If point A(-2 , b) lies on the line that passes through the points B(2,4) and C(-1,0), what is the value of b?
To which expression is \( \dfrac{\dfrac{x^2+1}{x+2}}{\dfrac{1}{x+2}+4} \) equivalent to for x > 6?
A) \( \dfrac{x^2+1}{4} \)
B) \( \dfrac{x^2+1}{4x + 9} \)
C) \( \dfrac{x^2+1}{x + 2} \)
D) \( \dfrac{1}{x + 2} \)
Find the real number c such that \((x - 2)^2 + 4 + c\) has a minimum value equal to 2.
A) -6
B) -4
C) -2
D) 4
t seconds after a ball is thrown vertically from ground, at a velocity of 30 meters per second, its height h changes with time as follows:
\( h(t) = -5 t^2 + 30 t \)
where h is in meters. For how long will the height of the ball be more than 25 meters?
t seconds after a ball is thrown vertically from ground, at a velocity 30 meters per second, its height h changes with time as follows:
\( h(t) = -5 t^2 + 30 t \)
where h is in meters. What is the change in the height of the ball between t = 1 and t = 2 seconds?
The graph of the cost \( C(x) = m x + b \) in US dollars as a function of the number of units produced x by a company, is shown below. m is the cost per unit and b is the fixed cost.
Use the graph to approximate m, the cost per unit, and the fixed cost b.
The graph of the revenue \( R(x) = a x \) in US dollars as a function of the number of units x produced by a company, is shown below. a is the revenue per unit sold.
Use the graph to approximate a.
The graphs of the revenue \( R(x) = a x \) and the cost \( C(x) = m x + b \) are shown below. R and C are in US dollars and x is the number of units produced by a company. The break even point is the point at which \( R(x) = C(x) \).
Find the revenue at the break even point in terms of m, a and b.
The resistances \( R_1 \) and \( R_2 \) of two resistors in parallel in an electric circuit are equivalent to a resistance \( R_e \) and are related by \( \dfrac{1}{R_e} = \dfrac{1}{R_1} + \dfrac{1}{R_2} \). Express \( R_e \) in terms of \( R_1 \) and \( R_2 \).
The magnitude of the universal gravitational force F between two bodies of masses \( m_1 \) and \( m_2 \) is given by \( F = \dfrac{G m_1 m_2}{d^2} \) where G is a constant and d is the distance between the two bodies. If the force between two bodies at a distance d is equal to 2000 Newtons, what is the magnitude of the force between the same bodies at a distance equal to 4d?
The graphs of a semi circle of diameter OB and two lines are shown below. Point O is the origin of the system of axes. Line L has the equation \( y = \frac{1}{3}x \) and intersects line M and the semi circle at the point C. Line M intersects the semi circle and the x axis at the point (4 , 0). Find an equation for line M.
A total of 200 students are registered in a high school. A student can register in several courses but must register in only one course of geology, geography or chemistry. The table below shows the registration of the students in these three courses.
How many boys are registered in chemistry?
Use the table in the last problem to find the probability p that a student selected at random, in that high school, is registered in geology or geography.
According to the theory of relativity, the mass m of a particle at a speed v, close to the speed of light c, is given by \[ m = \dfrac{m_0}{\sqrt{1- v^2 / c^2 }} \] where \( m_0 \) is the mass of the particle at rest. What is the mass of a particle with a speed \( v = 0.9 c \) and a mass at rest \( m_0 = 1 \) gram?
The graph of the equation \( x^2 + y^2 - 4x + 2y + 2 = 0 \) in the xy-plane is a circle. What is the area of the surface enclosed by this circle?
z is a complex number and \( \overline{z} \) its conjugate. What is z if \( 2z + 3\overline{z} - 3i = 4 + 7i \) where \( i = \sqrt{-1} \)?
Functions g and f are given by \( g(u) = 3u + 3 \) and \( f(t + 2) = g(2t - 3) \). What is \( f(x) \)?
m is a real number included in the equation \( 2x^2 + 3 m x = 4 - 2x \). For what value(s) of m is the sum of the solutions of the given equation greater than 5?
Triangle ABC is equilateral. What are the coordinates of point C?
What is the diameter of the circle whose area and perimeter have the same value?
John can read 15 pages of a document every 20 minutes. Linda can read 20 pages of the same document every 16 minutes. How many minutes are needed so that John and Linda read a total of 100 pages together of the same document?
x and y are integers. The remainder of the division of x by 3 is 1 and the remainder of the division of y by 3 is 2. What is the remainder of the division of \( 2x + 3y \) by 3?
Find the smallest positive integer x so that when it is divided by 5 the remainder is 4 and when it is divided by 6 the remainder is 5.
1 liter of water is poured into a cylindrical container of radius 10 cm. How high in cm will the water rise?
If the length of AB is \( \frac{1}{3} \) of the length of BO, what is the length of cord MN of the circle with center O and a radius 5 cm?
In the figure below, AB is tangent to a circle with diameter BC. Find the length of segment AD.
Lines m and n are parallel and lines k, n and J all intersect at the same point O. Find the size of angle x.
In the figure below, points A, B and C are on a circle of radius 5 cm, O is the center the circle and angle CAB has a size of \( 30^\circ \). What is, to one decimal place, the area of the shaded (blue) part?
