
Solve the absolute value equation |3x-5| = 7, identify two possible x values (4 and -2/3), and verify the results.
Use coordinates and right triangles to compute the slope from y2 - y1 over x2 - x1, then express the line in point-slope, slope-intercept, and standard forms and find intercepts.
Model ticket prices with x and y as student and adult tickets in a system of simultaneous equations. Use elimination on 3x+2y=29 and 5x+4y=54 to get x=4, y=8.5, 12.5 dollars.
Explore how to solve intersecting line angle problems by applying vertically opposite angles, straight-line sums, and angle partitioning to find measures like 55, 35, 90, 125, and 145 degrees.
determine a circle with center (4,3) tangent to the y-axis by sketching the radius, then express the equation in standard form (x-4)^2+(y-3)^2=16 and expanded form x^2+y^2-8x-6y+9=0.
Practice focuses on the composition of functions f and g, with f(x)=x^2+1 and g(x)=x-2, solving inside-out to find f(g(x))=x^2-4x+5 and g(f(x))=x^2-1, then f(g(3))=2.
Compute a_3 by applying the recursive rule a_n = a_{n-1} + 2/n with a_0 = 3. Trace the steps from a_0 to a_3, obtaining a_1 = 5, a_2 = 6, and a_3 = 20/3.
Use the zero product property to find roots of quadratics by factoring and setting factors to zero, solving for x in (2x-5)(3x-10)=0, x^2-3x-28=0, and x(x+2)=8.
Determine mean (x̄) as sum x over n ungrouped data. Compute median as middle values for even data, identify mode as most frequent, and define range as greatest minus least.
Solve a weighted-average problem for a class of 15 boys and 12 girls, an overall average of 81 and boys' average of 83, to find girls' average of 78.5.
Solve the equation 5x = 20 by dividing both sides by five to find x = 4, then compute 15x = 60.
Simplify the expression by collecting like terms, combining eight and three to yield eleven, resulting in d squared plus eleven. Reinforce finding the equivalent form as d squared plus eleven.
Compute the mean of ungrouped data using x-bar as the sum of observations divided by n. Apply the data values 2, 9, 14, 23, 32 to obtain 16.
Recognize that 256 W^2 and 676 are perfect squares, rewrite as (16W)^2 minus 26^2, and apply the difference of two squares to factor into (16W+26)(16W-26).
Substitute x with 9 in the function f(x) = 100x + 2 to compute f(9), which equals 902.
Apply the angle sum in a right triangle to find the other acute angle; with 59 degrees given, x equals 39 degrees (option B).
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