<h3>Answer: Approximately 191 bees</h3>
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Work Shown:
One way to express exponential form is to use
y = a*b^x
where 'a' is the initial value and 'b' is linked to the growth rate.
Since we're told 34 bees are there initially, we know a = 34.
Then after 4 days, we have 48 bees. So we can say,
y = a*b^x
y = 34*b^x
48 = 34*b^4
48/34 = b^4
24/17 = b^4
b^4 = 24/17
b = (24/17)^(1/4)
b = 1.090035
Which is approximate.
The function updates to
y = a*b^x
y = 34*(1.090035)^x
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As a way to check to see if we have the right function, plug in x = 0 and we find:
y = 34*(1.090035)^x
y = 34*(1.090035)^0
y = 34*(1)
y = 34
So there are 34 bees on day 0, ie the starting day.
Plug in x = 4
y = 34*(1.090035)^x
y = 34*(1.090035)^4
y = 34*1.4117629
y = 47.9999386
Due to rounding error we don't land on 48 exactly, but we can round to this value.
We see that after 4 days, there are 48 bees.
So we confirmed the correct exponential function.
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At this point we can find out how many bees there are expected to be after 20 days.
Plug in x = 20 to get
y = 34*(1.090035)^x
y = 34*(1.090035)^20
y = 190.672374978452
Round to the nearest whole number to get 191.
There are expected to be roughly 191 bees on day 20.
(a) m∠a = 100°
(b) m∠b = 80°
(c) m∠c = 100°
Solution:
Given 3rd and 4th street are parallel lines and King Ave is a transveral line.
<em>Sum of the adjacent angles in a straight line = 180°</em>
⇒ m∠a + 80° = 180°
⇒ m∠a = 180° – 80°
⇒ m∠a = 100°
∠c and ∠a are vertically opposite angles.
<em>If two lines are intersecting, then the vertically opposite angles are congruent.</em>
⇒ ∠c ≅ ∠a
⇒ m∠c = m∠a
⇒ m∠c = 100°
<em>If two parallel lines are cut by a transversal, then the corresponding angles in the same side of the transversal are congruent.</em>
80° and angle b are corresponding angles.
⇒ m∠b = 80°
Hence m∠a = 100°, m∠b = 80° and m∠c = 100°.
Answer:
Review the images
Step-by-step explanation:
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Unit form: 6 hundreds
standard form: 600
Answer:
x = √324 = 18
Step-by-step explanation:
x shows up only in the second problem, so I'll focus on that problem.
This is a right triangle because one of the three angles is 90 degrees.
Thus, the Pythagorean Theorem applies: x^2 + 24^2 = 30^2, or
x^2 = 900 - 576 = 324
Then x = √324 = 18