Slopes of Lines & Equations of Lines
Find the slope of the line passing through the points (-3, -3) and (5, 6)
9/8
x - y = 2
x + y = 6
{(4,2)}
x + y = 12
y = 3x
{(3, 9)}
2x - y = 12
3x + 2y = -3
{(3, -6)}
It's length is 78 ft and its width is 36 ft.
Let f(x) = 6x - 4
Find f(-1), f(2), and f(0)
-10, 8, -4
Eva is paid an hourly wage. One week she worked 43 hr and was paid $795.50. How much does she earn per hour?
Her hourly wage is $18.50
Determine whether the pair of lines is parallel, perpendicular, or neither:
x+4y=7
4x-y=3
Perpendicular
x - 2y = 6
x + 2y = 2
{(4, -1)}
7x + 4y = 13
x + y = 1
{(3, -2)}
2x + y = 8
5x - 2y = -16
{(0, 8)}
Leanna is a waitress at Bonefish Grill. During one particular day she sold 15 ribeye steak dinners and 20 grilled salmon dinners, totaling $559.15. Another day she sold 25 ribeye steak dinners and 10 grilled salmon dinners, totaling $582.15. How much did each type of dinner cost?
The ribeye steak dinner cost $17.29 and the salmon dinner cost $14.99.
Find (f+g)(x) and (f - g)(x)
(f+g)(x)=x^2+2x-9
(f-g)(x)=x^2-2x-9
The weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 200-lb astronaut would weigh 32 lb on the moon. How much would a 50-lb dog weigh on the moon?
8 lb
Write an equation of the line passing through the given points. Give the final answer in standard form.
(5, -2) and (-3, 14)
2x + y = 8
3x + y = 5
6x + 2y = 10
{(x, y) | 3x + y = 5}
5x + 2y = -15
2x - y = -6
{(-3, 0)}
3x + 3y = 33
5x - 2y = 27
{(7, 4)}
How many gallons each of 25% alcohol and 35% alcohol should be mixed to obtain 20 gal of 32% alcohol?
6 gallons of 25% alcohol and 14 gallons of 35% alcohol would be needed.
Find (fh)(x) and (fg)(x)
(fh)(x)=x^3-3x^2-9x+27
(fg)(x)=2x^3-18x
The volume of a can of tomatoes is directly proportional to the height of the can. If the volume of the can is 300 cm^3 when its height is 10.62 cm, find the volume to the nearest whole number of a can with a height of 15.92 cm.
450 cm^3
Write an equation of the line that satisfies the given conditions. Give the equation in slope-intercept form and in standard form.
Through (7, 2); parallel to 3x - y = 8
y = 3x - 19
3x - y = 19
-3x + y = -3
y = x - 3
{(0, -3)}
2x + y = 0
4x - 2y = 2
{(1/4, -1/2)}
24x + 12y = -7
16x - 18y = 17
{(1/8, -5/6)}
A train travels 150 km in the same time that a plane travels 400 km. If the rate of the plane is 20 km per hr less than three times the rate of the train, find both rates.
The rate of the train is 60 km per hr and the rate of the plane is 160 km per hr.
Find
(f/g)(x) and (f/h)(x)
(f/g)(x)=(x^2-9)/2x, x≠0
(f/h)(x) = x+3, x≠3
The frequency of a vibrating string varies inversely as its length. That is, a longer string vibrates fewer times in a second than a shorter string. Suppose a piano string 2 ft long vibrates 250 cycles per sec. What frequency would a string 5 ft long have?
100 cycles per sec
Write an equation of the line that satisfies the given conditions. Give the equation in slope-intercept form and in standard form.
Through (8, 5); perpendicular to 2x - y = 7
y=-1/2x+9
x+2y = 18
2x - y = 6
4x - 2y = 8
Ø
x = 2 - y
x + y = -5
Ø
0.5x + 3.4y = 13
1.5x - 2.6y = -25
{(-8, 5)}
Traveling for 3 hr into a steady head wind, a plane flies 1650 mi. The pilot determines that flying with the same wind for 2 hr, he could make a trip of 1300 mi. Find the rate of the plane and the wind speed.
The rate of the plane is 600 mph and the rate of the wind is 50 mph.
The amount of light (measured in foot-candles) produced by a light source varies inversely as the square of the distance from the source. If the illumination produced 1 m from a light source is 768 foot-candles, find the illumination produced 6 m from the same source.
21.33 foot-candles