1.### Y = 7x + 3
Where does this line cross the y-axis?

Answer:
(0,3)

Explanation:

In the equation y = 7x + 3, to find where the line crosses the y-axis, you need to determine the y-coordinate when x is equal to 0. This is because the y-axis is where x = 0.

So, substitute x = 0 into the equation:

y = 7(0) + 3

y = 0 + 3

y = 3

The line crosses the y-axis at the point (0, 3).

So, substitute x = 0 into the equation:

y = 7(0) + 3

y = 0 + 3

y = 3

The line crosses the y-axis at the point (0, 3).

2.### Ben pays $40 per month to attend a weekly yoga class. His sister Ilene gets a discount at her yoga class and pays $35 per month. Over the course of one year, how much more money does Ben pay a year to attend his yoga class?

Answer:
60

Explanation:

Ben pays $40 per month for his yoga class, while his sister pays $35 per month for hers. To calculate how much more money Ben pays a year, we need to find the difference between their monthly payments and multiply it by 12 (months in a year). The difference is $40 - $35 = $5. Therefore, Ben pays $5 more per month. Multiplying this by 12, we get $5 * 12 = $60. So, Ben pays $60 more a year to attend his yoga class.

3.### Robin Banks is driving away in her getaway car. Willie Ketchup is chasing him in his patrol car. Robin is driving 50 mph and is 100 miles away from the border. Willie is 50 miles behind Robin, and is driving 75 mph. Will Robin reach the border before Willie catches her?

Answer:
They will reach it at the same time.

4.### Solve for y in the equation: y – 13 = –3

Answer:
10

Explanation:

The answer is 10.Here's how to solve for y in the equation y – 13 = –3:Add 13 to both sides of the equation to isolate y on one side:y – 13 + 13 = –3 + 13Simplify both sides:y = 10Therefore, the solution to the equation y – 13 = –3 is y = 10.

5.### If p × q = p + q + p/q, the value of 8 × 2 is:

Answer:
14

Explanation:

To solve for 8 × 2 in the equation p × q = p + q + p/q, we need to plug in the values p = 8 and q = 2:8 × 2 = 8 + 2 + 8/2Now, let's solve the equation step-by-step:Division first: 8/2 = 4Addition: 8 + 2 + 4 = 14Therefore, the value of 8 × 2 in the given equation is 14.The other options are incorrect because:6: This result comes from incorrectly adding before dividing (8 + 2 = 10, then 10/2 = 5).10: This result comes from incorrectly multiplying before dividing (8 + 2 + 8 = 18, then 18/2 = 9).16: This result comes from incorrectly multiplying first (8 * 2 = 16).Remember, in the order of operations (PEMDAS), division and multiplication have the same priority and are done from left to right before addition and subtraction.

6.### If a * b = 2 (a + b), then 5 * 2 is equal to:

Answer:
14

Explanation:

In the equation a * b = 2 (a + b), where * represents a custom operation, the answer for 5 * 2 is not directly obtainable using conventional math operations like addition, subtraction, multiplication, or division.To solve for 5 * 2, we need to understand the logic behind the custom operation. Since the operation involves doubling the sum of a and b, it essentially multiplies both a and b by 2 and then adds them together.So, for 5 * 2:Double both 5 and 2: 2 * 5 = 10, 2 * 2 = 4Add the doubled values: 10 + 4 = 14Therefore, 5 * 2 in this custom operation equals 14.The other options are incorrect because:3: This result would be obtained if the operation simply involved multiplying a and b.10: This result would be obtained if the operation only doubled one of the numbers.20: This result is too high and doesn't follow the logic of the custom operation.

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