What is an equation of the line, in point-slope form, that passes through (8, -8); slope: 3

Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
Area = (1/2)(AB + AB/4)·h = (5/8)AB·h

The given dimensions let us determine the area of ∆BCE to be
Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²

The total area of the trapezoid is also the sum of the areas ...
Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h

Putting all of the above into the equation for the total area of the trapezoid, we have
Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
(5/8 -1/6 -1/12)AB·h = 30 cm²
AB·h = (30 cm²)/(3/8) = 80 cm²

Then the area of the trapezoid is
Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²

6 0

3 years ago

Simplify the expression, only odds 9-17

Elodia [21]

All exercises involve the same concept, so I'll show you how to do the first, then you can apply the exact same logic to all the others.

The first thing you need to know is that, when a certain quantity multiplies a parenthesis, you can distribute that number to every element in the parenthesis. This means that

$a(b+c) = ab+ac$

So, $a$ is multiplying the parenthesis involving $b$ and $c$ , and we distributed it: $a$ multiplies both $b$ and $c$ in the final result.

Secondly, you have to know how to recognize like terms, because they are the only terms you can sum. Two terms can be summed if they have the same literal expression. So, for example, you cannot sum $3x+2y$ , and neither $5x^2-4x$ exponents count.