Determine whether the given values of the variables are solutions of the equation.
(a) (b)
2.
Solve the equation.
3.
4.
Solve the equation for.
5.
The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation . Find the weight x of an elephant that consumes 400 lb of food per day.
6.
An executive in an engineering firm earns a monthly salary plus a Christmas bonus of $8,900. If she earns a total of $96,500 per year, what is her monthly salary?
7.
A pasture is four times as long as it is wide. Its area is. How wide is the pasture?
8.
Catalina paints with watercolors on a sheet of paper a = 22 inches wide by b = 17 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?
9.
What quantity of a 40% acid solution must be mixed with a 10% solution to produce 300 mL of a 30% solution?
10.
Solve the equation by factoring.
11.
Solve the equation by completing the square.
12.
Find all real solutions of the equation.
13.
Use the discriminant to determine the number of real solutions of the equation.
x^{2} - 5.66x + 2.52 = 0
14.
Evaluate the expression (5 + 10i)(7 - 9i) and write the result in the form a + bi.
15.
Evaluate the expression and write the result in the form a + bi.
16.
17.
Find all solutions of the equation and express them in the form a + bi.
18.
x ^{4} = 4x ^{2}
19.
20.
21.
A jeweler has three small solid spheres made of gold, of radius 1 mm, 2 mm, and 3 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be? Round the answer to one decimal place.
22.
Solve the inequality. Express the solution using interval notation.
23.
A car rental company offers two plans for renting a car.
Plan A:
$40 per day and $0.20 per mile.
Plan B:
$60 per day with free unlimited mileage.
For what range of miles will plan B save you money?
24.
25.
1.
(a) no (b) yes
-3
11
10,000 lb
240 ft
3
2
8,56
14
Determine whether the given value is a solution of the equation.
,
4(x + 6) + 7 = - 6(x + 11) + 67
The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation . Find the weight x of an elephant that consumes 200 lb of food per day.
Solve the inequality. Express the answer using interval notation.
Al paints with watercolors on a sheet of paper 22 inches wide by 17 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 102 inches. How wide is the strip of the mat showing around the picture?
Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be . During what time interval will the ball be at least 64 ft above the ground
5x - 3 = 6x + 4
yes
8, 56
$7,300
-7
Determine which of the given choices is a solution of the equation.
(a) 1 (b) - 1 (c) 0 (d) 2 (e) none of these
3(x + 11) + 1 = - 3(x + 5) + 7
(a) 3 (b) - 7 (c) 10 (d) 7 (e) - 18
(a) - 12 (b) 12 (c) 144 (d) 6 (e) 10
(a) (b) (c) (d) (e) none of these
(a) 15,000 lb (b) 20,000 lb (c) 10,000 lb (d) 5,000 lb (e) none of these
Caitlin paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?
(a) 8 inches (b) 4 inches (c) 6 inches (d) 2 inches (e) 3 inches
What quantity of a 50% acid solution must be mixed with a 20% solution to produce 300 mL of a 40% solution?
(a) 100 mL (b) 180 mL (c) 120 mL (d) 240 mL (e) 200 mL
(a)
(b)
(c)
(d)
(e) none of these
(a) x = -9, x = -4 (b) x = 9, x = -4 (c) x = -9, x = -8 (d) x = 9, x = 4 (e) none of these
Solve the inequality.
(a) (b) (c) (d) (e)
x^{2} - 5.79x + 2.37 = 0
(a) no real solutions
(b) exactly one real solution
(c) two real solutions
(d) more than two real solutions
Evaluate the expression (4 + 7i)(11 - 4i) and write the result in the form a + bi.
(a) 72 + 61i
(b) 44 + 77i
(c) 61 + 72i
(d) - 61 - 72i
(a) 4 + 5i (b) 4 - 5i (c) - 5 - 4i (d) 5 + 4i (e) none of these
(a) -1 (b) 1 (c) i (d) -i (e) none of these
Find all solutions of the equationand express them in the form a + bi.
(a) x = 3 + 2i, x = 3 - 2i
(b) x = 1 + 3i, x = 1 - 3i
(c) x = 1, x = - 1
(d) x = 4 + 12i, x = 4 - 12i
(e) no solutions
x ^{4} = 16x ^{2}
(a) x = 0, x = 4, x = -4
(b) x = 0
(c) x = 0, x = 16, x = -16
(d) x = 0, x = 16
(a) x = 0, x = 20 (b) x = 5, x = 20 (c) x = 0, x = -25 (d) x = 20, x = 80 (e) none of these
(a) 0 (b) 0, 11 (c) 11 (d) 1, 0 (e) -11
Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains of grain?
(a) ( -4, 2 ) (b) [ -4, 2 ] (c) [ -2, 4 ) (d) [ -4, 2 ) (e) [ -2, 4 ]
Solve the nonlinear inequality.
(e)
In the vicinity of a bonfire the temperature T in at a distance of x meters from the center of the fire was given by . At what range of distances from the fire’s center was the temperature less than 400?
b
d
e
c
a
(a) -1
(b) 1
(c) i
(d) - i
(d) -61 - 72i
(a) 100 mL
(b) 180 mL
(c) 120 mL
(d) 240 mL
(e) 200 mL
(a) 15,000 lb
(b) 20,000 lb
(c) 10,000 lb
(d) 5,000 lb
Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be . During what time interval will the ball be at least 64 ft above the ground?
(a) 1
(b) -1
(c) 0
(d) 2
(a) 4 + 5i
(b) 4 - 5i
(c) - 5 - 4i
(d) 5 + 4i
(a) - 18 (b) 7 (c) 3 (d) 10 (e) - 7
Josiah paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?
(a) 2 inches
(b) 8 inches
(c) 3 inches
(d) 6 inches
(e) 4 inches
(a) 61 + 72i
(c) 72 + 61i
(a) - ( - i ) (b) - i (c) 1 (d) -1 (e) none of these
Find all real solutions of the equation
(a) x = 0
(b) x = 0, x = 4, x = -4
(c) x = 0, x = 16
(d) x = 0, x = 16, x = -16
(a) -11 (b) 0, 11 (c) 11 (d) 1, 0 (e) 0
(a) [ -4, 2 ) (b) ( -4, 2 ) (c) [ -2, 4 ] (d) [ -2, 4 ) (e) [ -4, 2 ]
no
Joshua paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?
(a) 2 inches (b) 8 inches (c) 3 inches (d) 6 inches (e) 4 inches
|x + 19| = |4x + 7|
A pasture is four times as long as it is wide. Its area is. How long is the pasture?
960 ft
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