Kyote Algebra & trig Flashcards
- 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?
54
Distance=rate x time 208=(x+x+4)(2) 104=2x+4 100=2x x=50
- If a man walks at the rate of 2 feet per second, how many minutes will it take him to walk 4320 feet?
36
- One solution of x^2 − 5 x − 1 = 0 is
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
- Solve 56 − 7 x = 2 for x.
54/ 7
5. Simplify. (−6x^4)^2 A) −36x^8 B) 36x^6 C) −36x^6 D) 36x^8 E) −6x^8
36x^8
- The graph of the line with equation y = 7 x + 8 crosses the x-axis when x = ?
−8/ 7
y=0
0 = 7x+8
- 8=7x
- 8/7 x
7. Find the value of x − y ------- x when x = −2 and y = −3.
-1/2
- Multiply. 2(4 x + 2)(x − 1)
8 x^2 − 4 x − 4
- Add.
1/4 + 1/5
A) 1/20 B) 2/9 C) 9/20 D) 1/9 E) 1/10
9/20
- Solve
1/3x − 2/3 = 4 for x.
14
BUT HOW?!?
- Subtract
r/x −3s/y
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
- 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?
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
- Solve the system
{ x + 4 y = 1
{ − x + y = 4 .
What is the x-coordinate of this solution?
-3
- 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?
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
- Combine like terms and simplify.
6 x^2 − 6 x + 4) − (x^2 − 5 x − 9
5x^2 − x + 13
- Simplify. (−6)^2 − 4^2
20
- What is the perimeter, in feet, of a rectangle whose length is twice its width and whose width is 5
feet?
30
- Simplify. 5(5 − 2 x) − 2(4 − 3 x)
17 − 4x
- Multiply. 4 x (x − 1)^2
4 x^3 − 8x^2 + 4x
- Simplify.
6x^8-2x^2
________
2x^2
3x^6-1
- What is the area of the triangle whose vertices are (−4, 0), (−10, 0) and (−7, −6)?
18
- Solve 9 x + 8 y = 36 for x.
−8/9y + 4
9x = -8y + 36
divide everything by 9
x = -8/9y + 4
- Solve 2 x + 4 > 8 x − 8 for x.
x < 2
plug in numbers till the statement is true
- Add the mixed numbers.
6 5/7 + 9 1/2
16 3/14
- 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?
8640
- Find the value of
x^3 + x^2 − 3 x when x = −2.
2
- Simplify.
5 − (4 − 7 / 5 − 4)
8
- What is the greatest common factor of the two terms in the expression
x^5y^2 + x^2y^7z
x^2y^2
- Simplify, assuming x is a positive number.
√x^16 + 16 x^8
x^4√x^8 + 16
term coefficient
Number used to multiply a variable
