What is the decimal equivalent for the fraction 7/11
2 answers:
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When y=0,
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![\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%20%7B%202x%20%7D%5E%7B%202%2B1%20%7D%20%7D%7B%202%2B1%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%201%2B1%20%7D%20%7D%7B%201%2B1%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
![\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right] }_{ -3 }^{ \frac { 1 }{ 2 } }](https://tex.z-dn.net/?f=%5C%5C%20%5C%5C%20%3D%7B%20%5Cleft%5B%20-%5Cfrac%20%7B%202%7B%20x%20%7D%5E%7B%203%20%7D%20%7D%7B%203%20%7D%20-%5Cfrac%20%7B%205%7B%20x%20%7D%5E%7B%202%20%7D%20%7D%7B%202%20%7D%20%2B3x%20%5Cright%5D%20%20%7D_%7B%20-3%20%7D%5E%7B%20%5Cfrac%20%7B%201%20%7D%7B%202%20%7D%20%20%7D)
Answer: 343/24 units squared.
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Answer: 343/24 units squared.
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: