Waterloo Contest Q.
The five numbers 1/4, 4/10, 41/100, 0.04, 0.404 are to be listed from smallest to largest. Which number will be in the middle of the list?
4/10
A right triangle has angle A=35 degrees and the length of the adjacent side to A is 8 cm. Find the length of the hypotenuse.
9.77cm
Solve for x in the equation: ((2x+3)/4) - ((x-1)/3) = 5/6
x = -1.5
If f(x) = x3 - 4x2 + x - 4, find f(2).
f(2) = -10
Solve the quadratic equation 3x² - 10x + 8 = 0 using the quadratic formula.
x = 2 and x = 4/3
In the diagram, two 8 by 10 rectangles overlap to form a 4 by 4 square. What is the total area of the shaded region?
If sin(x) = 0.6 and x is an acute angle, find the value of cos(x). (hint: use pythagorean identity)
0.8
Factorize the quadratic expression x2 + 7x + 12
(x+3)(x+4)
Factorize the polynomial x3 + 2x2 - 9x - 18
(x+2)(x+3)(x-3)
If the roots of the quadratic equation x² + px + 15 = 0 are 3 and -5, find the value of p.
p = 2
A bus leaves the station at exactly 7:43 AM and arrives at its destination at exactly 8:22 AM on the same day. How long was the bus trip in minutes?
39
Find the value of tan45°+ sin30°
1.5
If y = 3x + 4 and y = 2x - 1, find the value of x and y
x = -5, y = -11
Divide 2x3 + 3x2 - 5x + 6 by x - 2 using synthetic division and find the quotient and remainder.
Quotient: 2x2 + 7x + 9
Remainder: 24
Find the roots of the equation x² + 6x + 10 = 0 by completing the square
x = -3 + i and x = -3 - i
A new mathematical operation, 6♦3 = 2x6 / 3 = 4. If a♦4 = 18, what is the value of a?
36
In a right triangle, if the opposite side to an angle θ is 7 cm and the hypotenuse is 25 cm, find sin(θ) and cos(θ).
sin(θ) = 0.28 and cos(θ) is 0.96
Expand and simplify (2x + 3)(x - 4)
2x2 - 5x - 12
Find the roots of the polynomial x2 - 7x + 12 = 0
x = 3, x = 4
x = 12, x = 13
The operation ▽ is defined by a▽b = (a+1)(b-2) for real numbers a and b. For example, 4▽5 = (4+1)(5-2) = 15. If 5▽x = 30, what is the value of x?
x = 7
Find the value of θ in the interval 0 degrees ≤ θ ≤ 180 degrees if sin(θ) = 0.5.
θ = 30° or θ = 150°
Solve the inequality 4 - 3x ≤ 2x + 9
x ≥ -1
If P(x) = x3 + ax2 + bx + 6 has roots 1, -2, and 3, find the values of a and b.
a = -2, b = -5
Solve for x in the equation 1/x + 1/x-2 = 3/4
x = 4, x = 2/3