-x+5 = <span>2x-1
-3x = -6
x = 2
</span><span>y=-x+5
y = -2 + 5
y = 3
solutions...
x = 2 and y = 3</span>
In a right triangle, the measure of one acute angle is 30 less than twice the measure of the other acute angle. Find the measure of each angle.
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The sum of the 2 acute angles is 90 degrees.
x + y = 90
x = 2y-30
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Substitute for "x" and solve for "y":
2y-30 +y = 90
3y = 120
y = 40
x = 90-y
x = 90-40
x = 50
Solve for d:
(3 (a + x))/b = 2 d - 3 c
(3 (a + x))/b = 2 d - 3 c is equivalent to 2 d - 3 c = (3 (a + x))/b:
2 d - 3 c = (3 (a + x))/b
Add 3 c to both sides:
2 d = 3 c + (3 (a + x))/b
Divide both sides by 2:
Answer: d = (3 c)/2 + (3 (a + x))/(2 b)
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Solve for x:
(3 (a + x))/b = 2 d - 3 c
Multiply both sides by b/3:
a + x = (2 b d)/3 - b c
Subtract a from both sides:
Answer: x = (2 b d)/3 + (-a - b c)
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Solve for b:
(3 (a + x))/b = 2 d - 3 c
Take the reciprocal of both sides:
b/(3 (a + x)) = 1/(2 d - 3 c)
Multiply both sides by 3 (a + x):
Answer: b = (3 (a + x))/(2 d - 3 c)
The method we need to use here is very particular to this type of a situation. The way we will find that polynomial, or the divisor, is to follow this formula:
. For us that will look like this:
. First we will simplify as much as possible that very long numerator there. It simplifies to
. What you do now is use long division of polynomials, which, unfortunately, is impossible to show in this forum. However, get familiar with the long division process if you are not already, and you will find that your polynomial g(x) is
.
