Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.

Using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:

11. x = 12

12. x = 13

13. x = 19

14. x = 4

15. x = 21; y = 8

16. x = 26; y = 9

17. x = 18; y = 11

Applying the knowledge of angle relationships, we can solve each given problem by first, creating a an equation from the relationship between angles, then solve for the variables.

11. are vertical angles.

12. are linear pair angles.

13. <DBE and <CBE are complementary angles.

14. Since QS bisects <PQR, therefore,

m<PQS = 1/2(PQR)

15. are linear pair angles.

Since are vertical angles, they are congruent. Therefore,

16. Since are linear pair, their sum equals 180 degrees. Therefore,

(angles on a straight line = 180 degrees)

17. Since NP bisects <MNQ, therefore,

(linear pair)

Therefore, using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:

11. x = 12

12. x = 13

13. x = 19

14. x = 4

15. x = 21; y = 8

16. x = 26; y = 9

17. x = 18; y = 11

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Step-by-step explanation:

11). 6x + 7 = 8x - 17 [Since vertical angles are equal in measure]

    8x - 6x = 17 + 7

    2x = 24

    x = 12

12). (11x - 15) + (5x - 13) = 180°

    16x - 28 = 180°

    16x = 180 + 28

    16x = 208

    x = 13

13). Since DB⊥AC,

    m∠CBD = 90°

    m∠CBE + m∠DBE = 90°

    (5x - 42) + (2x - 1) = 90°

     7x - 43 = 90

    7x = 133

     x = 19

14). Since QS bisects angle PQR,

    m∠PQS = m∠RQS

    10x + 1 =

    10x + 1 = 41

    10x = 40

    x = 4

15). 10x - 61 = 18y + 5 [Vertical angles]

     10x - 18y = 61 + 5

     10x - 18y = 66

     5x - 9y = 33 ------(1)

     (18y + 5) + (x + 10) = 180 [linear pair of angles are supplementary]

     18y + x + 15 = 180

     x + 18y = 165 ------(2)

     By adding equation (1)×2 and equation (2)

     (10x - 18y) + (x + 18y) = 66 + 165

     11x = 231

      x = 21

16). (5x - 17) + (3x - 11) = 180 [[linear pair of angles are supplementary]

      8x - 28 = 180

      8x = 180 + 28

      8x = 208

      x = 26

      (3x - 11)° = 78 - 11

                   = 67°

      67° + 90° + (2y + 5)°= 180° [Sum of angles on a line]

      162 + 2y = 180

      2y = 180 - 162

      2y = 18

      y = 9

17). NP bisects ∠MNQ.

    Therefore, m∠MNQ = 2(m∠PNQ)

    8x + 12 = 2×78

    8x + 12 = 156

    8x = 156 - 12

    8x = 144

    x = 18

    m∠MNQ = (8x + 12)° = 156°

    m∠RNM = m∠ONQ [Vertical angles]

    (3y - 9)° = 180° - m∠MNQ

    3y - 9 = 180 - 156

    3y - 9 = 24

    3y = 33

    y = 11

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

whatare you sayig

step-by-step explanation: