In the following diagram, A || B. Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x. Solve for x, showing all of your work. Find the measure of ∠6.

x = 24; m<6 = 79

Step-by-step explanation:

Lines A and B are parallel. Corresponding angles of parallel lines cut by a transversal are congruent. Angles 3x + 7 and 6 are corresponding angles. They are congruent.

m<6 = 3x + 7

Angles 6 and 4x + 5 are a linear pair. Angles in a linear pair are supplementary, so their measures add to 180.

m<6 + 4x + 5 = 180

but m<6 = 3x + 7, so we substitute m<6 with 3x + 7, obtaining the equation

3x + 7 + 4x + 5 = 180

Now we solve the equation above for x.

7x + 12 = 180

7x = 168

x = 24

Now that we have a value for x, we substitute into an expression for the measure of angle 6.

m<6 = 3x + 7 = 3(24) + 7 = 72 + 7 = 79

x = 24; m<6 = 79

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

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.

you 're wlecome! : )

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