On a number line, the directed line segment from Q to S has endpoints at -2 and S at 6. point R partitions the directed line segment from Q to S in the 3:2 ratio. rachel use the section formula to find the location of point R on the number line. her work is shown below. let m = 3, n = 2, x1 =-2, and x2 = 6. what is the location of point R on the number line?

Fiona and her friends are playing a game by guessing where a coin will land when it is randomly dropped inside the square shown below. fiona guesses that the coin is likely to land in the blue area. which explains whether or not fiona is correct and why?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

Given the quadratic function f(x)=3x^2-24x+49 a. use “completing the squares” to convert the quadratic function into vertex form b. state the vertex c. find the x and y intercepts d. graph the function