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1 answer:
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Answer:
B) the cube of 4 and then take the square root
Step-by-step explanation:
43/2 = 21.5
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The answer choices suggest you want ...
4^(3/2) . . . . . . . appropriate math symbols are very helpful
This can be evaluated several ways:
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Since the 3 is in the numerator of the fraction, it represents a cube, not a cube root. Any of the answer choices suggesting cube root is involved are incorrect. (Eliminating those leaves only the correct answer choice.)
Exterior angle theorem and properties of the isosceles triangles are used
prove the specified relations.
Correct responses:
9. ΔPAT ~ ΔPTB by AA similarity postulate
15. ║
by basic proportionality theorem
9. A two column proof is presented as follows;
Statement Reasons
1. ∠PTA = ∠B 1. Given
2. ∠PAT = ∠ATB + ∠B 2. Exterior angle of a triangle theorem
3. ∠BTP = ∠ATB + ∠PTA 3 Angle addition postulate
4. ∠BTP = ∠ATP + ∠B 4. Substitution property of equality
5. ∠PAT = ∠BTP 5. Substitution property
6. ΔPAT ~ ΔPTB 6. AA similarity postulate
The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.
15. A two column proof is presented as follows;
Statement Reasons
1. Given
2. ∠1 ≅ ∠G 2. Given
3. ΔKHG is an isosceles triangle 3. Definition
4. HK = HG 4. Legs of an isosceles triangle
5. Substitution property
6. ║
6. BPT, Basic Proportionality Theorem
Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.
Learn more about basic proportionality theorem, AA similarity postulate here: