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disa [49]
3 years ago
6

Based on the information marked in the diagram, ABC and DEF must be congruent.

Mathematics
2 answers:
ziro4ka [17]3 years ago
7 0
Hello!

As you can see, both AB and DE both have one dash mark. This means they are congruent. Angles C and F are congruent as well. A and D both have right angles. These triangles are congruent.

I hope this helps!
drek231 [11]3 years ago
3 0

Answer:

Option A is correct

True, ΔABC and ΔDEF must be congruent.

Explanation:

LA theorem or Postulates states that given two right triangles,  where one acute angle and a leg of one of the triangles are congruent to  an angle and a leg of the other triangle, then the two triangles are congruent.

In  ΔABC and ΔDEF

AB = DE              [Leg]                [Given in the figure]

\angle BAC = \angle EDF = 90^{\circ}     [Given]

\angle BCA = \angle EFD   [Acute angle]        [Given in the figure]

Then, by the LA theorem or Postulates;

therefore, ΔABC \cong ΔDEF .





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4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

  • The initial population of the fish is <u>200</u>

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

  • The growth rate =<u> 0.05</u>

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, <u>y = 0</u>

The table of values is presented as follows;

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. The domain is the possible x-values which is; 0 ≤ x < ∞

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Which gives;

  • Domain; [0, ∞)
  • Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

  • The population of the fish after 11 years is <u>346 (fishes)</u>

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