The degree of a polynomial is the highest power of one of its terms. For example, the degree of f(x) is 4 because of the x^4 term. I hope this gets you started.
The angles in a triangle add to 180 degrees.
39 + (34 + x) + (180 - 109) = 180
39 + 34 + x +71 = 180
x = 36
integers are (x) and (x+2)
\(x^2 + (x+2)^2 = 650\)
\(2x^2 +4x + 4 = 650\)
\(x^2 + 2x - 323 = 0\)
\((x+19)(x-17) = 0\)
The integers are positive, so x = 17.
The numbers are 17 and 19.
2x^2 + p = 2x - 2
2x^2 - 2x + (p + 2) = 0
Discriminant = b^2 - 4ac = 4 - 4(2)(p+2) = -8p - 12
p > -3/2 ==> discriminant < 0
width = x
length = x + 2
Use the Pythagorean Theorem.
\(x^2 + (x+2)^2 = 10^2\)
\(2x^2 + 4x + 4 = 100\)
\(x^2 + 2x + 2 = 50\)
\((x+8)(x-6) = 0\)
Distance can't be negative, so the width is 6 centimeters.
I answered this question a day or two ago:
https://web2.0calc.com/questions/find-an-equation-of-the-cubic-function-whose-graph#r1
Rational root theorem: All rational roots are factors of 72. Try plugging in simple numbers like 1 or 2 to get started.
\((x)(x+1)(x+3)(x+4)(x+6) = 0\)
The solutions are 0, -1, -3, -4, -6.
We are finding the number of arrangements of the number "122333".
This is equal to \(\frac{6!}{2! \cdot 3!} = \boxed{60}\)
Let her five friends be called A, B, C, D, and E.
There are 5 choose 2 = 10 ways to choose 2 people out of the 5.
meal price: 59
tax: 59 * 1.06
tip: 59 * 1.02
Total: 59 * 1.26 = 74.34
