Rick bought 3 shirts for $18 each, 2 pairs of socks for $3.99 a pair, and a pair of pants for $45.00. The sales tax
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The population size after 6 years and after 8 years are 147 and 169 population respectively
<h3>Exponential functions</h3>The standard exponential function is expressed as y = ab^x
where
a is the base
x is the exponent
Given the function that represents the population size P (t) of the species as shown;
For the population size after 6 years
For the population after 8 years
Hence the population size after 6 years and after 8 years are 147 and 169 population respectively
Learn more on exponential function here: brainly.com/question/2456547
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Given:
The table of values for the function f(x).
To find:
The values and
.
Solution:
From the given table, it is clear that the function f(x) is defined as:
We know that if (a,b) is in the function f(x), then (b,a) must be in the function . So, the inverse function is defined as:
And,
...(i)
Using (i), we get
Now,
Therefore, the required values are and
.
Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F =
m∠D = °.
Now, let m∠A = m∠B =
So, m∠C = m∠A + 30° =
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
Therefore, m∠F = 50°
m∠E = 50° and
m∠D =
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.