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a rectangle is 5 feet wide and 3x – 5 feet long. it has the same area as a triangle with a height of 10 feet and a base of x + 3 feet. what is the area of the triangle?

area of rectangle: a=lw area of triangle: a=12bh

x = ?
area of triangle = ?

x=4

Area of triangle=35 square feet

Step-by-step explanation:

Before I start the Area of triangle=1/2(bh) not 12bh.

From the question lw=1/2(bh)

and l=3x-5,w=5, b=x+3 and h=10

So the equation is 5(3x-5)=1/2(10(x+3))

since lw=wl and bh=hb

Then 15x-25=1/2(10x+30) and the LCM is 2 so multiply both sides by 2

2(15x-25)=2(1/2(10x+30)

30x-50=10x+30 since 1/2 eliminates 2

grouping like terms,

30x-10x=30+50

20x=80, dividing both sides by 20

x=4

Area of triangle=1/2(bh)

=1/2(10(x+3)) by inserting the value of x into the equation,

1/2(10(x+3))=1/2(10(4+3))

=1/2(10(7))

=1/2(70)

=35

So the answer is 35 square feet

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .