Nonlinear equations in one & two variables
|p| + 61 = 65
What value is a solution to the given equation?
a. 65/61
b. 126
c. 4
d. 130
c. 4
In the equation what is the initial value? (y-intercept)
f(x) = 7(3)x
7
The graph of the function f is a line in the xy-plane. If the line has slope 3/4 and f(0)=3, which of the following defines f?
a. f(x) = 3/4x - 3
b. f(x) = 3/4x + 3
c. f(x) = 4x - 3
d. f(x) = 4x + 3
b) f(x) = 3/4x + 3
Tony spends $80 per month on public transportation. A 10-ride pass costs $12.50, and a single-ride pass costs $1.50. If g represents the number of 10-ride passes Tony buys in a month and t represents the number of single-ride passes Tony buys in a month, which of the following equations best represents the relationship between g and t?
a. g + t = 80
b. g + t = 1.50 + 12.50
c. 1.50g + 12.50t = 80
d. 12.50g + 1.50t = 80
d. 12.50g + 1.50t = 80
x = 4
y = 5 - x
The solution to the given system of equations is (x, y).
What is the value of y?
a. 1
b. 4
c. 5
d. 9
a. 1
y = 5 - 4 = 1
x2 = 64
Which of the following values of x satisfies the given equation?
a. -8
b. 4
c. 32
d. 128
a. -8
The function f is defined by f(x) = 16/x. What is the value of f(x) when x=17?
a. 16/17
b. 17/16
c. 16
d. 17
a. 16/17
To repair a refrigerator, a technician charges $60 per hour for labor plus $120 for parts. Which function f represents the total amount, in dollars, the technician will charge for this job if it takes x hours?
a. f(x) = x +120
b. f(x) = 60x
c. f(x) = 60x + 120
d. f(x) = 60x -120
c. f(x) = 60x + 120
A line in the xy-plane has a slope of -1/2 and passes through the point (0, 3). Which equation represents this line?
a. y = -1/2x - 3
b. y = -1/2x + 3
c. y = 1/2x - 3
d. y = 1/2x + 3
b. y = -1/2x + 3
x + y = 20
2(x+y) +3y = 85
If (x, y) is the solution to the given system of equations, what is the value of y?
a. 10
b. 15
c. 60
d. 65
b. 15
graph in desmos find the y value of where the two lines intersect.
x = 49
y = sqrt(x) +9
The graphs of the given equations intersect at the point (x, y) in the xy-plane. What is the value of y?
a. 16
b. 40
c. 81
d. 130
HINT: graph in desmos
a. 16
The function g is defined by g(x) = x2 + 9. For which value of x is g(x) = 25?
a. 4
b. 5
c. 9
d. 13
a. 4
25 = x2 + 9
16 = x2
x = 4The function f is defined by f(x) = 3x - 8. What is the value of f(7)?
a. 29
b. 13
c. -5
d. -29
b. 13
3(7) - 8 = 21 - 8
A city's total expense budget for one year was x million dollars. The city budgeted y million dollars for the departmental expenses and 201 million dollars for all the expenses. Which of the following represents the relationship between x and y in this context?
a. x + y = 201
b. x - y = 201
c. 2x - y = 201
d. y - x = 201
b. x - y = 201
3x = 12
-3x + y = -6
The solution to the given system of equations is (x, y). What is the value of y?
a. -3
b. 6
c. 18
d. 30
b. 6
graph in desmos see where the two lines intersect
38x2 = 38(9)
What is the negative solution to the given equation?
-3
graph in desmos
An investment account opened with an initial value of $890. The value of the account doubled every 10 years. Which equation represents the value of the account M(t), in dollars, t years after the account was opened?
a. M(t) = 890(1/2)t/10
b. M(t) = 890(1/10)t/2
c. M(t) = 890(2)t/10
d. M(t) = 890(10)t/2
c. M(t) = 890(2)t/10
initial = 890
growth factor = 2
only doubles every 10 years hence t/10
f(x) = 7x + 1
The function gives the total number of people on a company retreat with x managers. What is the total number of people on a company retreat with 7 managers?
50
f(7) = 7(7) +1 = 49 +1
For a camping trip a group bought x one-liter bottles of water and y three-liter bottles of water, for a total of 240 liters of water. Which equation represents this situation?
a. x + 3y =240
b. x + y = 240
c. 3x + 3y = 240
d. 3x + y = 240
a. x + 3y =240
3x = 36y - 45
One of the two equations in a system of linear equations is given. The system has no solution. Which equation could be the second equation in this system?
a. x = 4y
b. 1/3x = 4y
c. x = 12y - 15
d. 1/3x = 12y -15
b. 1/3x = 4y
|-5x + 13| = 73
What is the sum of the solutions to the given equation?
a. -146/5
b. -12
c. 0
d. 26/5
d. 26/5 or 5.2
use desmos
The function f is defined by f(x) = (-8)(2)2 +22. What is the y-intercept of the graph of y = f(x) in the xy-plane?
a. (0, 14)
b. (0, 2)
c. (0, 22)
d. (0, -8)
HINT: graph in desmos
a. (0, 14)
y = 18 - 5x
The equation above represents the speed y, in feet per second, of Sheila's bicycle x seconds after she applied the brakes at the end of a ride. If the equation is graphed in the xy-plane, which of the following is the best interpretation of the x-coordinate of the line's x-intercept in the context of the problem?
a. The speed of Sheila's bicycle, in feet per second, before Sheila applied the brakes.
b. The number of feet per second the speed of Sheila's bicycle decreased each second after Sheila applied the brakes.
c. The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop.
d. The number of feet Sheila's bicycle traveled from the time she began applying the brakes until the bicycle came to a complete stop.
c. The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop
The graph of the equation ax + ky =6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2, -6) and (0, -3), what is the value of k?
a. -2
b. -1
c. 2
d. 3
a. -2
a(0) + (-3)k = 6
-3k = 6
k = -2
7/8y - 5/8x = 4/7 - 7/8y
5/4x +7/4 = py +15/4
In the given system of equations, p is a constant. If the system has NO solution, what is the value of p?
HINT: graph in desmos
p = 3.5