Kyote Algebra & trig

Question 1

1. An eastbound car is going 4 miles per hour faster than a westbound car. The cars are 208 miles apart
   2 hours after passing each other on a highway. What is the speed, in miles per hour, of the eastbound car?

Answer 1

54

Distance=rate x time
208=(x+x+4)(2)
104=2x+4
100=2x
x=50

Question 2

2. If a man walks at the rate of 2 feet per second, how many minutes will it take him to walk 4320 feet?

Answer 2

36

Question 3

3. One solution of x^2 − 5 x − 1 = 0 is

Answer 3

5 −√29
_____
2

Ax2+Bx+C = 0

        - B  ±  √ B^2-4AC   x =   ————————
                  2A 

        - (-5)  ±  √ (-5)^2-4(1)(-1)   x =   ————————
                  2(1) 

        5  ±  √ 25+4   x =   ————————
                  2 

        5  ±  √ 29   x =   ————————
                  2 

2 answers are

        5  -  √ 29   x =   ————————
                  2 

        5  +  √ 29   x =   ————————
                  2

Question 4

4. Solve 56 − 7 x = 2 for x.

Answer 4

54/ 7

Question 5

5. Simplify. (−6x^4)^2
A) −36x^8 
B) 36x^6
C) −36x^6
D) 36x^8 
E) −6x^8

Answer 5

36x^8

Question 6

6. The graph of the line with equation y = 7 x + 8 crosses the x-axis when x = ?

Answer 6

−8/ 7

y=0

0 = 7x+8

• 8=7x
• 8/7 x

Question 7

7. Find the value of 
x − y
-------
   x 
when x = −2 and y = −3.

Answer 7

-1/2

Question 8

8. Multiply. 2(4 x + 2)(x − 1)

Answer 8

8 x^2 − 4 x − 4

Question 9

9. Add.
   1/4 + 1/5

A) 1/20 
B) 2/9
C) 9/20
D) 1/9
E) 1/10

Answer 9

9/20

Question 10

10. Solve

1/3x − 2/3 = 4 for x.

Answer 10

14

BUT HOW?!?

Question 11

11. Subtract

r/x −3s/y

Answer 11

r y − 3 s x
________
x y

L. Mult. • L. Num. r • y
—————————————————— = —————
L.C.M xy

R. Mult. • R. Num. 3s • x
—————————————————— = ——————
L.C.M xy

Denonimators go mutliply to become a single denominator
xy

outside numbers bond
ry

inside numbers bond
-3s

these form the numerator

xy

Question 12

12. A line with slope 3 passes through the point (0, 10). What is the y-coordinate of the point on the
    line with x-coordinate 2?

Answer 12

16

y−y1=m(x−x1)
y−10=3(x−0)
y−10=3x
y=3x+10
Now plug in x=2 to get the answer.

y=3(2)+10y=16

Question 13

13. Solve the system

{ x + 4 y = 1
{ − x + y = 4 .
What is the x-coordinate of this solution?

Answer 13

-3

Question 14

14. A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if its
    length is 6 feet more than its width?

Answer 14

93

2(W + 6 + W) = 360
2(2W + 6) =360
2W + 6 = (360 / 2)
2W + 6 = 180
2W = 180 - 6
2W = 174
W = 87

hence, Width = 87 feet
but we are asked for length of the field
so length = W + 6
L = 87 + 6
L = 93 feet

Question 15

15. Combine like terms and simplify.

6 x^2 − 6 x + 4) − (x^2 − 5 x − 9

Answer 15

5x^2 − x + 13

Question 16

16. Simplify. (−6)^2 − 4^2

Answer 16

20

Question 17

17. What is the perimeter, in feet, of a rectangle whose length is twice its width and whose width is 5
    feet?

Answer 17

30

Question 18

18. Simplify. 5(5 − 2 x) − 2(4 − 3 x)

Answer 18

17 − 4x

Question 19

19. Multiply. 4 x (x − 1)^2

Answer 19

4 x^3 − 8x^2 + 4x

Question 20

20. Simplify.
    6x^8-2x^2
    ________
    2x^2

Answer 20

3x^6-1

Question 21

21. What is the area of the triangle whose vertices are (−4, 0), (−10, 0) and (−7, −6)?

Answer 21

18

Question 22

22. Solve 9 x + 8 y = 36 for x.

Answer 22

−8/9y + 4

9x = -8y + 36
divide everything by 9
x = -8/9y + 4

Question 23

24. Solve 2 x + 4 > 8 x − 8 for x.

Answer 23

x < 2

plug in numbers till the statement is true

Question 24

25. Add the mixed numbers.

6 5/7 + 9 1/2

Answer 24

16 3/14

Question 25

26. A buyer purchases 20 percent of the 12000 widgets in a warehouse’s inventory. The next day, another
    buyer purchases 10 percent of the remaining widgets. How many widgets are left in the warehouse?

Answer 25

8640

Question 26

27. Find the value of

x^3 + x^2 − 3 x when x = −2.

Answer 26

2

Question 27

28. Simplify.

5 − (4 − 7 / 5 − 4)

Answer 27

8

Question 28

29. What is the greatest common factor of the two terms in the expression
    x^5y^2 + x^2y^7z

Answer 28

x^2y^2

Question 29

30. Simplify, assuming x is a positive number.

√x^16 + 16 x^8

Answer 29

x^4√x^8 + 16

Question 30

term coefficient

Answer 30

Number used to multiply a variable