Which correctly compares 3 × (54 + 21) and 6 × (54 + 21) without doing any calculations? A.3 × (54 + 21) = 6 × (54 + 21) B.3 × (54 + 21) > 6 × (54 + 21) C.3 × (54 + 21) < 6 × (54 + 21) D.6 × (54 + 21) < 3 × (54 + 21)

C. 3 × (54 + 21) < 6 × (54 + 21)

Step-by-step explanation:

This is because, the factor 3 in from of the elements in parentheses on the left hand side is less than the factor 6 in from of the elements in parentheses on the right hand side. Thus, the product on the left hand side is less than the product on the right hand side, since the sum in parentheses on both sides are the same.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: