Deck 12: Review: Equations and Inequalities

Question 1

Draw a scatter plot for this data.x

Answer 1

Question 2

Draw a scatter plot for this data.x

Answer 2

Question 3

Draw a scatter plot for this data.x

Answer 3

Question 4

Draw a scatter plot for this data.x

Question 5

Draw a scatter plot for this data.x

Question 6

Use linear regression to determine the line of best fit for this data.x

Question 7

Use linear regression to determine the line of best fit for this data.x

Question 8

Use linear regression to determine the line of best fit for this data.x

Question 9

Use linear regression to determine the line of best fit for this data.x

Question 10

Given the regression equation y = 2.78x + 32.7, find the value of y when x is 8.

Question 11

Given the regression equation y = -24.2x + 48.5, find the value of y when x is 10.

Question 12

Given the regression equation y = -19x - 1.71, find the value of y when x is 6.

Question 13

Given the regression equation y = 2.76x - 17.7, find the value of y when x is -11.7.

Question 14

Given the regression equation y = 42.2x + 41.7, find the value of y when x is 15.3.

Question 15

Given the regression equation y = 4.8x - 3.75, find the value of y when x is 6.5.

Question 16

Determine if this relationship is a positive or negative association.x

Question 17

Determine if this relationship is a positive or negative association.x

Question 18

Determine if this relationship is a positive or negative association.x

Question 19

Write an equation that describes the variation. Use k as the constant of variation.
y varies directly proportional to
d

Question 20

Write an equation that describes the variation. Use k as the constant of variation.
Y varies directly with both q and p.

Question 21

Write an equation that describes the variation. Use k as the constant of variation.
S varies inversely with both

.

Question 22

Write an equation that describes the variation.
V varies inversely with cube of T.V= 1,040 when T = 6

Question 23

Write an equation that describes the variation.
when

Question 24

Write an equation that describes the variation.
when

Question 25

Write an equation that describes the variation.
when

Question 26

Write an equation that describes the variation.
when

A)

B)

C)

D)

Question 27

A force of 255 N will stretch the spring 34 cm. How far will a force of 622.5 N stretch the spring?

Question 28

A gas contained in a 42 ml container at a temperature of 320 K has a pressure of 1,120 atm. If the temperature increases to 380 K, what is the resulting pressure?

Question 29

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 203 N will stretch the spring 29 cm. How much force is required to stretch the spring 39 cm?

Question 30

A gas contained in a 5 ml container at a temperature of 300 K has a pressure of 3 atm. If the container changes to a volume of 6 ml, what is the resulting pressure?

Question 31

Levi's makes jeans in a variety of price ranges for juniors. The Silver Tab Baggy jeans sell for about $19, whereas the Offender jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 445,000 pairs of the Silver Tab Baggy jeans were bought, approximately how many of the Offender were bought? Round to the nearest integer.

Question 32

In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:
The solar radiation on the Earth is approximately 1050 watts per square meter. How much solar radiation is there on Mars? Round to the nearest hundredth of a watts per square meter.

Question 33

Write an equation that describes the variation. Use k as the constant of variation.
V varies directly with b ⁵

A)
B) V = k b
C)
D) V = k b ⁵

Question 34

Write an equation that describes the variation. Use k as the constant of variation.
V varies directly proportional to the square of x

A) V = k x ²
B) V = k x
C)
D)

Question 35

Write an equation that describes the variation. Use k as the constant of variation.
F varies inversely proportional to L ²

A) f = k L
B)
C)
D) f = k L ²

Question 36

Write an equation that describes the variation. Use k as the constant of variation.
Y varies inversely proportional to the square of t

A)
B)
C) y = k t
D) y = k t ²

Question 37

Write an equation that describes the variation. Use k as the constant of variation.
Y varies directly with both d ² and m ⁵

A) y = k d m ⁵
B) y = k d ² m ⁵
C)
D)

Question 38

Write an equation that describes the variation. Use k as the constant of variation.
Y varies inversely proportional to both z and b ⁴

A)
B)
C) y = k z b ⁴
D)

Question 39

Write an equation that describes the variation.
P varies directly proportional to the fourth power of z. P = 1,250 when z = 5

A)
B) P = 250 z
C) P = 2 z ⁴
D)

Question 40

Write an equation that describes the variation.
Y varies inversely proportional to the square of a. y = 8 when a = 4

A)
B)
C) y = 0.5 a ²
D) y = 2 a

Question 41

Write an equation that describes the variation. Use k as the constant of variation.
F varies directly proportional to both a ² and z . f = 7 when a = 1 and z = 7

A)
B) f = a z
C)
D) f = a ² z

Question 42

Write an equation that describes the variation.
F varies inversely with both $\lambda$ and L. F =

When $\lambda$ = 7 $\mu$ m and L = 600 km.

A)
B)
C)
D)

Question 43

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
Where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 364 N will stretch the spring 28 cm. How far will a force of 468 stretch the spring? Round to two decimal places.

A) 0.22 m
B) 21.78 m
C) 0.36 m
D) 36 m

Question 44

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
Where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 75 N will stretch the spring 15 cm. How much force to the nearest Newtons is required to stretch the spring 33 cm?

A) 34 N
B) 165 N
C) 37,125 N
D) 2 N

Question 45

In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:
The solar radiation on the Earth is approximately 1540 watts per square meter. How much solar radiation is there on Mars? Round to the nearest hundred watts per square meter.

A) 151,973,684.21 watts per square meter
B) 1,013.16 watts per square meter
C) 666.55 watts per square meter
D) 0.00 watts per square meter

Question 46

A gas contained in a 1 ml container at a temperature of 300 K has a pressure of 1.5 atm. If the temperature decreases to 270 K, what is the resulting pressure?

A) 121,500 atm
B) 1.7 atm
C) 450.0 atm
D) 1.4 atm

Question 47

A gas contained in a 2 ml container at a temperature of 350 K has a pressure of 1.5 atm. If the container changes to a volume of 3 ml, what is the resulting pressure?

A) 262.5 atm
B) 2.3 atm
C) 1.0 atm
D) 9.0 atm

Question 48

Levi's makes jeans in a variety of price ranges for juniors. The Flare 519 jeans sell for about $23, whereas the 646 Vintage Flare jeans sell for $110. The demand for Levi's jeans is inversely proportional to the price. If 405000 pairs of the Flare 519 jeans were bought, approximately how many of the 646 Vintage Flare were bought? Round to the nearest integer.

A) 1,936,957 pairs of the 646 Vintage Flare
B) 84,682 pairs of the 646 Vintage Flare
C) 3,682 pairs of the 646 Vintage Flare
D) 17,609 pairs of the 646 Vintage Flare

Question 49

Write an equation that describes the variation.
y varies directly with the square of z and inversely with x. When x = 3 and z = 6, y = 132.

Question 50

Find the slope of the line that passes through the points (0, -9) and (6, 8).

A)
B)
C)
D)

Question 51

Find the slope of the line that passes through the points (9, -4) and (9, 6)

A) 2
B) -10
C) undefined
D) 0

Question 52

Find the slope of the line that passes through the points (7, 8) and (-10, 8).

A)
B) 17
C) undefined
D) 0

Question 53

Find the slope of the line whose equation is given by x - 16y = 15.

A) 16
B) -16
C) 1/16
D) -1/16

Question 54

Find the slope of the line whose equation is given by 8x + y = 18

A) -8
B) 8
C) 1/8
D) -1/8

Question 55

Find the slope of the line whose equation is given by x = -8.

A) -8
B) 8
C) undefined
D) 0

Question 56

Find the slope of the line whose equation is given by y = 10.

A) 10
B) 1/10
C) undefined
D) 0

Question 57

Find the x- and y-intercepts of the line whose equation is given by 4x + 6y = 24.

A) x-intercept: (6, 0), y-intercept (0, 4)
B) x-intercept: (4, 0), y-intercept (0, 6)
C) x-intercept: (-6, 0), y-intercept (0, -4)
D) x-intercept: (-4, 0), y-intercept (0, -6)

Question 58

Find the x- and y-intercepts of the line whose equation is given by 10x - 6y = 60.

A) x-intercept: (-6, 0), y-intercept: (0, 10)
B) x-intercept: (-10, 0), y-intercept: (0, 6)
C) x-intercept: (6, 0), y-intercept: (0, -10)
D) x-intercept: (0, 6), y-intercept: (-10, 0)

Question 59

Find the x- and y-intercept of the line whose equation is given by y + 5 = -20.

A) no x-intercept, y-intercept: (0, -25)
B) no x-intercept, y-intercept: (0, 5)
C) no x-intercept, y-intercept: (0, -20)
D) x-intercept: (0,0), y-intercept: (0, -25)

Question 60

Write the equation of the line given the slope m = -14 and y-intercept (0, 17).

A) y = 17x - 14
B) y = 14x +17
C) y = -14x - 17
D) y = -14x + 17

Question 61

Write the equation of the line given the slope m = 1/12 and x-intercept (1/4, 0).

A)
B)
C)
D)

Question 62

Write the equation of the line given the slope m = -6/5 and a point (-11, 3) that lies on the line.

A)
B)
C)
D)

Question 63

Find the y- and x-intercepts and slope of the line 7x - 3y = 21, if they exist .

Question 64

Find the equation of the line that passes through the point (0, 19) and is parallel to the line y + 5x = 9.

Question 65

The cost of a one day car rental is the sum of the rental fee, $55, plus $0.48 per mile. Write an equation that models the total cost associated with the car rental.

Question 66

Find the equation of the line that passes through the point (5, 6) and is parallel to the line y -4x = 5. Express your answer in slope-intercept form, if possible.

Question 67

Find the equation of the line that passes through the point (15, -7) and is perpendicular to the line 2y + 3x = -9.

Question 68

For the graph, determine the slope.

A)
B)
C)
D)

Question 69

For the graph, determine the slope.

Question 70

For the graph, determine the slope.

A)
B)
C)
D)

Question 71

For the graph, determine the x- and y-intercepts.

Question 72

For the graph, determine the x- and y-intercepts.

A) x-intercept : (4, 0), y-intercept : (0, -2)
B) x-intercept : (-2, 0) , y-intercept : (0, 4)
C) x-intercept : 4, y-intercept : -2
D) x-intercept : -2 , y-intercept : 4

Question 73

For the graph, determine the slope.

Question 74

For the graph, determine the slope.

A) undefined
B) 0
C) 2
D) -2

Question 75

For the graph, determine the x- and y-intercepts.

Question 76

For the graph, determine the x- and y-intercepts.

A) x-intercept : ( 0 , 0 )y-intercept : ( 0 , 0 )
B) None
C) 0
D) Undefined

Question 77

For the graph, identify (by inspection) (a) the x- and y-intercepts and (b) classify the line as increasing, decreasing, horizontal, or vertical.

Question 78

For the graph, identify (by inspection) (a) the x- and y-intercepts and (b) classify the line as increasing, decreasing, horizontal, or vertical.

Question 79

The monthly costs associated with driving a new car are the monthly loan payment plus $ 23 every time you fill up the gasoline. If you fill up 3 times a month, your total monthly cost is $ 400. How much is your car loan?

Question 80

According to NOAA, a "standard day" is 15 C at sea level, and every 500-feet elevation above sea level corresponds to a 1 C temperature drop. Assuming the relationship between temperature and elevation is linear. What is the expected temperature at 3000 feet elevation on a "standard day"?