Answer:
22
Step-by-step explanation:
3.85+2.75= 6.6
6.6÷0.30= 22
1. m∠1 + m∠2 = 180°
2. Definition of bisector
3. m∠1 + m∠3 = 180°
4. Substitution Property of Equality
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function
, and then transform it into the function: ![g(x)=(x-4)^3-7](https://tex.z-dn.net/?f=g%28x%29%3D%28x-4%29%5E3-7)
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:
![\textsf{(a)} \quad (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}](https://tex.z-dn.net/?f=%5Ctextsf%7B%28a%29%7D%20%5Cquad%20%283x%29%5E%7B%5Ccirc%7D%2B%28x%2B14%29%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D)
![\textsf{(b)} \quad m \angle 1=\boxed{57}\:^{\circ}](https://tex.z-dn.net/?f=%5Ctextsf%7B%28b%29%7D%20%5Cquad%20m%20%5Cangle%201%3D%5Cboxed%7B57%7D%5C%3A%5E%7B%5Ccirc%7D)
![m \angle 2=\boxed{33}\:^{\circ}](https://tex.z-dn.net/?f=m%20%5Cangle%202%3D%5Cboxed%7B33%7D%5C%3A%5E%7B%5Ccirc%7D)
Step-by-step explanation:
From inspection of the given diagram:
<h3><u>Part (a)</u></h3>
A right angle is 90° and is represented by the ∟ symbol.
To find x, <u>equal</u> the sum of the angles to 90° and solve for x:
![\implies m \angle 1+m\angle2=90^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%201%2Bm%5Cangle2%3D90%5E%7B%5Ccirc%7D)
![\implies (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20%283x%29%5E%7B%5Ccirc%7D%2B%28x%2B14%29%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D)
![\implies 3x+x+14=90](https://tex.z-dn.net/?f=%5Cimplies%203x%2Bx%2B14%3D90)
![\implies 4x+14=90](https://tex.z-dn.net/?f=%5Cimplies%204x%2B14%3D90)
![\implies 4x+14-14=90-14](https://tex.z-dn.net/?f=%5Cimplies%204x%2B14-14%3D90-14)
![\implies 4x=76](https://tex.z-dn.net/?f=%5Cimplies%204x%3D76)
![\implies 4x \div 4=76 \div 4](https://tex.z-dn.net/?f=%5Cimplies%204x%20%5Cdiv%204%3D76%20%5Cdiv%204)
![\implies x=19](https://tex.z-dn.net/?f=%5Cimplies%20x%3D19)
<h3><u>Part (b)</u></h3>
To find the degree measure of each angle, substitute the found value of x into the expression for each angle.
![\implies m \angle 1=(3 \cdot 19)^{\circ}=57^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%201%3D%283%20%5Ccdot%2019%29%5E%7B%5Ccirc%7D%3D57%5E%7B%5Ccirc%7D)
![\implies m \angle 2=(19+14)^{\circ}=33^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%202%3D%2819%2B14%29%5E%7B%5Ccirc%7D%3D33%5E%7B%5Ccirc%7D)
Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .
How to interpret a standard deviation?
- The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
- The standard deviation calculates how much the data vary from the mean value. It is helpful for contrasting data sets that might have the same mean but a different range.
In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.
Learn more about "standard deviation"
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