The function g is defined as $g left parenthesis x right parenthesis equals fraction numerator 2 x over denominator 3 end fraction plus 3$ . What is the value of $g left parenthesis negative 30 right parenthesis$ ?

Name the theorem or postulate that justifies the given statement.
∠1 ≅ ∠2

A rope joins the points P ≡ (-10, 5) and Q ≡ (6, 9). At which point should we cut the rope to get two equal parts?

The parallel sides of a trapezium are in the ratio 3:4. If the distance between the parallel sides is 9cm and the area is 126cm², find the length of its parallel sides.

The functions f and g are defined by f(x) = 4x and g(x)= x². For what value of x does f (x)– g( x) =4 ?

Note:
Instead of solving the equation $x squared minus 4 x plus 4 equals 0$ in the above way, we could also use the quadratic formula, given by
$x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$

Where the quadratic equation is given by $a x squared plus b x plus c equals 0$
Or we could simply observe that it the expression of a perfect square

The functions f and g are defined by f(x) = 4x and g(x)= x². For what value of x does f (x)– g( x) =4 ?

Find the co-ordinates of the mid-point of AB, if A ≡ (1, 10) and B ≡ (3, -8).

The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.

The area of a parallelogram is 120 sq.cm and its altitude is 10 cm. Find the length of the base.

Maths-General

$text If end text x plus 3 equals 2 x minus 2 comma text what is the value of end text x minus 4 ?$

Note:
Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.

$text If end text x plus 3 equals 2 x minus 2 comma text what is the value of end text x minus 4 ?$

Find the value of x that satisfies the equation 7x + 22 = − 27 .

The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?

Joe’s age is 16 years less than 5 times Jim’s age. Find Jim’s age if Joe is 9 years old.

Are the two polygons congruent? Explain why or why not.

The area of a trapezium is 28 sq.cm and one of its parallel sides is 6 cm. If its altitude is 4 cm, find its other parallel side.

Maths-General

$2 x open parentheses x squared plus 1 close parentheses plus open parentheses 2 x squared minus 2 x close parentheses$
Which of the following expressions is equivalent to the expression above?

Note:
Another way of solving this problem is to expand all the terms in the expression
$2 x open parentheses x squared plus 1 close parentheses plus open parentheses 2 x squared minus 2 x close parentheses$
Then we get,
$2 x cubed plus 2 x plus 2 x squared minus 2 x$
Thus, we will get that
$2 x open parentheses x squared plus 1 close parentheses plus open parentheses 2 x squared minus 2 x close parentheses$
Can be written as
$2 x cubed plus 2 x squared$
This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.

$2 x open parentheses x squared plus 1 close parentheses plus open parentheses 2 x squared minus 2 x close parentheses$
Which of the following expressions is equivalent to the expression above?