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SpyIntel [72]
2 years ago
13

Activity

Mathematics
1 answer:
Sergio039 [100]2 years ago
5 0

Answer:

A:

Dylan’s weight is d.

Twice Dylan’s weight is 2d.

Three pounds more than twice Dylan’s weight is 2d + 3.

So, the expression for Alan’s weight in terms of Dylan’s weight is 2d + 3.

B:

Dylan’s weight is d.

Three times Dylan’s weight is 3d.

Twelve less than three times Dylan’s weight is 3d − 12.

So, the expression for Bruce’s weight in terms of Dylan’s weight is 3d − 12.

C:

Cecil’s weight is the sum of Alan's weight and Bruce's weight.

Alan’s weight in terms of Dylan's weight is 2d + 3.

Bruce’s weight in terms of Dylan's weight is 3d − 12.

So, the expression for Cecil’s weight in terms of Dylan’s weight is (2d + 3) + (3d − 12).

D:

Cecil's weight is (2d + 3) + (3d − 12).

Find Cecil's weight by substituting Dylan’s weight (d = 45) into the expression above:

(2 × 45 + 3) + (3 × 45 − 12)

=  (90 + 3) + (135 − 12)

=  93 + 123

=  216.

If Dylan weighs 45 pounds, then Cecil weighs 216 pounds.

E:

Yes, the expression can be simplified by using the Associative and Commutative Properties of addition and by combining the like terms in the expression.

F:

(2d + 3) + (3d − 12)

First remove the parentheses:

2d + 3 + 3d − 12.

Then group the like terms:

2d + 3d + 3 − 12.

Finally, add and subtract the like terms:

5d − 9.

The expression (2d + 3) + (3d − 12) simplifies to 5d − 9.

G:

Cecil’s weight in terms of Dylan’s weight is 5d – 9.

Find Cecil’s weight by substituting Dylan’s weight (d = 45) into the expression above:

(5 × 45) − 9

= 225 − 9

= 216.

If Dylan weighs 45 pounds, then Cecil weighs 216 pounds.

H:

Yes, the answers are the same. The expression from part D is equivalent to the expression from part G.

I:

Bruce's weight in terms of Dylan’s weight is 3d − 12.

Alan's weight in terms of Dylan’s weight is 2d + 3.

So, the expression (3d − 12) − (2d + 3) represents how much more Bruce weighs than Alan.

J:

The expression is (3d − 12) − (2d + 3).

Evaluate the expression by substituting Dylan’s weight (d = 45) into it:

(3 × 45 − 12) − (2 × 45 + 3)

= (135 − 12) − (90 + 3)

= (123) − (93)

= 30.

Bruce weighs 30 pounds more than Alan weighs.

K:

The expression (3d − 12) − (2d + 3) simplifies to d − 15.

L:

The expression is d − 15.

Evaluate the expression by substituting Dylan’s weight (d = 45) into it:

45 − 15 = 30.

Bruce weighs 30 pounds more than Alan. This is the same answer as in part J.

Do not copy, it's the exact answer from edmuentum

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