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juin [17]
3 years ago
6

Find x and TU Show all the work

Mathematics
1 answer:
Licemer1 [7]3 years ago
5 0

Answer:

x = 10

TU = 24

Step-by-step explanation:

To find the value of x, we use the trapezoid mid-segment theorem

The sum of the lengths of the two parallel sides is equal to twice the length of the mid segment

Mathematically, we have this as;

2(2x+ 4) = 2x-4 + 3x + 2

4x + 8 = 5x - 2

5x -4x = 8 + 2

x = 10

TU = 2x + 4 ; = 2(10) + 4 = 20 + 4 = 24

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the half-life of strontium-90 is approximately 29 years. how much of a 500 g sample of strontium-90 will remain after 58 years​
Yuliya22 [10]

Answer:  125 g

<u>Step-by-step explanation:</u>

A = P_o\cdot e^{kt}\\\\\text{First, use the given information to find k:}\\\\\bullet A=\dfrac{1}{2}P_o\\\\\bullet k = unknown\\\\\bullet t=29\text{ years}\\\\\dfrac{1}{2}P_o=P_o\cdot e^{k(29)}\\\\\\\dfrac{1}{2}=e^{k(29)}\qquad divided\ both\ sides\ by\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=ln\bigg(e^{k(29)}\bigg)\qquad applied\ ln\ to\ both\ sides\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=29k\qquad simplified-ln\ and\ e\ cancel\ out\\\\\\\dfrac{ln\bigg(\dfrac{1}{2}\bigg)}{29}=k\qquad divided\ 29\ from\ both\ sides\\\\\\-0.0239=k

\text{Now, use the following in the equation to solve for A:}\\\\\bullet A=unknown\\\bullet P_o=500\\\bullet k=-0.0239\\\bullet t=58\text{ years}\\\\A=500\cdot e^{(-0.0239)(58)}\\\\.\quad=500\cdot e^{-1.386}\\\\.\quad=125

8 0
4 years ago
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