Angle QRT is an exterior angle to the triangle. The rule is that the exterior angle of a triangle is equal to the sum of its remote interior angles. Those remote interior angles are angle RTS and angle TSR. So our equation is
. We can remove the parenthesis and simplify by combining like terms to get 9x = 5x + 9 + x and 9x = 6x + 9 and 3x = 9. That means that x = 3.
No
Arithmetic sequence has terms which decrease or increase by the same amount
for example 3,6,8,12 ....
this sequence is geometric where the terms are obtained by multiplying previous term by 10
25-4x=15-3x+10-x is all real numbers. You must simply both sides of the equation. The problem is then -4x+25= -4x+25 which is the same. If this happens the answer is always all real numbers.
Ann factored the trinomial completely
take out a common factor of 2
2(2x² - 3x - 2 )
to factor the trinomial consider the factors of the product 2 × - 2 = - 4 which sum to - 3
These are - 4 and + 1
Split the middle term using these factors
2x² - 4x + x - 2 ← ( factor by grouping )
= 2x(x - 2) + 1(x - 2) ← ( take out common factor (x - 2) )
=(x - 2)(2x + 1)
4x² - 6x - 4 = 2(x - 2)(2x + 1) ← ( fully factored )
