Algebra 1 Enrichment Answers and Notes

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1i) a.

1g) (-4) + (+6) + (-|-3|) + [- (-5)] = (-4) + (+6) + (-3) + (+5) = +4


2i) c.

2g) 12 - (8 ÷ 4) x 2 -(-2 )(-1) = 12 - 4 - 2 = 6


3i) b.

3g) Leftover area = area of the cardboard (50 x 60) - total area of the box: [2 x  (12 x 15 + 12 x 20 + 15 x 20)] = 3000 - 1440 = 1560; 1560 cm2


4i) c.

4g) (-1)3 (-2)2 (-1) = (-1)(+4) (-1) = +4


5i) a.

5g) b.


6i) b.

6g) a.


7i) a.

7g) Let the number of teachers be t. Then , so t = 27.


8i) b.

8g) d.


9i) The ordered pairs of (0, -2), (1, 1), and (-1, -5) satisfy the equation and are the coordinates of points on the line. (There are many other possibilities.)

9g) They intersect at (-1, 4).


10i) c.

10g) If the enrollment was p, then So p = 55,000 students.


11i)

11g)


12i) a.

12g) c.


13i) d.

13g) P (yellow, then red or blue) =


14i) b.

14g) f(x) = -3x + 10
f(x2 + 2) = -3(x2 + 2) + 10
f(x2 + 2) = -3x2 - 6 + 10
f(x2 + 2) = -3x2 + 4


15i) c.

15g) The equations are r = 2w + 3 and r + w = 78.

 To solve for r:  w = 78 - r
   r = 2(78 - r) + 3
   r = 156 - 2r + 3
   r = 159 - 2r
   3r = 159
   r = 53

 To solve for w:  53 + w = 78
   w = 78 - 53
   w = 25
   25 wrens, 53 robins

 


16i)

16g)


17i) Let the length of one side be x. Then two consecutive sides and the diagonal form a right triangle. Apply the Pythagorean theorem to write x2 + x2 = 64. The solution is The length of a side is

17g) Note that a right triangle forms. Use the Pythagorean theorem to find the required length: 12,000 ft.


18i) slope = -4/3; equation: y - 4 = -4/3(x + 3) or y = -4/3x

18g)


19i) a.

19g) Let the needed time be t. So 12 5 = 6 t, and t = 10; 10 hours.


20i) (no real number solutions)

20g) x2 + (x - 14)2 = 262. The positive solution of the equation is x = 24. The lengths of the sides are 24 cm and 10 cm.