A researcher creates a scatter plot that displays the relationship between the number of years in business, x, and the percentage of company business that is fair trade, y. The researcher creates a line of best fit, y=0.091x+0.060, and wants to find the residuals for the companies that have been in business for 3 years. Find the residuals for the two points representing companies that have been in business for 3 years, (3, 0.42) and (3, 0.3).

What is the residual for the company with the point (3, 0.42)?

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116

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step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.