 14 - 14
x = 0.
Therefore x = 0 and y = 7
Check: From equation (1)
x + 2y = 14
Now, put x = 0 and y = -2
Therefore, 0 +2(7) =14
0 +14 = 14