Spring 2018 | Professor Kate Poirier

# Author: Jorge

#7.

a) 3x + y = 4

x² – 3y = -32

First:

3x + y = 4

y = -3x + 4

Then:

x² – 3y = -32

x² – 3(-3x + 4) = -32

x² + 9x – 12 = -32

x² + 9x + 20 = 0

(x + 5) (x + 4) = 0

x + 5 = 0

x = -5

x + 4 = 0

x = -4

x = -5 AND x = -4

Next:

x² – 3y = -32

y = -3x + 4

y = -3(-5) + 4

y = 15 + 4

y = 19

y = -3x + 4

y = -3(-4) + 4

y = 12 + 4

y = 16

So:

(-5 , 19) ✓ AND (-4 , 16) ✓

Check:

3x + y = 4

x² – 3y = -32

3(-4) + 16 = 4

(-4)² – 3(16) = -32

-12 + 16 = 4

16 – 48 = -32

4 = 4 ✓

-32 = -32 ✓

(-4 , 16) ✓

AND

3x + y = 4

x² – 3y = -32

3(-5) + 19 = 4

(-5)² – 3(19) = -32

-15 + 19 = 4

25 – 57 = -32

4 = 4 ✓

-32 = -32 ✓

(-5 , 19) ✓

Solve the triangle △ABC.

A = ?

C = 32°

B = 81°

a = ?

b = 13

c = ?

32° + 81° + A = 180°

113° + A = 180

A = 67° ✓

13 / sin (81) = c / sin (32)

13 sin (32) / sin (81) = c

6.888950435 / .9876883406 = c

6.9748 = c ✓

a / sin (67) = 13 / sin (81)

a = 13 sin (67) / sin (81)

a = 12.1157 ✓

A = 67°

C = 32°

B = 81°

a = 12.1157

b = 13

c = 6.9748 ✓

Solve the triangle △ABC.

A = 90°

B = 25°

C = ?°

a = 8

b = ?

c = ?

90° + 25° + C = 180°

115° + C = 180°

C = 65° ✓

a / sin (A) = b / sin (B)

8 / sin (90) = b / sin (25)

8 * sin (25) / sin (90) = b

3.380946094 / 1 = b

3.3809 = b ✓

b / sin (B) = c / sin (C)

3.3809 / sin (25) = c / sin (65)

3.3809 * sin (65) / sin (25) = c

7.2505 = c ✓

A = 90°

B = 25°

C = 65°

a = 8

b = 3.3809

c = 7.2505 ✓

Version A Question #8

Determine the coordinates of the vertex of the parabola given by the equation: y = 2x²  + 12x + 13

a = 2 b = 12 c = 13

x = -b/2a

x = -(12)/2(2)

x = -12/4

x = -3

y = 2x²  + 12x + 13

y = 2(-3)²  + 12(-3) + 13

y = 18 – 36 + 13

y = -5

Vertex = (-3, -5) ✓

Webwork – DistanceFormula: Problem 1

Find the distance between these two points: (1,2) and (0,3)

d =  √ ( X2 – X1 ) ² + ( Y2 – Y1 ) ²

d = √ ( 0 – ( -1 ) ² + ( 3 – ( -2 )²

d = √ ( 0 + 1 ) ²  + ( 3 + 2 ) ²

d = √ ( 1 ) ² + ( 5 ) ²

d = √  1 + 25

d = √  26   ✓

Section 6.7, Problem #13.

√x  +  4  =  6

– 4     – 4

√x  =  2

(√x)²  =  (2)²

x  =  4

Check: x  =  4

LS: √4  +  4  RS: =  6

LS: 2  +  4  RS: =  6

6  =  6  ✓

Hello everyone, I’m a Computer Science Major and I chose this Major because I’ve always been interested in Technology. After this class I will be taking MAT 1375 aka Precalculus. After I graduate I hope to get a job somewhere in the gaming industry. I hope to become a better Math student by taking this class and receive a better understanding on Algebra and Trigonometry. I’m into gaming and my favorite animal is a Wolf.

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