Mathematics

Question

PLEASE HELP !!!!
1) A rectangular swimming pool with length b and width h is surrounded by a walkway which is 3 feet wide. Which equation below could be used to find the area of the walkway?

A) A=(b+6)(h+6)-bh

B) A=bh-(b+6)(h+6)

C) A=(b+3)(h+3)-bh

D) A=(b+6)(h+6)

2) The following table is an example of inverse variation.

X Y
-------------
4 48
6 32
8 24
16 12

Which equation models the relationship between x and y?

A) x=4/3 y

B) x=y/192

C) y=192/x

D) y=12x

3) The distance d that an object travels in t seconds is given by the formula d=1/2 at^2 , where a is the acceleration of the object. Which of the following expresses a in terms of d and t?

A) a=2dt^2

B) a= dt^2/2

C) a= d/2t^2

D) a= 2d/t^2

Thanks for your help:)

2 Answer

  • The first answer is A because (b+6) represents the sidewalk length. (With the pool length and the two corners, which equal 3 ft each.) Then, the sidewalk width would be (h+6) for the same reason. Multiply them and get the pool area plus the sidewalk area. But you only need the sidewalk area so you would subtract the pool area from the whole area, to get (b+6)(h+6)-bh, or A in the end.

    Unfortunately, I do not know the answers to the rest of the problems. I still hope this helped though!
  • The equation from the equations listed in the problem that can be used to find the area of the walkway is given by: Option C) A=(b+3)(h+3)-bh

    How does area of a rectangle, and its length and width are related?

    Area of a rectangle is the product of its length and width.

    If a rectangle has length L units and width of W units, then

    Area = L × W squared units.

    For the given condition, the walkway is the area between the bigger rectangle and smaller rectangle.

    Thus, its area can be found by subtracting area of smaller rectangle from the bigger rectangle(as area of composite figure = sum of areas of composing figures, or say, that bigger rectangle's area is sum of area of smaller rectangle and area of walkway)

    Area of bigger rectangle = Area of walkway + Area of smaller rectangle.

    Let we denote them by symbols as:

    • A = Area of walkway
    • B = Area of bigger rectangle
    • C = Area of smaller rectangle

    Thus, A = B - C

    Finding the value of B and C:

    • Value of B = Area of bigger rectangle

    Bigger rectangle has length = length of smaller rectangle + 3 feet = b +3

    Width of bigger rectangle = width of smaller rectangle + 3 feet = h + 3

    Thus, area of bigger rectangle =  (b+3)(h+3)   sq. feet.

    Thus, A = (b+3)(h+3) sq. feet

    • Value of C = Area of smaller rectangle(the rectangular swimming pool)

    Smaller rectangle's length = b

    Smaller rectangle's width = h

    Thus, area of smaller rectangle = bh

    (sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)

    • Value of A = Area of walkway

    [tex]\rm A = B - C\\A = (b+ 3)(h+3 ) - bh[/tex] (in sq. feet)

    Thus, the equation from the equations listed in the problem that can be used to find the area of the walkway is given by:

    Option C) A=(b+3)(h+3)-bh

    Learn more about area of rectangle here:

    https://brainly.com/question/349091

NEWS TODAY