The average score on a national assessment test for a subject was 194 points for fourth-graders who studied the subject about 45 minutes per week. the average score was 211 points for fourth-graders who studied the subject about 150 minutes per week. there is an approximate linear relationship between the number of hours fourth-graders study the subject per week and the average score on the test. estimate the average score for fourth-graders who study the subject about 235 minutes per week.

The average score for fourth-graders who study the subject about 235 minutes per week is 224.76.

Step-by-step explanation:

Let x be the number of hours fourth-graders study the subject per week and y be the average score on the test. It is given that there is an approximate linear relationship between x and y.

It is given that the average score on a national assessment test for a subject was 194 points for fourth-graders who studied the subject about 45 minutes per week. It means the line passes through (45, 194).

The average score was 211 points for fourth-graders who studied the subject about 150 minutes per week. It means the line passes through (150, 211).

If a line passes through two points then the equation of line is

The equation of required line is

Using distributive property,

Add 194 on both sides.

Substitute x=235 in the above equation.

Therefore the average score for fourth-graders who study the subject about 235 minutes per week is 224.76.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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step-by-step explanation: