[ Answer ]
Y = -12 / 5
[ Explanation ]
Expand:
-3y - 9 = 2y + 3
Add 9 to both sides:
-3y - 9 + 9 = 2y + 3 - 9
Simplify:
-3y = 2y + 12
Subtract 2y from both sides:
-3y - 2y = 2y + 12 - 2y
Simplify:
-5y = 12
Divide both sides by -5:
-5y / -5 = 12 / -5
Simplify:
Y = -12 / 5
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sin(π/6) is independent of x, so

Answer:
The amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Step-by-step explanation:
Let x be the amount in the account at 12% interest
So, 6000-x is the amount in the second account at 7% interest

First account:
Second account : 
We are given that At the end of the first year he had earned $590 in interest.
So, 
So,the amount in the account at 12% interest is $3400
The amount in the second account at 7% interest =6000-x=6000-3400=2600
Hence the amount in the account at 12% interest is $3400 and the amount in the second account at 7% interest is $2600
Answer:
x = 95°
Step-by-step explanation:
x and 95 are vertical angles and congruent, thus
x = 95°
You have two triangles, ADC and ABC.
Sides AD and AB are congruent.
Sides DC and BC are congruent.
Side AC is congruent to itself.
By SSS, triangles ADC and ABC are congruent.
Corresponding parts of congruent triangles are congruent.
That means that angles DAC and BAC are congruent.
Angles DCA and BCA are congruent.
Since m<DAC = 32, then m<BAC = 32
Since m<DCA = 41, then m<BCA = 41.
Now you know the measures of two angles of triangle ABC.
The measures of the interior angles of a triangle add to 180.
You can find the measure of angle B.
m<BAC + m<B + m<BCA = 180
32 + m<B + 41 = 180
m<B + 73 = 180
m<B = 107