Answer:
If y(t) is the mass (in mg) remaining after t years, then y(t) = y(0) (0.5)^{t/T} = 400 (0.5)^{t /4}, where T is the half-life period and y(0) is the amount at t = 0 years (initial).
Then at t = 20:
y(20) = 400 (0.5)^{20 /4} = \text{12.5 mg}
Step-by-step explanation:
Answer:
a = -3
General Formulas and Concepts:
<u>Algebra I</u>
- Solving Exponential Equations
- Exponential Property [Rewrite]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<u>Step 2: Solve for </u><em><u>a</u></em>
- Rewrite:
- Rewrite [Exponential Property - Rewrite]:
- Set:
Answer:
c = 17
Step-by-step explanation:
Use the Pythagorean Theorem to solve this problem.
The equation is a² + b² = c².
"a" and "b" are the length of the two shorter sides or values.
"c" is the length of the longest side or value, also the hypotenuse.
Since we know the two smaller values, we can <u>replace "a" and "b" with 8 and 15</u>. It does not matter which letter you decide to replace with which number.
Then<u> simplify and isolate "c" </u>to find the largest value.
a² + b² = c²
8² + 15² = c² Substitute "a" and "b". Square the numbers to simplify
64 + 225 = c² Add to simplify
289 = c²
√289 = √c² Square root both sides
√289 = c "c" will be isolated because √ and ² are reverse operations
c = √289 Put 'c' on the left side for standard formatting.
c = 17 Answer
Therefore the largest value, c, is 17 in the triple.
A is the true statement because the variable g us counted as 1 so then we subtract 6 from 1 =5g
The theorems used are:
First blank: side-angle-side theorem
Second blank: CPCTC
Third blank: 200 feet
Fourth blank: 1,700 feet.
<h3>What is the Side-angle-side Congruence Theorem (SAS):</h3>
Wen two triangles have a pair of included congruent angles and two pairs of corresponding congruent sides, then both triangles are congruent to each other by the side-angle-side theorem.
Furthermore, if two triangles are known to be congruent to each other, the CPCTC states that "corresponding parts of corresponding triangles are congruent". This means all angles and all sides that corresponds to each other are congruent.
Therefore:
Using the <u>side-angle-side theorem</u> it can be shown that the two triangles are congruent to each other.
Then using <u>CPCTC </u>, the length of the road from the intersection to the first turn would be <u>200 feet.</u>
The total length of the tour would be = 2(200 + 300 + 350)
= 1,700 feet.
Learn more about the side-angle-side theorem on:
brainly.com/question/10617589
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