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Q1 (4)   Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm

 

In case of a right triangle, the length of its hypotenuse is highest.  hypotenuse be h. Taking, 5cm, 12 cm By Pythagoras theorem, = given third side. Hence, it is a right triangle with h=13 cm.

Q14.    IQ of a person is given by the formula

                IQ= \frac{MA}{CA}\times 100

where MA is mental age and CA is chronological age. If 80\leq IQ\leq140 for a group of 12 years old children, find the range of their mental age.

Given that group of 12 years old children. For a group of 12 years old children,   CA =12 years  Putting the value of IQ, we obtain  Thus, the range of mental age of the group  of 12 years old children is         

Q13.    How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Let  x  litres of water is required to be added. Total mixture = (x+1125) litres  It is evident that amount of acid contained in the resulting mixture is 45% of 1125 litres. The resulting mixture contain  more than 25 % but less than 30%  acid.                     and                            and                                                                                                  ...

Q12.    A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Let x litres of 2% boric acid solution is required to be added. Total mixture = (x+640) litres  The resulting mixture is to be more than 4% but less than 6% boric acid.                     and                            and                                                                                                                                                                             ...

Q11.    A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by

            F = \frac{9}{5}C + 32?

Since the solution is to be kept between 68° F and 77° F.   Putting the value of   , we have   the range in temperature in degree Celsius (C) is between  20 to 25.

Solve the inequality and represent the solution graphically on number line.

    Q10.    5(2x-7)-3(2x+3)\leq 0,\quad 2x + 19 \leq 6x +47

Given :      The solution graphically on the number line is as shown :  

Solve the inequality and represent the solution graphically on number line.

    Q9.    3x - 7 > 2(x-6),\ 6-x > 11 - 2x

Given :            The solution graphically on the number line is as shown :  

Solve the inequality and represent the solution graphically on number line.

    Q8.    2(x-1)<x+5,\ 3(x+2)> 2 -x

Given :            The solution graphically on the number line is as shown :    

Solve the inequality and represent the solution graphically on number line.

    Q7.    5x + 1 > -24,\ 5x - 1 <24

Given :            The solution graphically on the number line is as shown :    

Solve the inequality

    Q6.    7 \leq \frac{(3x+ 11)}{2}\leq 11

Given the linear inequality   The solution set  of the given inequality is  

Solve the inequality

    Q5.    -12<4-\frac{3x}{-5} \leq 2

Given the inequality      Solution set is 

Solve the inequality

    Q4.    -15 < \frac{3(x-2)}{5} \leq 0

Given The inequality     The solution set is 

Solve the inequality

    Q3.    -3 \leq 4 - \frac{7x}{2}\leq 18

Given      Solution set is 

Solve the inequality

    Q2.    6 \leq -3(2x - 4) < 12

Given   Solution set is 

Solve the inequality

    Q1.    2\leq 3x-4\leq5

Given :     Thus, all the real numbers greater than equal to 2 and less than equal to 3 are solutions to this inequality. Solution set is   

Solve the following system of inequality graphically:

    Q15.    x+2y \leq 10, \ x +y \geq 1, \ x-y\leq 0, x\geq 0, \ y\geq 0

Graphical representation of    is given in graph below. For   The  solution to this inequality is region below the  line  including points on this line because  points on line also satisfy the inequality.  For , The  solution to this inequality is region above the line   including points on this line because  points on line also satisfy the inequality.  For , The  solution to this inequality...

Solve the following system of inequality graphically:

    Q14.    3x + 2y \leq 150, \ x +4y \leq 80,\ x\leq 15 \ y\geq 0, \ x\geq 0

Graphical representation of    is given in graph below. For   The  solution to this inequality is region below the  line  including points on this line because points on the line also satisfy the inequality.  For , The  solution to this inequality is region below the line   including points on this line because points on the line also satisfy the inequality.  For , The  solution to this...

Solve the following system of inequalities graphically:

    Q13.    4x + 3y \leq 60,\ y\geq 2x,\ x\geq 3,\ x,y\geq 0

Graphical representation of    is given in graph below. For   The  solution to this inequality is region below the  line  including points on this line because points on the line also satisfy the inequality.  For , The  solution to this inequality is region above the line   including points on this line because  points on the line also satisfy the inequality.  For , The  solution to this...

Solve the following system of inequalities graphically:

    Q12.    x -2y \leq 3, 3x + 4y \geq 12, x \geq 0, y\geq 1

Graphical representation of    is given in graph below. For  , The  solution to this inequality is region above the  line  including points on this line because  points on line also satisfy the inequality.  For , The  solution to this inequality is region above the line   including points on this line because  points on line also satisfy the inequality. For  The  solution to this inequality is...

Solve the following system of inequalities graphically:

    Q11.    2x +y \geq 4, \ x + y \leq 3, \ 2x - 3y \leq 6    

Graphical representation of   and    is given in graph below. For  , The  solution to this inequality is region above the line  including points on this line because  points on line also satisfy the inequality.  For , The  solution to this inequality is region below the line   including points on this line because  points on line also satisfy the inequality. For  The  solution to this...
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