Question

1.
alex’s height gain is represented by the expression 4y + 20. beth’s height gain is represented by the expression 8y + 40. which describes how the height gain by beth compares to the height gain by alex?
(a) the height gain by beth is 2 times the height gain by alex.
(b) the height gain by beth is 4 times the height gain by alex.
(c) the height gain by beth is 8 times the height gain by alex.
(d) the height gain by beth is 12 times the height gain by alex.
a car’s speed is represented by the expression 3m + 15. a motorcycle’s speed is represented by the expression 9m + 45. which describes how the motorcycle’s speed compares to the car’s speed?
(a) the motorcycle’s speed is 2 times the car’s speed.
(b) the motorcycle’s speed is 3 times the car’s speed.
(c) the motorcycle’s speed is 5 times the car’s speed.
(d) the motorcycle’s speed is 9 times the car’s speed.
2.

Explanation:

Problem 1 (Alex and Beth's Height Gain)

Step 1: Analyze the Expressions

Alex's height gain: \(4y + 20\)
Beth's height gain: \(8y + 40\)

Step 2: Factor Beth's Expression

Factor out 2 from \(8y + 40\):
\(8y + 40 = 2(4y + 20)\)

Step 3: Compare to Alex's Expression

Since Alex's expression is \(4y + 20\), Beth's height gain is \(2 \times\) (Alex's height gain).

Step 1: Analyze the Expressions

Car's speed: \(3m + 15\)
Motorcycle's speed: \(9m + 45\)

Step 2: Factor Motorcycle's Expression

Factor out 3 from \(9m + 45\):
\(9m + 45 = 3(3m + 15)\)

Step 3: Compare to Car's Expression

Since the car's speed is \(3m + 15\), the motorcycle's speed is \(3 \times\) (car's speed).

Answer:

(a) The height gain by Beth is 2 times the height gain by Alex.

Problem 2 (Car and Motorcycle Speed)