3-21. For each diagram below, solve for x. Explain what angle properties or relationship(s) you used for each problem.

The values of x in the diagrams obtained using the triangle theorem are 8 and 20 respectively

Triangle 1 :

The angle formed is right angled, hence it has a total of 90°

6x + (4x + 10) = 90°

6x + 4x + 10 = 90

10x + 10 = 90

10x = 90 - 10

10x = 80

x = 80/10

x = 8

Triangle 2 :

Sum of angles on a straight line = 180°

(5x + 13) + (3x + 7) = 180°

5x + 3x + 13 + 7 = 180°

8x + 20 = 180°

8x = 180 - 20

8x = 160

x = 160 / 8

x = 20°

Therefore, the values of X are 8 and 20 respectively.

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a. x = 8°

b. x = 20°

Step-by-step explanation:

a. 6x + 4x + 10 = 90 (this is complimentary and this is because there is a small square which indicates that it is 90 degrees)

10x = 90 - 10

10x = 80

x = 8°

b. 5x + 13 + 3x + 7 = 180 (supplementary. Straight lines add up to 180°)  

8x = 180 - 7 - 13

8x = 160

x = 20°

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

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step-by-step explanation: