Answer:
Blue
Step-by-step explanation:
The angle of B is ![\angle B=19^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20B%3D19%5E%7B%5Ccirc%7D)
Explanation:
It is given that
and ![a=8, b=3](https://tex.z-dn.net/?f=a%3D8%2C%20b%3D3)
To determine the
, let us use the law of sine formula.
Thus, we have,
![\frac{Sin A}{a} =\frac{Sin B}{b}](https://tex.z-dn.net/?f=%5Cfrac%7BSin%20A%7D%7Ba%7D%20%3D%5Cfrac%7BSin%20B%7D%7Bb%7D)
Substituting the values in the formula, we have,
![\frac{Sin 120}{8} =\frac{Sin B}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BSin%20120%7D%7B8%7D%20%3D%5Cfrac%7BSin%20B%7D%7B3%7D)
Multiplying both sides by 3,we get,
![\frac{3(0.866)}{8} ={Sin B}](https://tex.z-dn.net/?f=%5Cfrac%7B3%280.866%29%7D%7B8%7D%20%3D%7BSin%20B%7D)
Simplifying and dividing, we get,
![0.32475=Sin B](https://tex.z-dn.net/?f=0.32475%3DSin%20B)
Multiplying both sides by
, we get,
![\sin ^{-1}(0.32475)=B](https://tex.z-dn.net/?f=%5Csin%20%5E%7B-1%7D%280.32475%29%3DB)
Thus, ![B=18.95^{\circ}=19^{\circ}](https://tex.z-dn.net/?f=B%3D18.95%5E%7B%5Ccirc%7D%3D19%5E%7B%5Ccirc%7D)
Hence, The angle of B is ![\angle B=19^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20B%3D19%5E%7B%5Ccirc%7D)
Answer:
, ![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
, ![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Find the value of the constant of proportionality k
take any ordered pair from the data
For x=25, y=160
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
substitute the values of x and y
![k=\frac{160}{25}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B160%7D%7B25%7D)
simplify
![k=\frac{32}{5}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B32%7D%7B5%7D)
The linear equation is equal to
![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
or
![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)
To find how many times the length of Noah's ride is compared to Mal's, you would divide the two mixed numbers:
6 3/4 divided by 4 1/2
Convert the mixed numbers to improper fractions:
27/4 divided by 9/2
To solve, multiply 27/4 by the reciprocal of 9/2:
27/4 * 2/9 = 3/2 or 1 and 1/2
So Mal's ride is 1.5 times longer than Noah's.