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tchocho8621
20.04.2020 •
Mathematics
Two triangles are shown to be congruent by identifying a combination of translations, rotations, or reflections that move one figure onto the other. If ΔBAT ≅ ΔMAN, which line segment must be congruent to TB? Why?
A) AT because the triangles are isosceles.
B) NM because the triangles are isosceles.
C) AT because corresponding parts of congruent triangles are congruent.
D) NM because corresponding parts of congruent triangles are congruent.
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Ответ:
Ответ:
Since we want to solve for the variable x, we want to isolate x
a²x + (a - 1) = (a + 1)x ⇒ Distribute x to (a+1). Also, remove parentheses
a²x + a - 1 = ax + x ⇒ Subtract a from both sides
a²x - 1 = ax + x - a ⇒ Add 1 to both sides
a²x = ax + x - a + 1 ⇒ Subtract (ax + x) from both sides
a²x - (ax + x)= ax + x - a + 1 - (ax+x) ⇒ Simplify. Remember that multiplying positive by negative = negative
a²x - ax - x = ax + x - a + 1 - ax - x ⇒ Simplify
a²x - ax - x = -a + 1 ⇒ Factor out the x from a²x - ax - x
x(a² - a - 1) = -a + 1 ⇒ Divide both sides by (a² - a - 1)
x = (-a + 1) / (a² - a - 1)
However, we need to make sure that the denominator does not equal 0. Therefore, you set the denominator = 0 (just use the quadratic formula for this), and it gives that the denominator =0 when a = (1+√5)/2 AND (1-√5)/2
Therefore, the final answer is
x = (-a + 1) / (a² - a - 1) given that a ≠ (1+√5)/2, a ≠ (1-√5)/2