CATAGORY 2 PART 1 FEB BMK 2025

What value of x makes this equation true?

0.17x - 0.03 = 0.03x - 0.002

Enter your answer in the box provided.

Mathematical Equivalence

ON

A gas company charges a $16 monthly service fee and $0.6924 per hundred cubic feet of natural gas used during a month. Which equation best represents y, the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas?

• y = 0.6924x - 16

• y = 16x + 0.6924

• y = 16x - 0.6924

• y = 0.6924x + 16

After x hours of rainfall today, Yvette recorded the amount of rain in inches, y, in a rain gauge. The table shows the linear relationship for the recorded rainfall. How many inches of rain was in the gauge before the rain began today, and what was the rate at which the rain fell in inches per hour?

• There was 0 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.

• There was 2.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.

• There was 3 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

• There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

The two lines graphed on the coordinate grid represent a system of linear equations. Which ordered pair best represents a solution to both equations?

• (4, -11)

• (0, 4)

• (9, -2)

• (6, 11)

Which equation does NOT show a proportional relationship between x and y?

• y = x/12

• y = -15x

• y = 2/3x

• y = 7x - 9

An online candy store sells 3 pounds of fudge for $54.99. Which function represents the relationship between x, the number of pounds of fudge ordered, and y, the total cost in dollars?

• y = 3(54.99)x

• y = (54.99 - 3)x

• y = 54.99x - 3

Which situation can be represented by the inequality 2x + 18 < 3x + 11?

• Tori is on the 18th step from the bottom of a staircase and goes up 3 steps every second. Naoki is on the 11th step from the bottom and goes up 2 steps every second. After how many seconds, x, will Naoki pass Tori?

• Ana has made 18 bracelets and continues to make 2 bracelets each day. Elliot has made 11 bracelets and continues to make 3 bracelets each day. After how many days, x, will Elliot have more bracelets than Ana?

• Gina has $2 in her savings account and adds $18 each week. Hiram has $3 in his savings account and adds $11 each week. After how many weeks, x, will Gina have more money in her savings account than Hiram?

• Dhara has eaten 18 french fries and continues to eat 2 with each bite. Kendrick has eaten 11 french fries and continues to eat 3 with each bite. After how many bites, x, will Dhara have eaten more french fries than Kendrick?

A student took 32 minutes to complete a 20-question history assignment. Choose two points that lie on the line with the slope that best represents the number of questions completed per minute. Select TWO correct answers.

Determine whether each situation represents a proportional or a non-proportional relationship. Select one answer in each row.

Situation:

1. 1. The total number of text messages sent if 4 were already sent and 6 messages are sent per day.​ (a)  

2. 2. The number of characters in a text message if each word contains 6 characters.​ (b)  

3. 3. The number of minutes it takes to enter a text message at 50 characters per minute.​ (c)  

4. 4. The time it takes to send a text message if it takes 30 seconds to open the app and the sender enters 1 character per second.​ (d)  

• non-proportional
• proportional

Maren made an initial deposit into her savings account. Each month Maren deposits the same amount into the savings account. The graph shows the linear relationship between x, the number of months Maren's savings account has been open, and y, the amount of money in the account. Which amount best represents Maren's initial deposit in dollars?

• $450

• $900

• $1350

• $1575