Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e $M to the power of straight prime left parenthesis S right parenthesis greater than 0$ ., on the left side
and the function is decreasing, i. e $M to the power of straight prime left parenthesis s right parenthesis less than 0$ ., on the right hand side, then we say that is a local maxima.

The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where $20 less or equal than s less or equal than 75$ .
$M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50$
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?

Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.

Find the area of the polygon in the given picture, $text if end text MP equals 9 cm comma MD equals 7 cm comma MC equals 6$ cm, $MB equals 4 cm text and end text MA equals 2 cm$

A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.

A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.

In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.

From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?

Find the area of the figure. $GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12$
.

$y equals 2 x plus 4$
$y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis$
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
$x squared minus 3 x minus 10 equals 0$ by middle term factorisation, we could also use the quadratic formula, which is 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 standard form of equation is $a x squared plus b x plus c equals 0$

$y equals 2 x plus 4$
$y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis$
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?

Find the area of an isosceles trapezium ABCD, if the parallel sides are 6cm and 14 cm, its non parallel sides is 5cm each.

$fraction numerator x minus 2 over denominator 3 end fraction plus fraction numerator y minus 1 over denominator 4 end fraction equals 13 over 12$ and $fraction numerator 3 plus y over denominator 3 end fraction plus fraction numerator x minus 2 over denominator 2 end fraction equals 11 over 6$ Solve by using the elimination method.

The sides of a parallelogram are 12cm and 8cm. one of the diagonal is 10cm long. If d is the length of the other diagonal, then which of the following is correct?

Cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.