Rational and Irrational Numbers
Is 12/4 a rational or irrational number?
If Rational what subset?
Rational - Natural Number
Write 4,500 in scientific notation.
4.5 × 10³
Solve: x + 3 > 7.
x > 4.
Solve: x + 7 = 15.
X = 8
A cell phone plan costs $30/month plus a $20 sign-up fee. Write an equation for the total cost after x months.
C = 30x + 20.
Is √36 rational or irrational?
If Rational - What Subset?
Rational - Natural Numbers
Write 0.00062 in scientific notation.
6.2 × 10⁻⁴.
Solve: 5x – 2 ≤ 8.
x ≤ 2.
3x – 5 = 16.
X= 7
A taxi charges $2 per mile plus $4 base fee. Write an equation for the cost of x miles.
C = 2x + 4.
Identify if –√50 is rational or irrational.
Irrational
Convert 3.5 × 10⁶ into standard form.
3,500,000.
Solve: 2(x – 1) > 3x + 4.
x < −6.
2(x + 3) = 5x – 6.
x = 4.
A gym charges $25/month with a $50 fee. Another charges $40/month with no fee. Write an equation that represents when the two costs are equal.
25x + 50 = 40x.
Solve: 50 = 15x ⇒ x = 50/15 = 10/3 ≈ 3.33 months.
Order from least to greatest: ––√3, 1/2, 0, -2
-2, –√3, 0, 1/2
Convert 2.3 × 10-3 into standard form.
0.0023
Identify 3 solutions to: –2x + 5 ≥ 11.
x ≤ −3.
-3, -4, -5
Solve: 4x – 7 = 2x + 11.
x = 9.
A tank has 60 liters of water and leaks 2 liters per minute. Another tank starts with 20 liters and fills at 3 liters per minute. After how many minutes will they have the same amount of water?
t = 8 minutes.
A student says π/2 is rational. Explain why this is incorrect.
This is a long, non repeating decimal.
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A ride requires passengers to be at least 48 inches tall but less than 80 inches tall. Write and graph an inequality that represents the allowable height (h).
48 ≤ h < 80.
A rectangle’s length is (2x – 1) and width is (x + 4). If the perimeter is 38, write and solve an equation to find x.
x = 16/3
Company A charges $12 per hour plus $30 fee. Company B charges $15 per hour with no fee. After how many hours will the costs be equal, and which is cheaper after 10 hours?
h = 10 hours.
neither; costs are equal.