Algebra Arithmetic
Enter an expression equivalent to (3x2+2y2-3x)+(2x2+y2-2x)-(x2+3y2+x) using the fewest number of possible terms.
4x2-6x
Mike earns $6.50 per hour plus 4% of his sales.
Enter an equation for Mike's total earnings, E, when he works x hours and has a total of y sales, in dollars.
E = 6.5x + 0.04y
A student solved 3/(x - 4) = x/7 in six steps, as shown.
Step 1: 3 = x(x - 4)/7
Step 2: 21 = x(x - 4)
Step 3: 21 = x2 - 4x
Step 4: 0 = x2 - 4x - 21
Step 5: 0 = (x - 7)(x + 3)
Step 6: x = -3, x = 7
Which statement is an accurate interpretation of the student's work?
A. The student solved the equation correctly.
B.The student made an error in step 2.
C. The student made an error in step 5.
D. Only x = 7 is a solution to the original equation.
A
Select the expression that is equivalent to (m2 - 25).
A. (m2 - 10m + 25)
B. (m2 + 10m + 25)
C. (m - 5)(m + 5)
D. (m - 5)2
C
Maria is making a rectangular garden. The length of the garden is 2 yards greater than its width, w, in yards.
Enter the function, f(w), that describes the area, in square yards, of Maria's garden as a function of the width, w.
f(w) = w(w + 2)
Multiply & combine like terms to determine the product of these polynomials.
(2x-3)(5x+6)
10x2-3x-18
Jim can paint a house in 12 hours. Alex can paint a house in 8 hours.
Enter an equation that can be used to find the time in hours, t, it would take Jim and Alex to paint the house together.
1/12 + 1/8 = 1/t
Determine if the following equation has no real solutions, one real solution, or infinitely many real solutions.
5/20x = 1/4x
Infinitely Many Real Solutions
Select the expression that is equivalent to x2 - 4.
A. (x - 2)2
B. (x - 2)(x + 2)
C. x2 + 2x + 4
D. x2 - 2x + 4
B
A theater needs to place seats in rows. The function, f(r), as shown below, can be used to determine the number of seats in each row, where r is the row number.
f(1) = 8
f(r) = f(r - 1) + 3
Use the function to determine the number of seats in each of the first four rows of the theater.
Row 1 - 8 seats
Row 2 - 11 seats
Row 3 - 14 seats
Row 4 - 17 seats
Enter an expression that is equivalent to (4x2-5x+6)+(9x2-2x)-(11x-3), combining all like terms.
13x2-18x+9
Consider the given equation that models a train's distance from its departing station, where:
y represents the distance in miles,
x represents the speed of the train in miles per hour
t represents the time traveled from the departing station in hours.
y = xt
Enter an equation for which the solution is the speed of the train, in miles per hour, where the train's distance from the station is 162 miles and it has traveled for 3 hours.
162=3x
Enter the value of x that makes the equation true.
1/x = 5
x = 1/5
Select the expression that is equivalent to (x + 4)2 - (x - 2)(x + 4).
A. 4(x + 4)
B. 2(x + 1)(x + 4)
C. (x + 4) - (x - 2)
D. (x + 4)[(x + 4) - (x - 2)]
D
A company purchases $24,500 of new computer equipment. For tax purposes, the company estimates that the equipment decreases in value by the same amount each year. After 3 years, the estimated value is $9800.
Write an explicit function that gives the estimated value of the computer equipment n years after purchase.
f(n) = -4,900n + 24,500
Which expression is equivalent to (mx+5)+(2x-b)?
A. 2mx - 5b
B. (2+m)x-b+5
C. 2mx-5+b
D. 2mx-bmx+10x-5b
B
Consider the equation that gives the minimum stopping distance, d, in feet, for an automobile, where:
v represents the automobile speed, in feet per second
s represents the driver's response time, in seconds, to apply the brakes, and
m represents the coefficient of friction between the tires and the road.
d = vs + (v2/64m)
Enter an equation for which the solution is the speed, in feet per second, of an automobile with a stopping distance of 200 feet, a driver's response time of 0.5 second, and a coefficient of friction equal to 0.8.
200=0.5v+(v2/51.2)
Enter the value of t that makes the equation true.
1/(t - 4) = 3/t
t = 6
Determine if the equation is true for all values of x.
x2 + 4 = (x + 2)2
No
Draw the graph of the inverse of f(x) = -3/2x - 3 on the coordinate plane.
x-intercept: (-3, 0)
y-intercept: (0,-2)
Enter an expression equivalent to (-1/2 at) X (12t3) in the form Axmyn.
-6at4
An elementary school is having sand delivered for the playground. Sadie's Sand charges $5.00 per ton of sand plus a delivery fee of $200. Greg's Sand Pit charges $12.00 per ton of sand plus a delivery fee of $50.
Create two functions to represents the cost C of buying T tons of sand from each company.
Sadie's Sand: C = 5T + 200
Greg's Sand Pit: C = 12T + 50
Select whether the equation has no real solutions, one real solution, or infinitely many real solutions.
10/x = 20/(x + 20)
x = 20
Determine if the equation is true for all values of x.
23x = 6x
No
Using your knowledge of the graph of y = x2, draw the graph of the equation y = (x - 4)2 + 2.
Vertex of parabola: (4, 2)