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Grade 11 Trigonometry CCSS: HSG-SRT.D.10

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What is the missing reason in step 22?
  1. Given
  2. Sum of non-right angles in a triangle is 180°
  3. Sum of the angles on a straight line is 180°
  4. Exterior Angle Theorem
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.1

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Now that we have the lengths of the legs of the triangle, what theorem, property, or formula correctly relates them and why is it used?
  1. The formula for the area of a triangle, A=12(y-3)(x-4), since we know the height and base of the triangle.
  2. Heron's Formula, A=s(s-a)(s-b)(s-c), where s=2+(y-4)2+(x-3)22, because the length of all three sides is known.
  3. Pythagorean Theorem, (x-3)2+(y-4)2=4, since the lengths of the three sides of the right triangle are known, and this introduces no extra variables.
  4. Law of Cosines, |x-3|2=4+|y-4|2-22|y-4|cos90°, because the lengths of the three sides of the triangle, and the measure of the right angle, are known, and this introduces no extra variables.
Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.A.2

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What is the missing reason in step 6?
  1. Integers are closed under multiplication
  2. Multiplication Property of Equality
  3. Multiplying two real numbers always results in an integer
  4. Fundamental Theorem of Arithmetic
Grade 10 Circles

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What is the missing reason in step 5?
  1. Triangle ABD looks like a right triangle
  2. Tangent lines intersect all lines at a right angle
  3. A tangent line is perpendicular to the diameter
  4. The Pythagorean Theorem
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

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How does one go from step 3 to step 4?
  1. Use polynomial long division.
  2. Apply the fundamental theorem of algebra.
  3. Factor out common factors on both sides.
  4. Multiply each side by (1-r).
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