Triangle angle sum theorem What is the value of p?
1 answer:
The angle sum property of triangle states that the sum of all angles of a triangle should be equal to 180°...
According to this theorem,
<em>The value of </em><em>p</em><em> is </em><em>97</em><em>... </em>
Now, Let's find the value of all angles with the help of value of p
- Angle 1 = 54°
- Angle 2 = p-48 = 97-48 = 49°
- Angle 3 = p-20 = 97-20 = 77°
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Answer:
c) 3x - 45 = 10
Step-by-step explanation:
Cross multiply,
3*(x - 15) = 2*5
3*x - 3*15 = 10
3x - 45 = 10
If there are real roots to be found for this polynomial, the Rational Root Theorem and synthetic division are the best way to find them. I teach from a book that uses c and d for the possible roots of the polynomial. C is our constant, 2, and d is the leading coefficient, 1. The factors of 2 are +/- 1 and +/-2. The factors for 1 are +/-1 only. Meaning, in all, there are 4 possibilities as roots for this polynomial. But there are only 3 total (because our polynomial is a third degree), so we have to find the first one, at least, from our possibilities above. Let's try x = -1, factor form (x + 1). If there is no remainder when we do the synthetic division, then -1 is a root. Put -1 outside the "box" and the coefficients from the polynomial inside: -1 (1 2 -1 -2). Bring down the first coefficient of 1 and multiply it by the -1 outside to get -1. Put that -1 up under the 2 and add to get 1. Multiply 1 times the -1 to get -1 and put that -1 up under the -1 and add to get -2. -1 times -2 is 2, and -2 + 2 = 0. So we have our first root of (x+1). The numbers we get when we do the addition along the way are the coefficients of our new polynomial, the depressed polynomial (NOT a sad one cuz it hates math, but a new polynomial that is one degree less than that of which we started!). The new polynomial is 
. That can also be factored to find the remaining 2 roots. Use standard factoring to find that the other 2 solutions are (x+2) and (x-1). Our solutions then are x = -2, -1, 1, choice B from above.