Word Problems
The perimeter of a triangle is 45 cm. One side is 3 cm longer than the shortest side, and the third side is 4 cm longer than the shortest side. Find the length of the shortest side.
12.67 cm
6x=|1+3x|
x = 1/3
-1 < 4x+2 < 10
(-3/4,2)
Determine if the given relation is a function.
{(-1,8) (4,-7) (-1,6) (0,0)}
No, this relation is not a function
y = x^2 +3
3 units up
A drug is administered through an IV drip at a rate of 20 mg/h. After 5 hours, there is 50 mg of the drug in the system. If the drug is being cleared at a constant rate by the kidneys, how quickly is the drug being cleared?
10 mg/h
|4x+9|<3
-3 < x < -3/2
8 ≤ 3-5x < 12
(-9/5,-1]
Determine the slope of (-2,4) , (1,10)
m = 2
y=(x−2)^2
2 units to the right
A large pump can drain a pool one hour faster than a smaller pump. Working together, both pumps can drain the pool in 2 hours. How long would it take each pump to drain the pool alone?
Fast: 3.56 hr
Slow: 4.56 hr
|12x+1|≤-10
No solution
x^2-5x+6 ≤ 0
[2,3]
Convert 6x + 2y = 8 into slope-intercept form.
y=-3x+4
y=−2(x+1)^2
vertical stretch by a factor of 2
shifted 1 unit to the left
downwards reflection
A scientist needs to prepare 200 mL of a 12% salt solution. They have 8% salt solution and 20% salt solution available. How much of each solution should they mix to get the desired concentration?
133.33 mL of 8% salt solution
66.67 mL of 20% salt solution
|10-3x|≥4
x ≥ 14/3 or x ≤ 2
2 < 1/6 - 1/2 x ≤ 4
[-23/3,-11/3)
Find the equation of a line passing through (7,2) with slope m = -5/4
Point-slope = y-2=-5/4(x-7)
Slope-intercept = y=-5/4x+43/4
y= 3(x−4)^2 −5
shifted 4 units to the right
stretched vertically by a factor of 3
shifted 5 units downward
Vincent and Georgia are working together to paint a room with 4 identically shaped walls. Working alone, Georgia can paint one wall 10 minutes faster than Vincent. If it takes Georgia and Vincent 2 hours to paint the entire room, how long does it take Georgia to paint 1 wall by herself? How long would it take Georgie to paint the entire room by herself?
1 wall: 55.4 minutes
Entire room: 3.7 hours
|(2x-5)/3| ≥ 7
x ≤ −8 or x ≥ 13
1/2 (3+4x) ≤ 6(1/3-1/2 x)-1/4(2+10x)
(-∞,0]
Write an equation of a line passing through (2,8) and (12,16). Then write the equation of another line, perpendicular to the first one and passing through (3,5)
frist line: y=4/5x+32/5
second line: y=-5/4x+35/4
y=−1/2(x+3)^2 +2
shifted 3 units to the left
vertical stretch by a factor of 1/2
downwards reflection
shifted 2 units upwards