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1. The vertices of a triangle are A(25, 35), B(21, 15), and C(22, 12). If all the vertices are moved right and down by 2 units, find the new coordinates of B.

2. If 1" = 2.5 cm, convert 0.51 m into inches.

3. Simplify: [tex]72 + 18 (7 + 2)[/tex].

4. The present price of a book is Rs. 1275. There is a 32.5% discount. Find the original price of the book before the discount.

5. A car can travel 24.30 miles within 3 hours and 20 minutes. Find the speed of the car in km/hr if 1 mile = 1.6 km.

6. Divide 19.64 by 3.4.

Answer :


  1. New coordinates of B after moving right and down by 2 units:

    The original coordinates of B are [tex](21, 15)[/tex]. Moving the point right by 2 units adds 2 to the x-coordinate, and moving it down by 2 units subtracts 2 from the y-coordinate. Therefore:

    [tex]\text{New } x = 21 + 2 = 23 \\
    \text{New } y = 15 - 2 = 13[/tex]

    The new coordinates of B are [tex](23, 13)[/tex].


  2. Convert 0.51 meters to inches:

    Given that 1 inch = 2.5 cm, first convert meters to centimeters and then centimeters to inches. Since 1 meter = 100 cm:

    [tex]0.51 \text{ m} = 0.51 \times 100 \text{ cm} = 51 \text{ cm}[/tex]

    Now, convert centimeters to inches:

    [tex]\text{Inches} = \frac{51}{2.5} = 20.4[/tex]

    So, 0.51 meters is approximately 20.4 inches.


  3. Simplify: [tex]72 + 18(7 + 2)[/tex]:

    First, solve the expression inside the parentheses:

    [tex]7 + 2 = 9[/tex]

    Next, multiply by 18:

    [tex]18 \times 9 = 162[/tex]

    Add this product to 72:

    [tex]72 + 162 = 234[/tex]

    So, the simplified expression is 234.


  4. Find the original price of a book before a 32.5% discount:

    Let the original price be [tex]x[/tex]. Given that there is a 32.5% discount, the current price is 67.5% of the original price:

    [tex]0.675x = 1275[/tex]

    Solving for [tex]x[/tex]:

    [tex]x = \frac{1275}{0.675} \approx 1888.89[/tex]

    The original price of the book was approximately Rs. 1888.89.


  5. Find the speed of the car in km/h:

    The car travels 24.3 miles in 3 hours and 20 minutes. First, convert the time to hours:

    [tex]3 \text{ hours and } 20 \text{ minutes} = 3 + \frac{20}{60} = 3.333 \text{ hours}[/tex]

    Now, calculate the speed in miles per hour:

    [tex]\text{Speed in mph} = \frac{24.3}{3.333} \approx 7.29 \text{ mph}[/tex]

    Convert to kilometers per hour:

    [tex]\text{Speed in km/h} = 7.29 \times 1.6 \approx 11.66 \text{ km/h}[/tex]


  6. Divide 19.64 by 3.4:

    [tex]\frac{19.64}{3.4} \approx 5.776[/tex]

    Therefore, 19.64 divided by 3.4 is approximately 5.776.


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