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mathematics
precalculus

Questions and Answers of Precalculus

Add, subtract, or multiple, as indicated. Express your answer as a single polynomial in standard form.(x3 – 2x2 + 5x + 10) - (2x2 -4x +3)
Add, subtract, or multiple, as indicated. Express your answer as a single polynomial in standard form.(x3 + 3x2 + 2) + (x2 – 4x + 4)
Add, subtract, or multiple, as indicated. Express your answer as a single polynomial in standard form.(x2 + 4x = 5) + (3x – 3)
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x + 2x – 1 x² + x + 1
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. x² + 5 x3 – 1
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 10z2 + z
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 2y3 – √2
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3/x + 2
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x2 – 5/x
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. -π
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 5
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 1 - 4x
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x2 – 5
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 3x2 + 4
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. x2 + 2x – 5
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 2x2 x + 1
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 8x x? - 1
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 6x5 – 8x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -2x3 + 5x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -2x-3
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 8/x
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -4x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 2x3
True or False.3x3 – 2x2 – 6x + 4 = (3x - 2)( x2 + 2)
True or FalseThe polynomial x2 + 4 is prime.
To complete the square of the expression x2 + 5x, you _______ would the number ________ .
If factored completely, 3x3 – 12x = __________.
To check division, the expression that is being divided, the dividend, should equal the product of the________and the _________plus the________.
True or False. (x + a)(x2 + ax + a) = x3 + a3
True or False.-4x-2 is a monomial of degree -2.
(x – 2)(x2 + 2x + 4) = ______.
(x2 – 4)(x2+ 5)= _____.
The polynomial 3x4 – 2x3 + 13x2 – 5 is of degeree_____. The leading coefficient is _____.
The Gibb’s Hill Lighthouse, Southampton, Bermuda, in operation since 1846, stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that the
You have 1000 feet of flexible pool siding and wish to construct a swimming pool. Experiment with rectangularshaped pools with perimeters of 1000 feet. How do their areas vary? What is the shape of
Suppose that m and n are positive integers with m > n. If a = m2 – n2, b = 2mm and c = m2 + n2 show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. The deck of a destroyer is 100 feet above sea level. How far can a person see from the deck? How far can a person see
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. A person who is 6 feet tall is standing on the beach in Fort Lauderdale, Florida, and looks out onto the Atlantic
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. The conning tower of the U.S.S. Silversides, a World War II submarine now permanently stationed in Muskegon,
Karen is doing research on the Bermuda Triangle, which she defines roughly by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. On her atlas Karen measures the straight-line
The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew
A circular swimming pool, 20 feet in diameter, is enclosed by a wooden deck that is 3 feet wide. What is the area of the deck? How much fence is required to enclose the deck? 20' II
A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown in the illustration. How much wood frame is needed to enclose the window? 6' 4'
Refer to the figure. Square has an area of 100 square feet; square has an area of 16 square feet. What is the area of the triangle CGF? A
In the figure shown, is a square, with each side of length 6 feet. The width of the border (shaded portion) between the outer square and is 2 feet. Find the area of the border. A B 6 ft 2 ft н
How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?
How many feet does a wheel with a diameter of 16 inches travel after four revolutions?
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 10 -125° 50° 50 5°. -B х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 20 /60° 95° 45 25° 30 х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 30° 16 V75° 12 75° х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 60° .06 4 30° 8
Find the area of the shaded region. 2 2.
Find the area of the shaded region. 2.
Find the area of the shaded region. 2
Find the area of the shaded region. 2 2.
Find the volume V and surface area S of a right circular cylinder with radius 8 inches and height 9 inches.
Find the volume V and surface area S of a right circular cylinder with radius 9 inches and height 8 inches.
Find the volume V and surface area S of a sphere of radius 3 feet.
Find the volume V and surface area S of a sphere of radius 4 centimeters.
Find the volume V and surface area S of a rectangular box with length 9 inches, width 4 inches, and height 8 inches.
Find the volume V and surface area S of a rectangular box with length 8 feet, width 4 feet, and height 7 feet.
Find the area A and circumference C of a circle of radius 2 feet.
Find the area A and circumference C of a circle of radius 5 meters.
Find the area A of a triangle with height 9 centimeters and base 4 centimeters.
Find the area A of a triangle with height 4 inches and base 2 inches.
Find the area A of a rectangle with length 9 centimeters and width 4 centimeters.
Find the area A of a rectangle with length 4 inches and width 2 inches.
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 5, 4, 7
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 4, 3
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 10, 24, 26
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 7, 24, 25
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 2, 2, 3
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 4, 5, 6
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 8, 10
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 3, 4, 5
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 14, b = 48
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 7, b = 24
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 4, b = 3
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 10, b = 24
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 6, b = 8
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 5, b = 12
True or False.The triangles shown are similar. 3 120° 120° 3. 2.
True or False.The triangles shown are similar. 25 25° 100° 100°
True or False.The triangles shown are congruent. 10 30 30 29 29 10
True or False.The volume of a sphere of radius r is 4/3πr2.
True or False.The triangle with sides of length 6, 8, and 10 is a right triangle.
True or False.In a right triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.
Two triangles are________ if corresponding angles are equal and the lengths of the corresponding sides are proportional.
The formula for the circumference C of a circle of radius r is _______.
For a triangle with base b and altitude h, a formula for the area A is _______.
A(n)_______ triangle is one that contains an angle of 90 degrees. The longest side is called the _________ .
Give a reason why statement 5 < 8 is true.
I’m thinking of a number! It lies between 1 and 10; its square is rational and lies between 1 and 10. The number is larger than π. Correct to two decimal places (that is, truncated to two decimal
Is there a positive real number “closest” to 0?
Does 2/3 equal 0.666? If not, which is larger? By how much?
Does 1/3 equal 0.333? If not, which is larger? By how much?
Normal human body temperature is 98.6 F. A temperature x that differs from normal by at least 1.5 F is considered unhealthy. A formula that describes this is |x - 98.6| ≤ 1.5(a) Show that a
The FireBall Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within 0.01
In some countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is |x - 220| ≤ 8(a)
In the United States, normal household voltage is 110 volts. It is acceptable for the actual voltage x to differ from normal by at most 5 volts. A formula that describes this is |x - 110| ≤

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