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Yuri [45]
3 years ago
14

Evaluate the expression using the values in the left column to complete the table

Mathematics
1 answer:
egoroff_w [7]3 years ago
7 0

Answer/Step-by-step explanation:

A. 4b + 3b

Using b = 2

4(2) + 3(2) = 8 + 6 = 14

Using b = 4

4(4) + 3(4) = 16 + 12 = 28

Using b = 6

4(6) + 3(6) = 24 + 18 = 42

Using b = 8

4(8) + 3(8) = 32 + 24 = 56

Using b = 10

4(10) + 3(10) = 40 + 30 = 70

Using b = 2

4(12) + 3(12) = 48 + 36 = 84

B. 3(x - 2)

Using x = 3

3(3 - 2) = 3(1) = 3

Using x = 5

3(5 - 2) = 3(3) = 9

Using x = 7

3(7 - 2) = 3(5) = 15

Using x = 9

3(9 - 2) = 3(7) = 21

Using x = 11

3(11 - 2) = 3(9) = 27

Using x = 13

3(13 - 2) = 3(11) = 33

C. 5(4a - 1)

Using a = 2

5(4(2) - 1) = 5(8 - 1) = 5(7) = 35

Using a = 3

5(4(3) - 1) = 5(12 - 1) = 5(11) = 55

Using a = 4

5(4(4) - 1) = 5(16 - 1) = 5(15) = 75

Using a = 5

5(4(5) - 1) = 5(20 - 1) = 5(19) = 95

Using a = 6

5(4(6) - 1) = 5(24 - 1) = 5(23) = 115

Using a = 7

5(4(7) - 1) = 5(28 - 1) = 5(27) = 135

D. 6y - 2y + 4

Using y = 2

6(2) - 2(2) + 4 = 12 - 4 + 4 = 12

Using y = 3

6(3) - 2(3) + 4 = 18 - 6 + 4 = 18 - 2 = 16

Using y = 5

6(5) - 2(5) + 4 = 30 - 10 + 4 = 30 - 6 = 24

Using y = 10

6(10) - 2(10) + 4 = 60 - 20 + 4 = 60 - 16 = 44

Using y = 8

6(8) - 2(8) + 4 = 48 - 16 + 4 = 48 - 12 = 36

Using y = 6

6(6) - 2(6) + 4 = 36 - 12 + 4 = 36 - 8 = 28

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Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
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Answer: k = -1 +/- √769

<u>Step-by-step explanation:</u>

48x - ky = 11

<u>-48x        </u>  <u> -48x</u>

         -ky = -48x + 11

         \frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}    

           y =\frac{48x}{k} - \frac{11}{k}

Slope: \frac{48}{k}

*************************************************************************

 (k + 2)x + 16y = -19

<u>- (k + 2)x          </u>   -<u>(k + 2)x </u>

                 16y = -(k + 2)x - 19

                  \frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}

                  y = -\frac{(k + 2)x}{16} - \frac{19}{16}

Slope: -\frac{(k + 2)}{16}

**********************************************************************************

\frac{48}{k} and -\frac{(k + 2)}{16} are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

-\frac{(k + 2)}{16} *  \frac{k}{48} = -1

\frac{(k + 2)k}{16(48)} = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769



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