The area of a room is 96 square feet. the length is (x+1) feet and the width is (x-3) feet. find the dimensions of the room

length = 12 feet and width = 8 feet

Step-by-step explanation:

since the area = 96 ft² then

(x + 1)(x - 3) = 96 ( A = lw )

expand the factors on the left side

x² - 2x - 3 = 96 ( subtract 96 from both sides )

x² - 2x - 99 = 0 ← in standard form

(x - 11)(x + 9) = 0 ← in factored form

equate each factor to zero and solve for x

x - 11 = 0 ⇒ x = 11

x + 9 = 0 ⇒ x = - 9

but x > 0 ⇒ x = 11

length = 11 + 1 = 12 feet and width = 11 - 3 = 8 feet

57 732

step-by-step explanation:

i dont really.know

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12