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Rita is spending more time at home to study and practice math. Her efforts are finally paying off. On her first assessment she scored 58 points, then she scores 63 and 68 on her next two assessments. If her scores continued to increase at the same rate, on which assessments will she be scoring above 85?

Respuesta :

RASEA23
This is a pattern in which you add five points to the next assessment. 
1st= 58, 2nd=63, 3rd=68, 4th=73, 5th= 78, 6th=83, 7th=88 points
So on her seventh assessment, she will get higher than 85 points. 
Hope this helps. 
cerverusdante

Answer

She will be scoring above 85 after her 7 assessment.

Explanation

We can model this situation using a line equation.

We know that on her first assessment, Rita scored 58 points, so our first point is (1, 58)

We also know that on her second assessment, Rita scored 63 points, so our second point is (2, 63)

To find the rate, which is the slope of our line, we are using the slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where

[tex](x_{1},y_{1})[/tex] are the coordinates of the first point

[tex](x_{2},y_{2})[/tex] are the coordinates of the second point

From our points we can infer that [tex]x_{1}=1[/tex], [tex]y_{1}=58[/tex], [tex]x_{2}=2[/tex], [tex]y_{2}=63[/tex]. Let's replace the values in our slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{63-58}{2-1}[/tex]

[tex]m=\frac{5}{1}[/tex]

[tex]m=5[/tex]

Now we know that Rita's score is increasing 5 points every assessment.

To complete the equation of our line, we are using the point slope formula:

[tex]y-y_{1}=m(x-x_{1})[/tex]

[tex]y-58=5(x-1)[/tex]

[tex]y-58=5x-5[/tex]

[tex]y=5x+53[/tex]

Finally, we just need to replace [tex]y[/tex] with 85 in our line equation and solve for [tex]x[/tex] to find after which assessment she will score above 85:

[tex]85=5x+53[/tex]

[tex]32=5x[/tex]

[tex]x=\frac{32}{5}[/tex]

[tex]x=6.4[/tex]

Since we can't have 0.4 assessment, she will be scoring above 85 after her 7 assessment.  


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