Answer: Weeping Woods or Slurpy Swamp.
X=amount of canned juice with 25% of orange juice
y=amount of other canned juice with 10% of orange juice.
25%=25/100=1/4
10%=10/100=1/10
17%=17/100
We can suggest this system of equations:
(1) x+y=15
(2) (x/4+y/10) / (x+y)=17/100 ⇒100(x/4 + y/10)=17(x+y) ⇒25x+10y=17x+17y ⇒8x-7y=0
Finally, we have this system of equations:
x+y=15
8x-7y=0
We can solve this system by substitution method.
x+y=15 ⇒ y=15-x
8x-7(15-x)=0
8x-105+7x=0
15x=105
x=105/15
x=7
y=15-x=15-7=8
answer: we should mix 7 liters of juice (with 25% orange juice) and 8 liters of juice (with 10% orange juice).
Answer:
The values of x that make the triangles congruent.
x = 6 and x = 3
Step-by-step explanation:
Given
Given that the triangles are congruent.
According to the SAS (Side-Side-Side)
AC = DC
AB = DB
so
AC = DC
substituting AC = 5x-2 and DC = 3x+10
5x-2 = 3x+10
5x-3x = 10+2
2x = 12
divide both sides by 2
2x/2 = 12/2
x = 6
and
AB = DB
substituting AB = 5x and DB = 4x+3
5x = 4x+3
5x-4x = 3
x = 3
Therefore, the values of x that make the triangles congruent.
x = 6 and x = 3
see the attached figure to better understand the problem
Let
2L---------> lenght side of hexagon
we know that
in one of those triangles
sin 30=1/2
sin 30=L/hypotenuse
solve for L
L=hypotenuse*sin 30-------->L=( 1 8 √ 3 )*(1 /2)------> L=9√3 units
Find the perimeter
perimeter=(2L)*6--------> L*12-------> Perimeter=9√3*12--------->108√3 units
therefore
the answer is
the perimeter of the regular hexagon is 108√3 units
