The new exponential equations to represent Alison, Cindy, and Javier would be 1/(1+e^-x) representing an s curve showing a lot of growth.
<h3>What is an exponential equation?</h3>
The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}.
Here, he new exponential equations to represent Alison, Cindy, and Javier would be 1/(1+e^-x) representing an s curve showing a lot of growth while Cindy and Javier would be ln(x) and x^(1/2) as they will grow somewhat fast at first and then die out.
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<h2>The missing measures of the angles are:</h2>
![m\angle 1= 60^{\circ}\\\\m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%201%3D%2060%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%202%3D%2039%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%203%3D%2021%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%204%20%3D%2039%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%205%20%3D%2021%5E%7B%5Ccirc%7D)
<u>Given</u>:
![m\angle Z = 138^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20Z%20%3D%20138%5E%7B%5Ccirc%7D)
<em><u>Note the following:</u></em>
- An equilateral triangle has all its three angles equal to each other. Each angle =
.
- This implies that, since
is equilateral, therefore, ![m\angle Y = m\angle XWY = m\angle XYW = 60^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20Y%20%3D%20m%5Cangle%20XWY%20%3D%20m%5Cangle%20XYW%20%3D%2060%5E%7B%5Ccirc%7D)
- Base angles of an isosceles triangle are congruent to each other.
- This implies that, since
is isosceles, therefore, ![m\angle 3 = \angle 5](https://tex.z-dn.net/?f=m%5Cangle%203%20%3D%20%5Cangle%205)
Applying the above stated, let's find the measure of each angle:
- Find
![m\angle 1](https://tex.z-dn.net/?f=m%5Cangle%201)
(an angle in an equilateral triangle equals 60 degrees)
- Find
![m\angle 2](https://tex.z-dn.net/?f=m%5Cangle%202)
![m\angle 2 = 60 - m \angle 3](https://tex.z-dn.net/?f=m%5Cangle%202%20%3D%2060%20-%20m%20%5Cangle%203)
![(Note: \frac{1}{2}(180 - 138) = 1 $ base $ angle $ of $ \triangle WZY)](https://tex.z-dn.net/?f=%28Note%3A%20%5Cfrac%7B1%7D%7B2%7D%28180%20-%20138%29%20%3D%201%20%24%20base%20%24%20angle%20%24%20of%20%24%20%5Ctriangle%20WZY%29)
![m\angle 2 = 60 -21\\\\m\angle 2 = 39^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%202%20%3D%2060%20-21%5C%5C%5C%5Cm%5Cangle%202%20%3D%2039%5E%7B%5Ccirc%7D)
- Find
and
(base angles of isosceles triangle WZY)
![m\angle 3 = \frac{1}{2}(180 - 138) (1 $ base $ angle $ of $ \triangle WZY)](https://tex.z-dn.net/?f=m%5Cangle%203%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%28180%20-%20138%29%20%281%20%24%20base%20%24%20angle%20%24%20of%20%24%20%5Ctriangle%20WZY%29)
![m\angle 3 = \frac{1}{2}(42) \\\\m\angle3 = 21^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%203%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%2842%29%20%5C%5C%5C%5Cm%5Cangle3%20%3D%2021%5E%7B%5Ccirc%7D)
(base angles of isosceles triangle are congruent)
Therefore,
![m\angle5 = 21^{\circ}](https://tex.z-dn.net/?f=m%5Cangle5%20%3D%2021%5E%7B%5Ccirc%7D)
- Find
![m\angle 4](https://tex.z-dn.net/?f=m%5Cangle%204)
![m\angle 4 = 60 - m\angle 5](https://tex.z-dn.net/?f=m%5Cangle%204%20%3D%2060%20-%20m%5Cangle%205)
Substitute
![m\angle 4 = 60 - 21\\\\m\angle 4 = 39^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%204%20%3D%2060%20-%2021%5C%5C%5C%5Cm%5Cangle%204%20%3D%2039%5E%7B%5Ccirc%7D)
The missing measures of the angles are:
![m\angle 1= 60^{\circ}\\\\ m\angle 2= 39^{\circ}\\\\m\angle 3= 21^{\circ}\\\\m\angle 4 = 39^{\circ}\\\\m\angle 5 = 21^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%201%3D%2060%5E%7B%5Ccirc%7D%5C%5C%5C%5C%20m%5Cangle%202%3D%2039%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%203%3D%2021%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%204%20%3D%2039%5E%7B%5Ccirc%7D%5C%5C%5C%5Cm%5Cangle%205%20%3D%2021%5E%7B%5Ccirc%7D)
Learn more here:
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Answer:
You are m + 1 years old.
Step-by-step explanation:
Let's say that you are x years old, and Mack is m years old.
x = 1/2( two plus twice m)
x = 1/2(2 + 2m)
x = 1 + m
x = m + 1
Hope this helps!
Answer:
Yes
Step-by-step explanation:
Statement Reason
ab = bd Given
ac=cd Given
bc = cb definiton of reflex line
triangle abc is congruent to triangle dbc side side side postulate
Answer:
0.375
Step-by-step explanation: