EOC Algebra 1 Practice Test #5

A decorator charges $40 for an initial consultation, then $80 per hour. Another decorator just charges $90 per hour. How long is a job for which the two decorators charge the same price?

A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.09x² + 34x − 100, and the cost of distributing by trucks can be modeled as −0.04x² + 22x − 175, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks.

You are painting the walls in your bedroom and have determined that since you have to paint two coats, one gallon of paint will cover 200 square feet. Which input/output (I/O) model correctly displays the domain and range of this situation where f, the number of square feet that can be painted is a function of g, the number of gallons of paint purchased?

Multiply. Write the product in simplest form.

√2 (√2 + √5)

A patio will be built in the shape of a trapezoid. The bases of the trapezoid will measure 14.5 ft and 22.5 ft. What is the minimum height of the trapezoid if the patio is to have an area of no less than 259 sq ft?

Rebecca has t pounds of grapes. She serves p pounds of the grapes to her friends as a snack on Tuesday and q pounds for dessert on Wednesday. She now has 2.7 pounds left. Use the equation 2.7 = t − p − q to find p, the number of pounds Rebecca served as a snack on Tuesday.

Write an equation for the line that contains the point (-1, 2) and is perpendicular to the line y = 3

Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have the same volume of water? What is that volume of water?

Brenda is building a rectangular pen for her dog. She has enough fencing to build the pen so that its
perimeter is 34 feet and its area is 60 feet. What are the dimensions of the dog pen?

Give the domain and range of the relation.

Charlie has $75 saved and wants to buy DVDs, which cost $9.00 per DVD. The linear equation y = −9x + 75 represents this situation where y is the number of dollars remaining from his savings and x is the number of DVDs that have been purchased.

What is the x-intercept? What does the x-intercept represent?

Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack. Which inequality shows the relationship between the number of packs of regular cards ( r ) and the number of packs of foil cards ( ƒ ) Justin can afford to buy?

In a basketball game, Marlene made 16 fields goals. Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals.

Part B

How many three-point field goals did Marlene make in the game? Enter your answer in the box.

In a basketball game, Marlene made 16 fields goals. Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals.

Part A

Let x represent the number of two-point field goals and y represent the number of three-point field goals. Which equations can be used as a system to model the situation? Select ALL that apply.

On the day of the field trip, each teacher must call the parents of any student who has not returned a permission slip. All of Mr. Gomez's students returned their permission slips, so he did not have to make any calls. Mrs. Hooper and Mr. Anderson had to call a total of eight parents. Mrs. Hooper needed to call two more students than Mr. Anderson. Which set of equations correctly describes the phone calls made? (Let H = Mrs. Hooper's calls and A = Mr. Anderson's calls.)

Which graph best represents the solution to this system of inequalities?

Which is a graph of the solution set of the inequality 3x - 4y ≤ 24

Which quadrant will be completely shaded by the graph of the inequality y < 3x ?

What is the y-coordinate in the solution for the system of linear equations below?

-3x + 2y =6
4x - y = 2

The enrollment at High School R has been increasing by 20 students per year. Currently High School R has 200 students attending. High School T currently has 400 students, but its enrollment is decreasing in size by an average of 30 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment?

Sandy has a total of 35 coins in her money jar. If Sandy's jar contains only nickels and dimes and the value of all the coins is $2.50, how many nickels does Sandy have?

The Smith Family Reunion and the Jones Family Reunion both include a visit to a family friendly amusement park in Florida. The Smith family pays $ 882.00 for passes for 10 adults and 18 children. The Jones family pays $ 951.00 for passes for 11 adults and 19 children. Which equation below can be used to solve for the price of the adult and child admissions?

A construction company spends w weeks extending an existing road. The existing road is 5 miles long. Each week the company completes 0.2 miles of the extension. Which equation models the total length ( L ) of the road over time?

Max purchased a box of green tea mints. The nutrition label on the box stated that a serving of three mints contains a total of 10 Calories.

• On the axes below, graph the function,C , where C (x) represents the number of Calories in x mints.

A full box of mints contains 180 Calories. Use the equation to determine the total number of mints in the box.

Eddie's Towing Company charges $40 to hook a vehicle to the truck and $1.70 for each mile the vehicle is towed.Which equation best represents the relationship between the number of miles towed, , and the total charges, c?

Kesha is planning to rent a van for her trip to Mt. Rainier. Two of her friends each rented the same type of van from the same car rental company last week. This is what they told her:

John: “The cost of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for five days and I drove it 200 miles.”

Katie: “The cost of my rental was only $100. I drove it for 100 miles and had it for two days.”

Kesha plans to get the same type of van that John and Katie had from the same car rental company. Kesha estimated her trip would be 250 miles, and she would have the vehicle for four days.
Let = cost, = miles, and = days
Which equation could Kesha use to figure out how much her rental would cost?

Tim was asked to solve the equation for x . His solution is shown below

In which step did Tim make his first mistake when solving the equation?

Determine which of the following graphs represent a function.

A strip of uniform width is to be added to all four sides of a 9 ft. by 12 ft. rectangle to form a new rectangle of area 180 square feet. How wide is the strip?

Find the intersection of the pair of sets.
M = {1, 2, 3, 4, 5, 6}; N = {2, 3, 4, 5, 6, 7}

The trajectory of a model rocket launched from a rocket launcher on the ground at an angle of 50 degrees with an initial speed of 55 meters per second can be modeled by the parabola: f(x) = 1.19x – 0.0039x², where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the model rocket travels before hitting the ground.

A baker has 16 cups of chocolate chips. His recipe for chocolate chip cookies calls for 1 \frac12  cups of
chocolate chips per batch. Which inequality can be solved to find b, the number of batches of chocolate chip cookies the baker can make?

Solve 8.7 = 3.5y − 2.5(5.4 − 6y).

Which inequality is shown by the graph below?

Miguel has $85 saved and wants to buy DVDs, which cost $8.50 per DVD. The linear equation y = −8.50x + 85 represents the number of dollars y remaining from his savings after x DVDs have been purchased. Graph the equation and explain the meaning of the slope as a rate of change.

Graph the line described by the equation 4x − 4y = 8.

ABCD is a parallelogram.

What is the equation of the line containing \overline{\rm CD} ?

Alicia has invented a new app for smart phones that two companies are interested in purchasing for a 2-year contract. Company A is offering her $10,000 for the first month and will increase the amount each month by $5000.

Company B is offering $500 for the first month and will double their payment each month from the previous month.

Monthly payments are made at the end of each month. For which monthly payment will company B’s payment first exceed company A’s payment?

Ramon disagrees with Jasmine and claims that the number of canned goods collected can be modeled by a linear function.

Which statement is true about the number of cans predicted to be collected on the 6th day based on the two models?

During the 1st day of a canned-goods drive, Jasmine’s homeroom teacher collected 2 cans. During the 3rd day, the teacher collected 8 cans. Let D represent each collection day, and let N represent the number of canned goods collected on that day.

Part A

Based on the situation, Jasmine claims that the number of canned goods collected can be modeled by an exponential function. What is the number of canned goods collected on the 6th day based on an exponential
model? Enter your answer in the box.