Algebra

Question 1: (1 point)

Solve.

10x−19=2x−15

x= ____________

Question 2: (1 point)

Solve.

3(3−y)+8=−8(y−3)−5

If the answer is not an integer, enter it as a fraction. If there is no solution, enter “none”. If all real numbers are solutions, enter "all".

 y= ____________

Question 3: (1 point)

Solve.

7−6w3=3(w+2)4

If the answer is not an integer, enter it as a fraction. If there is no solution, enter “none”. If all real numbers are solutions, enter "all".

 w= ____________

Question 4: (1 point)

Solve.

11−x8=8(x+2)3

If the answer is not an integer, enter it as a fraction. If there is no solution, enter “none”. If all real numbers are solutions, enter "all".

x= ____________

Question 5: (1 point)

Solve.

−26w+11=116w−3

If there is no solution, enter “no solution”.

 w= ____________

Question 6: (1 point)

Solve.

−8y9y−5+2=59y−5

 If there is no solution, enter “no solution”.

y= ____________

Question 7: (1 point)

Solve for w.

−4y+6w=9

w= __________

Question 8: (1 point)

Solve for t.

−4−s=4tj+10

If the expression for t is a rational expression, enter it as a single term in simplest form. For example, if the expression is 3t−g,enter 3−gtt.

t=__________

Question 9: (1 point)

Solve for z.

x=y4(11−z)

Enter the expression in simplest form.

z=

Question 10: (1 point)

Sophie earns a salary of $550per month for working 5hours a day. In May, Sophie worked additional hours at $16per hour and earned $630for the month.

Write an equation to model this situation where xis the number of additional hours she worked in May.

__________

Find the number of additional hours she worked in May.

Additional hours = ____________

Question 11: (1 point)

A student's grade in a course is the average of 4 test grades and a final exam that is worth twice as much as each test. Suppose a student has test grades of 89, 89, 90, and 92. Write an equation to model this situation where xis the student's grade on the final exam and yis the student's average for the course.

__________

Then find the score they will need to receive on their final exam if they want to have a grade of 91 for the course.

Final exam score needed = ____________

Question 12: (1 point)

Suppose your average, after taking 4 quizzes, is 74 (out of 100). What must your average be on the next 4 quizzes to increase your average to 82 out of 100?

Required average = ____________

Question 13: (1 point)

The product of two consecutive integers is 12less than the square of the smaller integer. Find the larger of the two integers.

The larger of the two integers is ____________.

Question 14: (1 point)

Find the largest of three consecutive odd integers whose sum is 273.

The largest of the three integers is ____________.

Question 15: (1 point)

A concert ticket is marked 25%off and the sale price is $27.00.What was the original price?

Original price:   $ ____________

Question 16: (1 point)

Kelly earns 10% more than Cici, and together they earn $1155.00per week. How much does Kelly earn per week?

If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed.

Kelly earns $ ____________each week.

Question 17: (1 point)

Amy invests money in two simple interest accounts. She invests three times as much in an account paying 10% as she does in an account paying 5%. If she earns $131.25 in interest in one year from both accounts combined, how much did she invest altogether?

Total Principal in Both Accounts =  $ ____________

Question 18: (1 point)

A cone has volume V=13πr2h,where ris the radius of the cone's base and his the height of the cone. Find the height in centimeters of a cone with volume 84πcm3and radius 6centimeters.

Height of cone:  ____________  centimeters

Question 19: (1 point)

A 10-foot tree casts a 12-foot shadow. At the same time, a nearby cell tower casts a 60-foot shadow. How tall (in feet) is the cell tower?

Height of cell tower: ____________feet

Question 20: (1 point)

Amy drove from Los Angeles to Ventura during rush hour at an average speed of 45miles per hour, and then drove back the same way at an average speed of 30miles per hour.

If the round trip took 3 hour and 15 minutes, how many miles is Amy's one-way  trip from Ventura to Los Angeles?

If the answer is not an integer, enter it as an exact decimal.

____________miles

Question 21: (1 point)

Express commuter train #12 leaves the downtown station and travels at an average speed of 45miles per hour towards the north side station, which is33.75miles away. Fifteen minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 45miles per hour towards the downtown station.

At the moment when the two trains pass each other, how far (in miles) is the #12 train from the downtown station and how long (in minutes) has the #12 train have been traveling?

If the answer is not an integer, enter it as an exact decimal.

#12 train is    ____________    miles from the downtown station and has been traveling for   ____________   minutes.

Question 22: (1 point)

Two pumps can fill a water tank in 295minutes when working together. Alone, the second pump takes 5times as long as the first to fill the tank.

How many minutes would it take the first pump to fill the tank?

It will take ____________  minutes for the first pump to fill the tank.