Complete the square to determine if the equation is a circle, quadratic (parabola) or other. Show all work and graph the circles and quadratics on a grid.
16x² + 4y^2 + 96x - 8y + 84 = 0

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)

Afamily has two cars. the first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. during one particular week, the two cars went a combined total of 1025 miles, for a total gas consumption of 55 gallons. how many gallons were consumed by each of the two cars that week?

Aresearch study is studying the effects of a new drug for osteoporosis alzheimer's disease (ad) for women above the age of 65 years. a group of individuals with osteoporosis is randomized into two groups. one group is treated conventionally, and the second group is treated with the new medication. assessments are made at 3, 6, 12, 36, and 48 months. the conventionally treated group is assessed for ad using a serum blood test, and the treatment group is assessed for ad using a pet radiotracer that binds to beta-amyloid plaques. in comparing these 2 trial arms, the authors of the study may encounter which type of bias? a. selection bias on the risk of developing b. measurement bias c. confounding bias d. recall bias e. lead-time bias