College Algebra
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Find out the length of the side of a square if its perimeter is equal to the square of its diagonal.
Find out the radius of the circular top of a cylindrical water bottle if the height of the bottle is 86 cm and the total surface area is 8800 cm2.
Find the solutions to the following equation. h2 = 256
Find the solutions to the following equation. h2 = - 256
Find the solutions to the following equation. k2 + 361 = 0
Find the solutions to the following equation. k2 - 361 = 0
Among the following equations, select which one can be directly solved by using the zero-factor property and work out the value(s) of x.1. 4x2 - 23x - 35 = 02. (3x + 1)2 = 43. x2 - x = 724. (9x - 4)(x - 5) = 0
Among the following equations, select which one can be directly solved by using the square root property and work out the value(s) of x.
1. 4x2 - 23x - 35 = 02. (3x + 1)2 = 43. x2 - x = 724. (9x - 4)(x - 5) = 0
Among the following equations, select which one can solved by skipping the first step in completing the square and work out the value(s) of x.
Among the following equations, select which one can be directly solved by using the quadratic formula and work out the value(s) of x.
Use the zero-factor rule to solve the given quadratic equation.
x2 - 9x + 20 = 0
x2 + x - 30 = 0
3x2 - x = 24
-8x2 + 17x = -21
x2 - 81 = 0
49x2 - 126x + 81 = 0
64x2 + 176x + 121 = 0
Use the square root rule to solve the given quadratic equation.
x2 = 225
125 - x2 = 0
75 - x2 = 0
x2 = -900
(7x + 1)2 = 96
In the given equation, complete the square and solve it.m2 -4m -1 = 0
In the given equation, complete the square and solve it.18x2 +x = 4
In the given equation, complete the square and solve it.28x2 +9x = 37
In the given equation, complete the square and solve it.-2x2 + 26x -81 = 0
In the given equation, complete the square and solve it.4x2 - 24x +111= 0
Use the quadratic formula to find x.2x2 - 74x + 673= 0
Use the quadratic formula to find x.3x2 - 14x + 10 = 0
Use the quadratic formula to find x.x2 -26x +159=0
Use the quadratic formula to find x.x2 -6x +58=0
Use the quadratic formula to find x.4x2 -32x + 101=0
Use the quadratic formula to find x.(1/2)x2 + (1/4)x - 25/8 = 0
Use the quadratic formula to find x.x2 + (14/8)x -147/16=0
Use the quadratic formula to find x.16(8x -1)(x + 1) = -15
Use the quadratic formula to find x.(11x + 2)(x - 17) = 7x
Make use of factoring and the quadratic formula to solve the given cubic equation.8x3 -343 = 0
Make use of factoring and the quadratic formula to solve the given cubic equation.512x3 +1 = 0
Solve for b in the following equation:k = (1/8)ab2
The following equation has a non-zero variable in the denominator. Solve for p.
L = xBp2/t
For the following equation, solve for g.
c2 = c1 + mg2
For the following equation, solve for L.
z = - 9L2 + xL + y
For the following equation, express x in terms of y:
13x2 + 8xy - 10y2 = 6
For the following equation, express y in terms of x:
9x2 - 15xy + 5y2 = 7
Identify the number of distinct solutions of the following quadratic equation by calculating its discriminant. Then, classify the solutions (nonreal complex number, rational, or irrational):
x2 - 36x + 324 = 0
13x2 + 44x + 15 = 0
7x2 = 11x - 3
12x2 - 5x + 2 = 0
3x2 - 588 = 0
Suppose 3 and 2 are the solutions of the equation ax2 + bx + c = 0. Find the values of a, b and c.
Suppose 2i and -2i are the solutions of the equation ax2 + bx + c = 0. Find the values of a, b and c.
The product of two consecutive integers is 90. Find the two integers.
The product of two consecutive even integers is given as 360. Find the two integers.
The product of two consecutive odd integers is 99. Find the two integers.
Find two consecutive odd integers if the sum of their squares is 394.
Find two consecutive even integers if the sum of their squares is 100.
Find two positive consecutive even integers if the difference of their squares is 124.
Find two positive consecutive odd integers if the difference of their squares is 48.
Two squares of unknown lengths and different sizes are compared. They cover a total area of 194 ft2, and the side of the larger square is 8 ft longer than the other. Work out the side lengths of these two squares.
A rectangular garden is designed such that its length is 20 cm more than thrice its width. If the total area covered by this garden is 124,000 cm2, calculate the garden's length and width.
A titanium bar has a length that is 20 cm more than its width. From all corners of this bar, squares each having an area of 16 cm2 are cut so that the flaps could be bent and eventually folded towards the top to form a hollow box that is open from the top. This titanium box now has a volume of 176 cm3. Solve for the dimensions of the titanium bar used.
Harley wants to ferment a strange fruit and decides to store his mixture inside a barrel that has a surface area of 1128π in2. For safety, there should be a free space for the vapors and vigorous gases that the process will produce, hence this cylindrical barrel should have a height of 35 in. Harley wants to design a perfect circular cover to complete the storage. Calculate the radius of this cover.
A playground that has the shape of a right triangle will be fenced. The length of the shorter leg is 7 m shorter than the longer one. Also, the hypotenuse is 9 m longer than the shorter leg. Calculate the length of the shorter leg.
The height (in meters) of a toy rocket in t seconds after its release from the ground is defined by y = - 4.9t2 + v0t. If the initial velocity is v0 = 23 m/s, determine the times that this toy will reach a height of 14 m. Also, determine how long it will take to hit the ground. Approximate the answers to the nearest hundredth.
Solve the quadratic equation given below for x.
3x2 + 17x - 56 = 0
-3x2 + 5x = -22
(3x - 4)(x - 3) = 5x
x2 - √6x - 1 = 0
(x + 3)(x + 6) = 3x
Which of the following quadratic equations has two real and distinct solutions?
(x - 9)2 = -13
(-3x + 7)2 = -135
In the given equation, complete the square and solve it.p2 +8p -33 = 0
In the given equation, complete the square and solve it.121x2 -242x + 101 = 0
Which of the following equations represent the sides of a triangle given below?
A vinyl flooring is to be laid in a study room with a length of 15 meters and a width of 10 meters. The owner wants to leave a consistent strip of flooring surrounding the vinyl surface that he plans to cover with foam. 66 m2 of vinyl flooring is currently available. What should be the length and width of the vinyl flooring?
Which of the following quadratic equations has two nonreal complex roots?
Identify the number and type of solutions for the given quadratic equation by calculating its discriminant.
4x² = -5x - 11
-6x2 + 5x = 13
28x2 + 15 = -41x
In a right triangle ABC, the measure of shortest side (AB) is 1 in. shorter than the measure of middle side (AC) and the measure of the hypotenuse (BC) is 8 in. longer than the measure of the middle side (AC). Find the measure of AB, AC and BC.
Identify the following function's graph by first solving for its x-intercepts and then matching it with the given graphs.
y = 2x2 -8x +9