A trapezoid has a base of two and six and an area of 24 square units. What is the height?

1 answer:

8 0

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=&\stackrel{bases}{parallel}\\ &sides\\ h=&height\\ \cline{1-2} a=&2\\ b=&6\\ A=&24 \end{cases}\implies 24=\cfrac{h(2+6)}{2}\implies 24=\cfrac{h(8)}{2} \\\\\\ 24=4h\implies \cfrac{24}{4}=h\implies 6=h$

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Henry is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Henr

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Geometric sequence general form: a * r^n
For Greg, we are given the elimination of the medicine as a geometric nth term equation:
200 * (0.88)^t
The amount of medicine starts at 200 mg and every hour, decreases by 12%;
To compare the decrease in medicine in the body between the two, it is useful to get them in a common form;
So, using the data provided for Henry, we will also attempt to find a geometric nth term equation that will work if we can:
As a geometric sequence, the first term would be a and the second term would be ar where r = multiplier;
If we divide the second term by the first term, we will therefore get r, which is 0.94 for Henry;
We can check that the data for Henry can be represented as a geometric sequence by using the multiplier (r) to see if we can generate the third value of the data;
We do this like so:
282 * (0.94)^2 = 249.18 (correct to 2 d.p)
We can tell that the data for Henry is also a geometric sequence.
So now, we just look at the multiplier for Henry and we find that every hour, the medicine decreases by 6%, half of the rate of decrease for Greg.

The answer is therefore that Henry's body eliminated the antibiotic at half of the rate at which Greg's body eliminated the antibiotic.

3 0

2 years ago

Read 2 more answers

Y varies directly with x. If y=25 when x=5, find y when x =-4 y =

alina1380 [7]

Answer:

y = -20

Step-by-step explanation:

Given that y varies directly with x it means changing x will also cause change in y

Mathematically it can be written as:

y∝x

Removing the proportionality symbol