P^2=-3p+40 factor this problem

Mathematics

1 answer:

Marrrta [24]2 years ago

3 0

$p^2=-3p+40\\
p^2+3p-40=0\\
p^2+8p-5p-40=0\\
p(p+8)-5(p+8)=0\\
(p-5)(p+8)=0\\
p=5 \vee p=-8
$

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Step-by-step explanation:

The area of a trapezoid with bases b₁ and b₂ and height h is given by the formula

$A=\left(\dfrac{b_1+b_2}{2}\right)h$

If you're wondering how we get this formula, check the attached illustration (remember the area of a parallelogram is its base multiplied by its height)! Moving on to our trapezoid, the pairs of points (-5,-3)(4,-3) and (6,-7)(-7,-7) form two horizontal segments, which form b₁ and b₂, and our height is the distance between the y-coordinates -3 and -7, which is 4. We can find b₁ and b₂ by finding the distance between the x coordinates in their pairs of points:

$b_1=|-5-4|=|-9|=9\\b_2=|6-(-7)|=|6+7|=13$