Decide which is the better value based on the unit prices. ( show your work).
1 answer:
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Answer:
6
Step-by-step explanation:
This problem centers on recognizing the relationship between fractions and repeating decimals.
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Note the following:
or more simply
This means that
Going back to the original expression, simplifies to
Next, adding mixed numbers. For adding mixed numbers, whole number parts and fractional parts can be added separately <em>(this is because of the associative and commutative properties of addition)... because </em>
means the same thing as
Changing the order, we can write it as
Adding the whole number parts, 3+2 is 5.
Next, adding the fraction parts:
For adding fractions, one must have a common denominator (the bottom part of the fraction must be the same). Once they are the same, the denominator just sort of "hangs out" until the end without changing, and the numerators (the tops) are added together.
Fortunately, the denominators are already the same. So, add the numerators, and the denominator will stay as a 3.
It is important to recognize that any fraction* where the number on the top matches the number on the bottom, the fraction is equivalent to 1.
<em>*(except if the number we're talking about is zero)</em>
So, the fraction parts added together, are equivalent to 1, and the whole number parts added were equal to 5. Returning to our expression...
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: