Question 1

Solve the formula for B . Volume of a pyramid: 
A) 
B) 
C) 
D) 
E) none of these

Accepted Answer

The answer of Solve the formula for B . Volume...

Question 2

Solve the equation. 37 = -5 - 11 b
A) 
B) 
C) 
D) 
E)

Accepted Answer

To solve the equation, we need to isolate the variable b by performing inverse operations.

First, we can add 5 to both sides of the equation:

37 + 5 = -11b

Simplifying:

42 = -11b

Next, we can divide both sides by -11:

-3.82 = b

So the solution is b = -3.82, which corresponds to choice B.

Question 3

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 7 less than two-thirds of the number.
A) 21
B) 42
C) 35
D) 49
E) 28

Accepted Answer

The answer of Use an algebraic approach to solve the...

Question 4

Solve A = P + Prt for A , given that P = $1100,  , and t = 11 years.
A) A = $2,057.50
B) A = $2,007.50
C) A = $907.50
D) A = $2,307.50
E) A = $1,907.50

Accepted Answer

The answer of Solve A = P + Prt for...

Question 5

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 34 inches. Find the length and width of the rectangle.
A) 6 inches wide, 11 inches long
B) 3 inches wide, 14 inches long
C) 4 inches wide, 13 inches long
D) 5 inches wide, 12 inches long
E) 8 inches wide, 9 inches long

Accepted Answer

Let the length be L and the width be W. According to the problem, W = (1/4)L + 2. The perimeter is given by 2L + 2W = 34. Substituting W in the perimeter equation gives 2L + 2((1/4)L + 2) = 34. Solving this equation, L = 12 and W = 5.

Question 6

Solve the formula  for the variable  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the formula  for the variable...

Question 7

Use an algebraic approach to solve the problem: A board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.
A) 35 feet
B) 7 feet
C) 21 feet
D) -7 feet
E) 14 feet

Accepted Answer

Let the length of the shorter piece be $x$ feet. Then, the length of the longer piece is $\frac{2}{3}x$ feet. Since the total length of the board is 35 feet, we have the equation $x + \frac{2}{3}x = 35$. Solving for $x$, we find that $x = 14$ feet, which is the length of the shorter piece.

Question 8

The city's water department charges $8 per month, plus 44 cents for every 100 gallons of water used. Last month, one homeowner used 1,900 gallons and received a bill for $17.98. Was the billing correct? If the billing is not correct, what is the correct billing amount for this homeowner given these facts?
A) no; the billing amount is $15.59
B) yes; the billing amount is $17.98
C) no; the billing amount is $16.36
D) no; the billing amount is $15.38
E) none of these

Accepted Answer

The fixed charge is $8, so we subtract that from the total bill to get the amount charged for water usage: $17.98 - $8 = $9.98. We can then set up the equation 0.44x = 9.98, where x is the number of 100 gallons used. Solving for x, we get x ≈ 22.68, which means the homeowner used about 2,268 gallons of water. To check, we can calculate the actual cost for this amount of water: $8 + 22.68($0.44) = $8 + $9.97 = $17.97, which is very close to the billed amount but not exact. Therefore, the correct billing amount is $16.36 (the fixed charge of $8 plus the cost of water usage, which is 19 times $0.44 or $8.36).

Question 9

The perimeter  of a rectangle with length  and width  is given by the formula  . Solve this formula for  . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The perimeter  of a rectangle with...

Question 10

The power  lost when an electric current  passes through a resistance  is given by the formula  . Solve for  . If  is 2,900 watts and  is 16 amperes, calculate  to the nearest hundredth of an ohm.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The power  lost when an electric...

Question 11

The masses of two objects are MS1U1B11S1U1B0 and MS1U1B12S1U1B0. The force of gravitation  between the masses is given by  where  is a constant and  is the distance between them. Solve for M S1U1B12S1U1B0.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The masses of two objects are MS1U1B11S1U1B0...

Question 12

Solve the formula  for the variable r . Then substitute numbers i = 56 , p = 100, and t = 7 to find the variable's value.
A) r = 37
B) r = - 51
C) r = 0.08
D) r = 163
E) r = 0.56

Accepted Answer

The answer of Solve the formula  for the variable...

Question 13

Solve the formula  for the variable  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the formula  for the variable...

Question 14

Solve the equation. 2.8 = -10 t + 7.2
A) t = 7.44
B) t = 0.44
C) t = -0.56
D) t = 1.44
E) none of these

Accepted Answer

Start by isolating the variable "t" on one side of the equation. Subtracting 7.2 from both sides, we get:
2.8 - 7.2 = -10t
-4.4 = -10t
Dividing both sides by -10, we get:
0.44 = t
Therefore, the solution is t = 0.44 which corresponds to choice B.

Question 15

Use an equation to solve the problem. A sport jacket that sells for $170 has a markup of $80. Find the wholesale price.
A) $70
B) $85
C) $75
D) $90
E) $100

Accepted Answer

The answer of Use an equation to solve the problem....

Question 16

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $7,400. What was the average price of a home last year?
A) $89,500
B) $90,500
C) $93,500
D) $92,500
E) $88,500

Accepted Answer

Let x be the average price of a home last year.
Then, the new average price is 0.92x (8% decrease is the same as multiplying by 0.92).
We also know that 0.92x = x - 7,400 (the new price is $7,400 less than the old price).
Solving for x, we get x = $92,500.
Therefore, the answer is choice D, $92,500.

Question 17

A call to Tucson from a pay phone in Chicago cost 85 cents for the first minute and 27 cents for each additional minute or portion of a minute. If a student has $9.00 in change, how long can she talk?
A) 42 min
B) 30 min
C) 34 min
D) 31 min
E) 38 min

Accepted Answer

The first minute costs 85 cents, leaving $8.15 ($9.00 - $0.85). Each additional minute costs 27 cents. $8.15 divided by $0.27 equals 30.18, which means 30 additional minutes plus the first minute equals 31 minutes total.

Question 18

The illustration below is a schematic diagram of a resistor connected to a voltage source of 60 volts. As a result, the resistor dissipates power in the form of heat. The power P lost when a voltage V is placed across a resistance R is given by the formula  If P is 12 watts and E is 60 volts, find R .
A) R = 300 ohms
B) R = 400 ohms
C) R = 250 ohms
D) R = 320 ohms

Accepted Answer

The answer of The illustration below is a schematic diagram...

Question 19

Solve the formula  for the variable  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the formula  for the variable...

Question 20

Use an equation to solve the problem. Sales tax on a $11 compact disc is $0.55. At what rate is sales tax computed?
A) 9%
B) 5%
C) 4%
D) 8%
E) 6%

Accepted Answer

The sales tax rate can be found by dividing the sales tax amount ($0.55) by the price of the item ($11) and then multiplying by 100 to convert to a percentage: ($0.55 / $11) * 100 = 5%.

Quiz 2: Equations and Inequalities

Solve the formula for B . Volume of a pyramid:

Solve the equation. 37 = -5 - 11 b

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 7 less than two-thirds of the number.

Solve A = P + Prt for A , given that P = $1100, , and t = 11 years.

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 34 inches. Find the length and width of the rectangle.

Solve the formula for the variable .

Use an algebraic approach to solve the problem: A board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

The perimeter of a rectangle with length and width is given by the formula . Solve this formula for . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

The power lost when an electric current passes through a resistance is given by the formula . Solve for . If is 2,900 watts and is 16 amperes, calculate to the nearest hundredth of an ohm.

The masses of two objects are M₁ and M₂. The force of gravitation between the masses is given by where is a constant and is the distance between them. Solve for M ₂.

Solve the formula for the variable r . Then substitute numbers i = 56 , p = 100, and t = 7 to find the variable's value.

Solve the formula for the variable .

Solve the equation. 2.8 = -10 t + 7.2

Use an equation to solve the problem. A sport jacket that sells for $170 has a markup of $80. Find the wholesale price.

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $7,400. What was the average price of a home last year?

A call to Tucson from a pay phone in Chicago cost 85 cents for the first minute and 27 cents for each additional minute or portion of a minute. If a student has $9.00 in change, how long can she talk?

Solve the formula for the variable .

Use an equation to solve the problem. Sales tax on a $11 compact disc is $0.55. At what rate is sales tax computed?

Quiz 2: Equations and Inequalities

Solve the formula for B . Volume of a pyramid:

Solve the equation. 37 = -5 - 11 b

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 7 less than two-thirds of the number.

Solve A = P + Prt for A , given that P = $1100, , and t = 11 years.

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 34 inches. Find the length and width of the rectangle.

Solve the formula for the variable .

Use an algebraic approach to solve the problem: A board 35 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

The perimeter of a rectangle with length and width is given by the formula . Solve this formula for . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

The power lost when an electric current passes through a resistance is given by the formula . Solve for . If is 2,900 watts and is 16 amperes, calculate to the nearest hundredth of an ohm.

The masses of two objects are M1 and M2. The force of gravitation between the masses is given by where is a constant and is the distance between them. Solve for M 2.

Solve the formula for the variable r . Then substitute numbers i = 56 , p = 100, and t = 7 to find the variable's value.

Solve the formula for the variable .

Solve the equation. 2.8 = -10 t + 7.2

Use an equation to solve the problem. A sport jacket that sells for $170 has a markup of $80. Find the wholesale price.

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $7,400. What was the average price of a home last year?

A call to Tucson from a pay phone in Chicago cost 85 cents for the first minute and 27 cents for each additional minute or portion of a minute. If a student has $9.00 in change, how long can she talk?

Solve the formula for the variable .

Use an equation to solve the problem. Sales tax on a $11 compact disc is $0.55. At what rate is sales tax computed?

The masses of two objects are M₁ and M₂. The force of gravitation between the masses is given by where is a constant and is the distance between them. Solve for M ₂.