Step 1 involves you listing out all the ways to multiply to 56, and then adding up those factors. For instance, the first row has 1 and 56 which add to 57 in the third column. The second row has -1 + (-56) = -57. The third row has 2+28 = 30. And so on. The idea is to fill out the table completely with the other ways to have factors of 56 added up. The table is shown in the attached image below.
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Step 2 then uses the table to figure out which pair of factors (of 56) add to -15. This would be -7 and -8. In other words,
-7 plus -8 = -15
-7 times -8 = 56
We have found the right pair of numbers. In the table I have provided, this is shown as the highlighted yellow row.
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Step 3 is then using those pair of numbers found in step 2 to set up the factorization. We would say that x^2-15x+56 factors to (x-7)(x-8). This is the same as (x-8)(x-7) as we can multiply two numbers in any order we want.
This is the area of a trapezoid and the formula for that is:
.5(h)(b1 + b2) where h is height and b1 and b2 are the base length or the length of the parallel sides. therefore, our area is:
.5(16)(6+12)
8(18)
144
if you're wondering why the area formula works, construct another trapezoid but this time upside-down. now flip it along it's height axis so you can align one of the side lengths of the 2 trapezoids and you have a parallelogram.
the base of this parallelogram is b1+b2 of the original trapezoid and the height still remains h so the area of this parallelogram is (h)(b1 + b2). however, we want to find the area of the trapezoid but we find that the parallelogram is twice the area of our trapezoid so the area of the trapezoid is half the area of the parallelogram. so area = .5(h)(b1 + b2).
let me know if you have any questions!
Answer: C 1*10^5
Step-by-step explanation:
There are 10^2 cm in a meter, and 10^3 meter in a kilometer, so there are 10^2 * 10^3 = 10^5 cm in a kilometer
