Sequence will look like this:
Term 1: 20 --------- 20 + 5(0)
Term 2: 25 --------- 20 + 5(1)
Term 3: 30 --------- 20 + 5(2)
Term 4: 35 --------- 25 + 5(3)
ETC.
It cab noted that the numbers in the bracket (that is, 0, 1, 2, 3, 3, etc) = n-1
Then, the explicit formula will be;
an = 20 + 5(n-1).
The correct answer is D.
Step-by-step explanation:
remember, when you multiply 2 expressions, you need to multiply every term of one expression with every term of the other expression and then add the results up (while considering their individual signs, of course).
1)
2(s + 8) = -(4s + 2)
2×s + 2×8 = -4s + -2
2s + 16 = -4s - 2
6s + 16 = -2
6s = -18
s = -3
2)
-(8 - 7b) = 6(2 + b)
-8 - -7b = 6×2 + 6×b
-8 + 7b = 12 + 6b
-8 + b = 12
b = 20
3)
6(4x - 11) = 9 - x
6×4x - 6×11 = 9 - x
24x - 66 = 9 - x
25x - 66 = 9
25x = 75
x = 3
4)
-5(4 - x) = 2(-x - 3)
-5×4 - -5×x = 2×-x - 2×3
-20 + 5x = -2x - 6
-20 + 7x = -6
7x = 14
x = 2
5)
-6(y - 1) = 4(9 + y)
-6×y - -6×1 = 4×9 + 4×y
-6y + 6 = 36 + 4y
-10y + 6 = 36
-10y = 30
y = -3
6)
7(2s + 6) = 5(s - 6)
7×2s + 7×6 = 5×s - 5×6
14s + 42 = 5s - 30
9s + 42 = -30
9s = -72
s = -8
7)
z + 4 = 8(-z + 5)
z + 4 = 8×-z + 8×5
z + 4 = -8z + 40
9z + 4 = 40
9z = 36
z = 4
8)
-2(3 + 5x) + 3(1 - x) = 10
-2×3 + -2×5x + 3×1 - 3×x = 10
-6 - 10x + 3 - 3x = 10
-3 - 13x = 10
-13x = 13
x = -1
Step-by-step explanation:
ΔACX is an isosceles triangle, so ∠AXC = ∠XAC. We'll call the measure of this angle x°.
∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180. That means ∠BXC = 180 − x.
ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB. We'll call the measure of this angle y°.
Angles of a triangle add up to 180, so:
y + y + (180 − x) = 180
2y = x
y = x/2
∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.
x + y = 90
x + x/2 = 90
3/2 x = 90
x = 60
Therefore, ∠AXC = ∠XAC = 60°.