1.1
Write the Phrase as an expression.
The difference of a number t and 9.
t-9
Write the decimal as a fraction or mixed number in the simplest form.
3.82
3 41/50
−2(x + 3) + 5x = −39
x = −11
x − 8 = x − 1
No solution
y + 8 = −11
y = −19
x+12=7
x=-5
1.1x+1.2x-5.4=-10
x=-2
0.1x = 0.2(x + 2)
x = −4
Is the equation a literal equation? Explain.
y = 4
No; The equation only contains 1 variable.
− t/4 = −3π
t = 12π
5/6 = 1/6 + d
d= 2/3
2/3 h − 1/3 h + 11 = 8
h=-9
Write and solve an equation to find the number of miles you must drive to have the same cost for each of the car rentals.
$20 plus $0.50 per mile & $30 plus $0.25 per mile
20 + 0.5m = 30 + 0.25m; 40 mi
4.2x − 1.4y = 2.1
y = 3x − 1.5
The circumference C of a circle is 24π inches. Use the formula C = 2πr to find the radius r of the circle.
12 in
m/π(pi) =7.3
m=7.3π
.
You order two servings of pancakes and a fruit cup. The cost of the fruit cup is $1.50. You leave a 15% tip. Your total bill is $11.50. How much does one serving of pancakes cost?
One serving of pancakes costs $4.25.
1/3(9x + 3) = 3x + 1
infinitely many solutions
The formula K = C + 273.15 converts temperatures from degrees Celsius C to Kelvin K. a. Convert 200 degrees Celsius to Kelvin. b. Solve the formula for C. c. Convert 300 Kelvin to degrees Celsius.
a. 473.15 K
b. C = K − 273.15
c. 26.85°C
To solve 2/5 x = 14, you multiply both sides of the equation by 5/2. Your friend divides both sides of the equation by 2/5. Who is correct? Explain.
Both are correct; Sample answer: Dividing by 2/5 is the same as multiplying by its reciprocal, 5/2.
After earning interest, the account balance is $420. The new balance is 7/6 of the original balance. How much interest did it earn?
$60
Your friend solves the equation. Is your friend correct? Explain your reasoning.
21.) −2(7 − y) + 4 = −4
−14 − 2y + 4 = −4
−10 − 2y = −4
−2y = 6
y = −3
No; Your friend did not distribute the −2 properly.
One serving of oatmeal provides 16% of the fiber you need daily. You must get the remaining 21 grams of fiber from other sources. How many grams of fiber should you consume daily?
25 g; x = 21 + 0.16x
0.84x = 21
x = 25
The volume of a square pyramid with a height of 30 feet is 360 cubic feet. What are the side lengths of the base? Justify your answer.
6 ft; V = Bh/3,
B = 3V/h = — 3(360) 30 = 36.
Because B is the area of the square base, the side lengths of the base are 6 feet.
The boiling point of a liquid is the temperature at which the liquid becomes a gas. The boiling point of mercury is about 41/200 of the boiling point of lead. Write and solve an equation to find the boiling point of lead.
41 — 200 x = 357; 1741°C