Solve $fraction numerator x minus 8 over denominator 3 end fraction equals fraction numerator x minus 3 over denominator 5 end fraction$

In the xy-plane, the point (2, 6) lies on the graph of $y equals k over x$ where k is a constant. Which of the following points must also lie on the graph?

Note:
Whenever there is an unknown constant in the given equation, we must always try to find the value of that constant first with the help of the given conditions. Another way to solve this question is; observe that the equation can be written as x y = k , that is, the product of the x co-ordinate and y co-ordinate always remains a constant. As the point (2, 6) satisfies it, we get that constant to be 12. So we check for which of the points in the options, the product of x co-ordinate and y co-ordinate is 12.

In the xy-plane, the point (2, 6) lies on the graph of $y equals k over x$ where k is a constant. Which of the following points must also lie on the graph?

Find the value of 'x' in the following expressions:(a) 12x – 9 = 5

Solve the following equations. (b) 4m + 11 = 55

y=x²- a
In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

$fraction numerator 2 x plus 6 over denominator left parenthesis x plus 2 right parenthesis squared end fraction minus fraction numerator 2 over denominator x plus 2 end fraction$
The expression above is equivalent to $fraction numerator a over denominator left parenthesis x plus 2 right parenthesis squared end fraction$ , where a is a positive constant and
x ≠ −2. What is the value of a ?

x²+ 20x + y²+ 16y = -20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?

The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y ?

Intersecting lines r, s and t are shown below .

The surface area of a cube is 6(a/4)²,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

$table attributes columnspacing 1em end attributes row cell y equals x squared end cell row cell 2 y plus 6 equals 2 left parenthesis x plus 3 right parenthesis end cell end table$
If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

In triangle ABC above, side AC is extended to
point D. What is the value of y-x?

Note:
It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

In triangle ABC above, side AC is extended to
point D. What is the value of y-x?

A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?