8m - 5n + 2m + 6n =Simplifying
8m + -5n + 2m + 6n = 0
Reorder the terms:
8m + 2m + -5n + 6n = 0
Combine like terms: 8m + 2m = 10m
10m + -5n + 6n = 0
Combine like terms: -5n + 6n = 1n
10m + 1n = 0
Solving
10m + 1n = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-1n' to each side of the equation.
10m + 1n + -1n = 0 + -1n
Combine like terms: 1n + -1n = 0
10m + 0 = 0 + -1n
10m = 0 + -1n
Remove the zero:
10m = -1n
Divide each side by '10'.
m = -0.1n
Simplifying
m = -0.1n.
Step-by-step explanation:
x + y = 16 (*)
x^2 + y^2 = 146 (**)
(*) <=> x= 16-y
substitute x = 16 - y
(**) <=> (16-y)^2 + y^2 = 146
<=> y^2 - 2.16.y + 16^2 + y^2 = 146
<=> 2y^2 - 32y + 110 = 0
<=> y^2 - 16y + 55 = 0
<=> (y-11)(y-5) = 0
<=> y=11 or y= 5
For y = 11, we have x= 16-11=5
For y=5, we have x= 16-5=11
Answer: (x,y) = (11,5) ; (5,11)
Answer:
ΔDCE by ASA
Step-by-step explanation:
The marks on the diagram show AE ≅ DE. We know vertical angles AEB and DEC are congruent, and we know alternate interior angles BAE and CDE are congruent. The congruent angles we have identified are on either end of the congruent segment, so the ASA theorem applies.
Matching corresponding vertices, we can declare ΔABE ≅ ΔDCE.
Write out the ratio. 12/x=4/6. From here you can see that to get from 12 to 4, you divide by three. To find x, multiply 3 to 6. Your answer is 18 inches.
