Exam 1: A Review of Basic Algebra

A 70% alcohol solution is to be mixed with a 46% alcohol solution. How many liters of the 46% alcohol solution should be used to make 40 liters of a 52% alcohol solution?

-2 is an example of a(n) ___________ number.

Translate the verbal model into a mathematical model. The perimeter P of an equilateral triangle can be found by tripling the length of one of its sides s .

Find the value of the expression. |6.9|

Solve the equation. Check the result. $a + 17 = 3 a - 2 + a$

Solve: 7 - 2(3 x - 7) = -4 x - 2 x + 21. If the equation is an identity or a contradiction, so indicate.

To help move his furniture, a man rents a truck for $55.50 per day plus 35 cents per mile. If he has budgeted $150 for transportation expenses, how many miles will he be able to drive the truck if the move takes 1 day? __________ miles

Solve the formula for the specified variable. $A = \frac { 1 } { 2 } h \left( B _ { 1 } + B _ { 2 } \right) \text { for } B _ { 1 }$

A bookstore sells a textbook for $40.30. If the bookstore makes a profit of 30% on each sale, what does the bookstore pay the publisher for each book? ( Hint: The retail price = the wholesale price + the markup.)

Perform the operation. Subtract $\frac { 12 } { 13 }$ from $\frac { 1 } { 26 }$ .

The measure of the vertex angle of an isosceles triangle is 140∘ more than twice the measure of a base angle. Find the measure of the vertex angle. ________ ∘

Evaluate the expression for the given values. $\frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } }$ for $x _ { 1 } = - 1 , x _ { 2 } = 5 , y _ { 1 } = 38 , y _ { 2 } = - 4$

Perform the indicated operation: $\left( - \frac { 5 } { 6 } \right) \div \left( - \frac { 15 } { 14 } \right)$

A jet ski can go 12 mph in still water. If a rider goes upstream for 5 hours against a current of 5 mph, how long will it take the rider to return? ( Hint: Upstream speed is (12 - 5) mph; how far can the rider go in 5 hours? )

Variables and/or numbers can be combined with mathematical operations to create algebraic __________.

Solve: $\frac { 5 x + 2 } { 3 } - \frac { x + 2 } { 2 } = \frac { x - 1 } { 6 }$

The illustration shows the angle a needle should make with the skin when administering a certain type of injection. Find the measure of both angles labeled.

Estimate the height of the candle after it has burned for $5 \frac { 1 } { 2 }$ hours. Please round the answer to the nearest inch.

A man has 220 feet of fencing to build the two-part pen shown in the illustration. If one part is a square and the other a rectangle, find the outside dimensions of the pen. ________ $\mathrm { ft }$ by________ $\mathrm { ft }$

The owner of a candy store wants to make a 30-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for 91 cents per pound and lemon gumdrops sell for $1.36 per pound, how many pounds of each should be used? __________ lb of 91 cents candy; __________ lb of $1.36 candy