C) $2.39
.53 x 4.5 = 2.385
Answer:
![m = -\frac{23}{42}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B23%7D%7B42%7D)
Step-by-step explanation:
here is the equation for slope (m):
![m = \frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
where:
y₂ = y-coordinate of 2nd point = -10
y₁ = y-coordinate of 1st point = 36
x₂ = x-coordinate of 2nd point = 93
x₁ = x-coordinate of 1st point = 9
plug values into equation:
![m =\frac{-10-36}{93-9} \\\\m = \frac{-46}{84} \\](https://tex.z-dn.net/?f=m%20%3D%5Cfrac%7B-10-36%7D%7B93-9%7D%20%5C%5C%5C%5Cm%20%3D%20%5Cfrac%7B-46%7D%7B84%7D%20%5C%5C)
reduce the fraction:
![m = -\frac{23}{42}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B23%7D%7B42%7D)
Answer:
![ML = 58](https://tex.z-dn.net/?f=ML%20%3D%2058)
Step-by-step explanation:
Given
![JK=3x+11, ML=10x-12, NP=45](https://tex.z-dn.net/?f=JK%3D3x%2B11%2C%20ML%3D10x-12%2C%20NP%3D45)
See attachment
Required
Length ML
First, calculate x using the following equivalent ratios
![JK : NP = NP : ML](https://tex.z-dn.net/?f=JK%20%3A%20NP%20%3D%20NP%20%3A%20ML)
Express as fraction
![\frac{JK }{ NP} = \frac{NP }{ ML}](https://tex.z-dn.net/?f=%5Cfrac%7BJK%20%7D%7B%20NP%7D%20%3D%20%5Cfrac%7BNP%20%7D%7B%20ML%7D)
Cross Multiply
![JK * ML = NP * NP](https://tex.z-dn.net/?f=JK%20%2A%20ML%20%3D%20NP%20%2A%20NP)
Substitute values:
![(3x +11) * (10x - 12) = 45 * 45](https://tex.z-dn.net/?f=%283x%20%2B11%29%20%2A%20%2810x%20-%2012%29%20%3D%2045%20%2A%2045)
Expand
![30x^2 - 36x + 110x - 132 = 2025](https://tex.z-dn.net/?f=30x%5E2%20-%2036x%20%2B%20110x%20-%20132%20%3D%202025)
![30x^2 +74x - 132 = 2025](https://tex.z-dn.net/?f=30x%5E2%20%2B74x%20-%20132%20%3D%202025)
Collect like terms
![30x^2 +74x - 132 - 2025=0](https://tex.z-dn.net/?f=30x%5E2%20%2B74x%20-%20132%20-%202025%3D0)
![30x^2 +74x -2157=0](https://tex.z-dn.net/?f=30x%5E2%20%2B74x%20-2157%3D0)
Using a calculator:
and ![x \approx 7](https://tex.z-dn.net/?f=x%20%5Capprox%207)
Given that:
![ML=10x-12](https://tex.z-dn.net/?f=ML%3D10x-12)
Substitute values for x
![ML=10*-10-12 = -100 - 12 = -112](https://tex.z-dn.net/?f=ML%3D10%2A-10-12%20%3D%20-100%20-%2012%20%3D%20-112)
![ML=10*7-12 = 70 - 12 = 58](https://tex.z-dn.net/?f=ML%3D10%2A7-12%20%3D%2070%20-%2012%20%3D%2058)
ML cannot be negative; So:
![ML = 58](https://tex.z-dn.net/?f=ML%20%3D%2058)