Answer:
w = -3
Step-by-step explanation:
8w + 12 = -12
use inverse operations:
8w + 12 = -12
-12 -12
8w = -24
/8 /8
w = -3
Answer:
D
Step-by-step explanation:
60°+75°+105°+120°=360°
[Sum of 4 angles of a quadrilateral is 360°]
The first thing you want to do is plug in x and y into both equations:
a(3) + b(4) = 4
b(3) + a(4) = 8
rearrange to line up a’s and b’s
3a + 4b = 4
4a + 3b = 8
now you want to choose a or b and multiply each equation by a number to make them have the same amount of a’s or b’s.
4(3a + 4b = 4) = 12a + 16b = 16
3(4a + 3b = 8) = 12a + 9b = 24
Now we subtract the bottom equation from the top and solve for b:
12a + 16b - (12a + 9b) = 16 - 24
7b = -8
b = -8/7
Now we plug back in for b to one of the original equations:
3a + 4(-8/7) = 4
3a + (-32/7) = 4
3a - (32/7) = 4
3a = 4 + (32/7)
3a = (28/7) + (32/7)
3a = 60/7
a = (60/7)/3 = 20/7.
Finally, plug a and b in together to double check using the second equation.
4a + 3b = 8
4(20/7) + 3(-8/7) = ?
(80/7) - (24/7) = ?
56/7 = 8.
In this item, we are to calculated for the 6th term of the geometric sequence given the initial value and the common ratio. This can be calculated through the equation,
An = (A₀)(r)ⁿ ⁻ ¹
where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms.
Substitute the known values to the equation,
An = (5)(-1/2)⁶ ⁻ ¹
An = -5/32
Hence, the answer to this item is the third choice, -5/32.
