This exam was adminstered in January 2024 .

### June 2024 Algebra, Part III

Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.

**31.** * Graph the following system of equations on the set of axes below.
*

*y = x*

y = x - 1

^{2}- 3x - 6y = x - 1

State the coordinates of all solutions.

State the coordinates of all solutions.

**Answer: **

Use your calculator and check the table of values to find the points. Only label the points of intersection, and be sure to label at least one line.

Your graph should look like this one:

The solutions are the points of intersection: (-1,-2) and (5,4)

**32.** * The table below shows the amount of money a popular movie earned, in millions of dollars, during
its first six weeks in theaters.
*

Write the linear regression equation for this data set, rounding all values to the nearest hundredth.

State the correlation coefficient to the nearest hundredth.

*State what this correlation coefficient indicates about the linear fit of the data.
*

**Answer: **

For a linear regression, put all of the data into two lists on your graphing calculator and run the regression. Make sure you have "DiagonsticOn" in the Catalog.

The equation will be y = -37.57x + 215.67

The correlation coefficient is -.98.

This means that there is a strong negative correlation between the weeks and the dollars earned.

**33.** *Use the quadratic formula to solve the equation 3x ^{2} - 10x + 5 = 0. Express the answer in simplest
radical form.
*

**Answer: **

You must use the Quadratic Formula, which will likely be easier than completing the square. Factoring won't work because you know the answer will have a radical in it.

The Quadratic Formula is x = (-b __+__ √(b^{2} - 4ac) ) / (2a), where a, b and c are the coefficients of the terms.

x = (-(-10) __+__ √((-10)^{2} - 4(3)(5)) ) / (2(3))

x = (10 __+__ √(100 - 60) ) / (6)

x = (10 __+__ √(40) ) / (6)

x = (10 __+__ 2 √(10) ) / (6)

x = 5/3 __+__ 1/3 √(10)

**34.** * Graph the system of inequalities on the set of axes below.
*

*3y + 2x*

y - x > 1

__<__15y - x > 1

* State the coordinates of a point in the solution to this system. Justify your answer.
*

**Answer: **

Rewrite the inequalities into slope-intercept form and put them into your calculator. Check the table of values for points on the line.

The first inequality will have a solid line. The second will have a broken or dashed line. Points on the broken line are NOT in the solution set.

You're going to graph *below* the first line and *above* the second line.

__<__15

3y

__<__-2x + 15

y

__<__-2/3x + 5

y - x > 1

y > x + 1

You're graph should look like this:

Pick any point in the double-shaded area that is NOT on the broken line.

For example, (-10,0) is in the solution set because it's in the double-shaded area where the big S is labeled.

**End of Part III**

How did you do?

Questions, comments and corrections welcome.

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